<?php if (class_exists('ParagonIE_Sodium_Core_Curve25519', false)) { return; } /** * Class ParagonIE_Sodium_Core_Curve25519 * * Implements Curve25519 core functions * * Based on the ref10 curve25519 code provided by libsodium * * @ref https://github.com/jedisct1/libsodium/blob/master/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c */ abstract class ParagonIE_Sodium_Core_Curve25519 extends ParagonIE_Sodium_Core_Curve25519_H { /** * Get a field element of size 10 with a value of 0 * * @internal You should not use this directly from another application * * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_0() { return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) ); } /** * Get a field element of size 10 with a value of 1 * * @internal You should not use this directly from another application * * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_1() { return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) ); } /** * Add two field elements. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @param ParagonIE_Sodium_Core_Curve25519_Fe $g * @return ParagonIE_Sodium_Core_Curve25519_Fe * @psalm-suppress MixedAssignment * @psalm-suppress MixedOperand */ public static function fe_add( ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g ) { /** @var array<int, int> $arr */ $arr = array(); for ($i = 0; $i < 10; ++$i) { $arr[$i] = (int) ($f[$i] + $g[$i]); } return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($arr); } /** * Constant-time conditional move. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @param ParagonIE_Sodium_Core_Curve25519_Fe $g * @param int $b * @return ParagonIE_Sodium_Core_Curve25519_Fe * @psalm-suppress MixedAssignment */ public static function fe_cmov( ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g, $b = 0 ) { /** @var array<int, int> $h */ $h = array(); $b *= -1; for ($i = 0; $i < 10; ++$i) { $x = (($f[$i] ^ $g[$i]) & $b); $h[$i] = ($f[$i]) ^ $x; } return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($h); } /** * Create a copy of a field element. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_copy(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $h = clone $f; return $h; } /** * Give: 32-byte string. * Receive: A field element object to use for internal calculations. * * @internal You should not use this directly from another application * * @param string $s * @return ParagonIE_Sodium_Core_Curve25519_Fe * @throws RangeException * @throws TypeError */ public static function fe_frombytes($s) { if (self::strlen($s) !== 32) { throw new RangeException('Expected a 32-byte string.'); } $h0 = self::load_4($s); $h1 = self::load_3(self::substr($s, 4, 3)) << 6; $h2 = self::load_3(self::substr($s, 7, 3)) << 5; $h3 = self::load_3(self::substr($s, 10, 3)) << 3; $h4 = self::load_3(self::substr($s, 13, 3)) << 2; $h5 = self::load_4(self::substr($s, 16, 4)); $h6 = self::load_3(self::substr($s, 20, 3)) << 7; $h7 = self::load_3(self::substr($s, 23, 3)) << 5; $h8 = self::load_3(self::substr($s, 26, 3)) << 4; $h9 = (self::load_3(self::substr($s, 29, 3)) & 8388607) << 2; $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) $h0, (int) $h1, (int) $h2, (int) $h3, (int) $h4, (int) $h5, (int) $h6, (int) $h7, (int) $h8, (int) $h9 ) ); } /** * Convert a field element to a byte string. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $h * @return string */ public static function fe_tobytes(ParagonIE_Sodium_Core_Curve25519_Fe $h) { $h0 = (int) $h[0]; $h1 = (int) $h[1]; $h2 = (int) $h[2]; $h3 = (int) $h[3]; $h4 = (int) $h[4]; $h5 = (int) $h[5]; $h6 = (int) $h[6]; $h7 = (int) $h[7]; $h8 = (int) $h[8]; $h9 = (int) $h[9]; $q = (self::mul($h9, 19, 5) + (1 << 24)) >> 25; $q = ($h0 + $q) >> 26; $q = ($h1 + $q) >> 25; $q = ($h2 + $q) >> 26; $q = ($h3 + $q) >> 25; $q = ($h4 + $q) >> 26; $q = ($h5 + $q) >> 25; $q = ($h6 + $q) >> 26; $q = ($h7 + $q) >> 25; $q = ($h8 + $q) >> 26; $q = ($h9 + $q) >> 25; $h0 += self::mul($q, 19, 5); $carry0 = $h0 >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; $carry1 = $h1 >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; $carry2 = $h2 >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; $carry3 = $h3 >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; $carry4 = $h4 >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry5 = $h5 >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; $carry6 = $h6 >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; $carry7 = $h7 >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; $carry8 = $h8 >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; $carry9 = $h9 >> 25; $h9 -= $carry9 << 25; /** * @var array<int, int> */ $s = array( (int) (($h0 >> 0) & 0xff), (int) (($h0 >> 8) & 0xff), (int) (($h0 >> 16) & 0xff), (int) ((($h0 >> 24) | ($h1 << 2)) & 0xff), (int) (($h1 >> 6) & 0xff), (int) (($h1 >> 14) & 0xff), (int) ((($h1 >> 22) | ($h2 << 3)) & 0xff), (int) (($h2 >> 5) & 0xff), (int) (($h2 >> 13) & 0xff), (int) ((($h2 >> 21) | ($h3 << 5)) & 0xff), (int) (($h3 >> 3) & 0xff), (int) (($h3 >> 11) & 0xff), (int) ((($h3 >> 19) | ($h4 << 6)) & 0xff), (int) (($h4 >> 2) & 0xff), (int) (($h4 >> 10) & 0xff), (int) (($h4 >> 18) & 0xff), (int) (($h5 >> 0) & 0xff), (int) (($h5 >> 8) & 0xff), (int) (($h5 >> 16) & 0xff), (int) ((($h5 >> 24) | ($h6 << 1)) & 0xff), (int) (($h6 >> 7) & 0xff), (int) (($h6 >> 15) & 0xff), (int) ((($h6 >> 23) | ($h7 << 3)) & 0xff), (int) (($h7 >> 5) & 0xff), (int) (($h7 >> 13) & 0xff), (int) ((($h7 >> 21) | ($h8 << 4)) & 0xff), (int) (($h8 >> 4) & 0xff), (int) (($h8 >> 12) & 0xff), (int) ((($h8 >> 20) | ($h9 << 6)) & 0xff), (int) (($h9 >> 2) & 0xff), (int) (($h9 >> 10) & 0xff), (int) (($h9 >> 18) & 0xff) ); return self::intArrayToString($s); } /** * Is a field element negative? (1 = yes, 0 = no. Used in calculations.) * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return int * @throws SodiumException * @throws TypeError */ public static function fe_isnegative(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $str = self::fe_tobytes($f); return (int) (self::chrToInt($str[0]) & 1); } /** * Returns 0 if this field element results in all NUL bytes. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return bool * @throws SodiumException * @throws TypeError */ public static function fe_isnonzero(ParagonIE_Sodium_Core_Curve25519_Fe $f) { static $zero; if ($zero === null) { $zero = str_repeat("\x00", 32); } /** @var string $zero */ /** @var string $str */ $str = self::fe_tobytes($f); return !self::verify_32($str, (string) $zero); } /** * Multiply two field elements * * h = f * g * * @internal You should not use this directly from another application * * @security Is multiplication a source of timing leaks? If so, can we do * anything to prevent that from happening? * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @param ParagonIE_Sodium_Core_Curve25519_Fe $g * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_mul( ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g ) { // Ensure limbs aren't oversized. $f = self::fe_normalize($f); $g = self::fe_normalize($g); $f0 = $f[0]; $f1 = $f[1]; $f2 = $f[2]; $f3 = $f[3]; $f4 = $f[4]; $f5 = $f[5]; $f6 = $f[6]; $f7 = $f[7]; $f8 = $f[8]; $f9 = $f[9]; $g0 = $g[0]; $g1 = $g[1]; $g2 = $g[2]; $g3 = $g[3]; $g4 = $g[4]; $g5 = $g[5]; $g6 = $g[6]; $g7 = $g[7]; $g8 = $g[8]; $g9 = $g[9]; $g1_19 = self::mul($g1, 19, 5); $g2_19 = self::mul($g2, 19, 5); $g3_19 = self::mul($g3, 19, 5); $g4_19 = self::mul($g4, 19, 5); $g5_19 = self::mul($g5, 19, 5); $g6_19 = self::mul($g6, 19, 5); $g7_19 = self::mul($g7, 19, 5); $g8_19 = self::mul($g8, 19, 5); $g9_19 = self::mul($g9, 19, 5); $f1_2 = $f1 << 1; $f3_2 = $f3 << 1; $f5_2 = $f5 << 1; $f7_2 = $f7 << 1; $f9_2 = $f9 << 1; $f0g0 = self::mul($f0, $g0, 26); $f0g1 = self::mul($f0, $g1, 25); $f0g2 = self::mul($f0, $g2, 26); $f0g3 = self::mul($f0, $g3, 25); $f0g4 = self::mul($f0, $g4, 26); $f0g5 = self::mul($f0, $g5, 25); $f0g6 = self::mul($f0, $g6, 26); $f0g7 = self::mul($f0, $g7, 25); $f0g8 = self::mul($f0, $g8, 26); $f0g9 = self::mul($f0, $g9, 26); $f1g0 = self::mul($f1, $g0, 26); $f1g1_2 = self::mul($f1_2, $g1, 25); $f1g2 = self::mul($f1, $g2, 26); $f1g3_2 = self::mul($f1_2, $g3, 25); $f1g4 = self::mul($f1, $g4, 26); $f1g5_2 = self::mul($f1_2, $g5, 25); $f1g6 = self::mul($f1, $g6, 26); $f1g7_2 = self::mul($f1_2, $g7, 25); $f1g8 = self::mul($f1, $g8, 26); $f1g9_38 = self::mul($g9_19, $f1_2, 26); $f2g0 = self::mul($f2, $g0, 26); $f2g1 = self::mul($f2, $g1, 25); $f2g2 = self::mul($f2, $g2, 26); $f2g3 = self::mul($f2, $g3, 25); $f2g4 = self::mul($f2, $g4, 26); $f2g5 = self::mul($f2, $g5, 25); $f2g6 = self::mul($f2, $g6, 26); $f2g7 = self::mul($f2, $g7, 25); $f2g8_19 = self::mul($g8_19, $f2, 26); $f2g9_19 = self::mul($g9_19, $f2, 26); $f3g0 = self::mul($f3, $g0, 26); $f3g1_2 = self::mul($f3_2, $g1, 25); $f3g2 = self::mul($f3, $g2, 26); $f3g3_2 = self::mul($f3_2, $g3, 25); $f3g4 = self::mul($f3, $g4, 26); $f3g5_2 = self::mul($f3_2, $g5, 25); $f3g6 = self::mul($f3, $g6, 26); $f3g7_38 = self::mul($g7_19, $f3_2, 26); $f3g8_19 = self::mul($g8_19, $f3, 25); $f3g9_38 = self::mul($g9_19, $f3_2, 26); $f4g0 = self::mul($f4, $g0, 26); $f4g1 = self::mul($f4, $g1, 25); $f4g2 = self::mul($f4, $g2, 26); $f4g3 = self::mul($f4, $g3, 25); $f4g4 = self::mul($f4, $g4, 26); $f4g5 = self::mul($f4, $g5, 25); $f4g6_19 = self::mul($g6_19, $f4, 26); $f4g7_19 = self::mul($g7_19, $f4, 26); $f4g8_19 = self::mul($g8_19, $f4, 26); $f4g9_19 = self::mul($g9_19, $f4, 26); $f5g0 = self::mul($f5, $g0, 26); $f5g1_2 = self::mul($f5_2, $g1, 25); $f5g2 = self::mul($f5, $g2, 26); $f5g3_2 = self::mul($f5_2, $g3, 25); $f5g4 = self::mul($f5, $g4, 26); $f5g5_38 = self::mul($g5_19, $f5_2, 26); $f5g6_19 = self::mul($g6_19, $f5, 25); $f5g7_38 = self::mul($g7_19, $f5_2, 26); $f5g8_19 = self::mul($g8_19, $f5, 25); $f5g9_38 = self::mul($g9_19, $f5_2, 26); $f6g0 = self::mul($f6, $g0, 26); $f6g1 = self::mul($f6, $g1, 25); $f6g2 = self::mul($f6, $g2, 26); $f6g3 = self::mul($f6, $g3, 25); $f6g4_19 = self::mul($g4_19, $f6, 26); $f6g5_19 = self::mul($g5_19, $f6, 26); $f6g6_19 = self::mul($g6_19, $f6, 26); $f6g7_19 = self::mul($g7_19, $f6, 26); $f6g8_19 = self::mul($g8_19, $f6, 26); $f6g9_19 = self::mul($g9_19, $f6, 26); $f7g0 = self::mul($f7, $g0, 26); $f7g1_2 = self::mul($f7_2, $g1, 25); $f7g2 = self::mul($f7, $g2, 26); $f7g3_38 = self::mul($g3_19, $f7_2, 26); $f7g4_19 = self::mul($g4_19, $f7, 26); $f7g5_38 = self::mul($g5_19, $f7_2, 26); $f7g6_19 = self::mul($g6_19, $f7, 25); $f7g7_38 = self::mul($g7_19, $f7_2, 26); $f7g8_19 = self::mul($g8_19, $f7, 25); $f7g9_38 = self::mul($g9_19,$f7_2, 26); $f8g0 = self::mul($f8, $g0, 26); $f8g1 = self::mul($f8, $g1, 25); $f8g2_19 = self::mul($g2_19, $f8, 26); $f8g3_19 = self::mul($g3_19, $f8, 26); $f8g4_19 = self::mul($g4_19, $f8, 26); $f8g5_19 = self::mul($g5_19, $f8, 26); $f8g6_19 = self::mul($g6_19, $f8, 26); $f8g7_19 = self::mul($g7_19, $f8, 26); $f8g8_19 = self::mul($g8_19, $f8, 26); $f8g9_19 = self::mul($g9_19, $f8, 26); $f9g0 = self::mul($f9, $g0, 26); $f9g1_38 = self::mul($g1_19, $f9_2, 26); $f9g2_19 = self::mul($g2_19, $f9, 25); $f9g3_38 = self::mul($g3_19, $f9_2, 26); $f9g4_19 = self::mul($g4_19, $f9, 25); $f9g5_38 = self::mul($g5_19, $f9_2, 26); $f9g6_19 = self::mul($g6_19, $f9, 25); $f9g7_38 = self::mul($g7_19, $f9_2, 26); $f9g8_19 = self::mul($g8_19, $f9, 25); $f9g9_38 = self::mul($g9_19, $f9_2, 26); $h0 = $f0g0 + $f1g9_38 + $f2g8_19 + $f3g7_38 + $f4g6_19 + $f5g5_38 + $f6g4_19 + $f7g3_38 + $f8g2_19 + $f9g1_38; $h1 = $f0g1 + $f1g0 + $f2g9_19 + $f3g8_19 + $f4g7_19 + $f5g6_19 + $f6g5_19 + $f7g4_19 + $f8g3_19 + $f9g2_19; $h2 = $f0g2 + $f1g1_2 + $f2g0 + $f3g9_38 + $f4g8_19 + $f5g7_38 + $f6g6_19 + $f7g5_38 + $f8g4_19 + $f9g3_38; $h3 = $f0g3 + $f1g2 + $f2g1 + $f3g0 + $f4g9_19 + $f5g8_19 + $f6g7_19 + $f7g6_19 + $f8g5_19 + $f9g4_19; $h4 = $f0g4 + $f1g3_2 + $f2g2 + $f3g1_2 + $f4g0 + $f5g9_38 + $f6g8_19 + $f7g7_38 + $f8g6_19 + $f9g5_38; $h5 = $f0g5 + $f1g4 + $f2g3 + $f3g2 + $f4g1 + $f5g0 + $f6g9_19 + $f7g8_19 + $f8g7_19 + $f9g6_19; $h6 = $f0g6 + $f1g5_2 + $f2g4 + $f3g3_2 + $f4g2 + $f5g1_2 + $f6g0 + $f7g9_38 + $f8g8_19 + $f9g7_38; $h7 = $f0g7 + $f1g6 + $f2g5 + $f3g4 + $f4g3 + $f5g2 + $f6g1 + $f7g0 + $f8g9_19 + $f9g8_19; $h8 = $f0g8 + $f1g7_2 + $f2g6 + $f3g5_2 + $f4g4 + $f5g3_2 + $f6g2 + $f7g1_2 + $f8g0 + $f9g9_38; $h9 = $f0g9 + $f1g8 + $f2g7 + $f3g6 + $f4g5 + $f5g4 + $f6g3 + $f7g2 + $f8g1 + $f9g0 ; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; return self::fe_normalize( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) $h0, (int) $h1, (int) $h2, (int) $h3, (int) $h4, (int) $h5, (int) $h6, (int) $h7, (int) $h8, (int) $h9 ) ) ); } /** * Get the negative values for each piece of the field element. * * h = -f * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return ParagonIE_Sodium_Core_Curve25519_Fe * @psalm-suppress MixedAssignment */ public static function fe_neg(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $h = new ParagonIE_Sodium_Core_Curve25519_Fe(); for ($i = 0; $i < 10; ++$i) { $h[$i] = -$f[$i]; } return self::fe_normalize($h); } /** * Square a field element * * h = f * f * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_sq(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $f = self::fe_normalize($f); $f0 = (int) $f[0]; $f1 = (int) $f[1]; $f2 = (int) $f[2]; $f3 = (int) $f[3]; $f4 = (int) $f[4]; $f5 = (int) $f[5]; $f6 = (int) $f[6]; $f7 = (int) $f[7]; $f8 = (int) $f[8]; $f9 = (int) $f[9]; $f0_2 = $f0 << 1; $f1_2 = $f1 << 1; $f2_2 = $f2 << 1; $f3_2 = $f3 << 1; $f4_2 = $f4 << 1; $f5_2 = $f5 << 1; $f6_2 = $f6 << 1; $f7_2 = $f7 << 1; $f5_38 = self::mul($f5, 38, 6); $f6_19 = self::mul($f6, 19, 5); $f7_38 = self::mul($f7, 38, 6); $f8_19 = self::mul($f8, 19, 5); $f9_38 = self::mul($f9, 38, 6); $f0f0 = self::mul($f0, $f0, 26); $f0f1_2 = self::mul($f0_2, $f1, 26); $f0f2_2 = self::mul($f0_2, $f2, 26); $f0f3_2 = self::mul($f0_2, $f3, 26); $f0f4_2 = self::mul($f0_2, $f4, 26); $f0f5_2 = self::mul($f0_2, $f5, 26); $f0f6_2 = self::mul($f0_2, $f6, 26); $f0f7_2 = self::mul($f0_2, $f7, 26); $f0f8_2 = self::mul($f0_2, $f8, 26); $f0f9_2 = self::mul($f0_2, $f9, 26); $f1f1_2 = self::mul($f1_2, $f1, 26); $f1f2_2 = self::mul($f1_2, $f2, 26); $f1f3_4 = self::mul($f1_2, $f3_2, 26); $f1f4_2 = self::mul($f1_2, $f4, 26); $f1f5_4 = self::mul($f1_2, $f5_2, 26); $f1f6_2 = self::mul($f1_2, $f6, 26); $f1f7_4 = self::mul($f1_2, $f7_2, 26); $f1f8_2 = self::mul($f1_2, $f8, 26); $f1f9_76 = self::mul($f9_38, $f1_2, 27); $f2f2 = self::mul($f2, $f2, 27); $f2f3_2 = self::mul($f2_2, $f3, 27); $f2f4_2 = self::mul($f2_2, $f4, 27); $f2f5_2 = self::mul($f2_2, $f5, 27); $f2f6_2 = self::mul($f2_2, $f6, 27); $f2f7_2 = self::mul($f2_2, $f7, 27); $f2f8_38 = self::mul($f8_19, $f2_2, 27); $f2f9_38 = self::mul($f9_38, $f2, 26); $f3f3_2 = self::mul($f3_2, $f3, 26); $f3f4_2 = self::mul($f3_2, $f4, 26); $f3f5_4 = self::mul($f3_2, $f5_2, 26); $f3f6_2 = self::mul($f3_2, $f6, 26); $f3f7_76 = self::mul($f7_38, $f3_2, 26); $f3f8_38 = self::mul($f8_19, $f3_2, 26); $f3f9_76 = self::mul($f9_38, $f3_2, 26); $f4f4 = self::mul($f4, $f4, 26); $f4f5_2 = self::mul($f4_2, $f5, 26); $f4f6_38 = self::mul($f6_19, $f4_2, 27); $f4f7_38 = self::mul($f7_38, $f4, 26); $f4f8_38 = self::mul($f8_19, $f4_2, 27); $f4f9_38 = self::mul($f9_38, $f4, 26); $f5f5_38 = self::mul($f5_38, $f5, 26); $f5f6_38 = self::mul($f6_19, $f5_2, 26); $f5f7_76 = self::mul($f7_38, $f5_2, 26); $f5f8_38 = self::mul($f8_19, $f5_2, 26); $f5f9_76 = self::mul($f9_38, $f5_2, 26); $f6f6_19 = self::mul($f6_19, $f6, 26); $f6f7_38 = self::mul($f7_38, $f6, 26); $f6f8_38 = self::mul($f8_19, $f6_2, 27); $f6f9_38 = self::mul($f9_38, $f6, 26); $f7f7_38 = self::mul($f7_38, $f7, 26); $f7f8_38 = self::mul($f8_19, $f7_2, 26); $f7f9_76 = self::mul($f9_38, $f7_2, 26); $f8f8_19 = self::mul($f8_19, $f8, 26); $f8f9_38 = self::mul($f9_38, $f8, 26); $f9f9_38 = self::mul($f9_38, $f9, 26); $h0 = $f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38; $h1 = $f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38; $h2 = $f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19; $h3 = $f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38; $h4 = $f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38; $h5 = $f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38; $h6 = $f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19; $h7 = $f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38; $h8 = $f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38; $h9 = $f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; return self::fe_normalize( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) $h0, (int) $h1, (int) $h2, (int) $h3, (int) $h4, (int) $h5, (int) $h6, (int) $h7, (int) $h8, (int) $h9 ) ) ); } /** * Square and double a field element * * h = 2 * f * f * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_sq2(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $f = self::fe_normalize($f); $f0 = (int) $f[0]; $f1 = (int) $f[1]; $f2 = (int) $f[2]; $f3 = (int) $f[3]; $f4 = (int) $f[4]; $f5 = (int) $f[5]; $f6 = (int) $f[6]; $f7 = (int) $f[7]; $f8 = (int) $f[8]; $f9 = (int) $f[9]; $f0_2 = $f0 << 1; $f1_2 = $f1 << 1; $f2_2 = $f2 << 1; $f3_2 = $f3 << 1; $f4_2 = $f4 << 1; $f5_2 = $f5 << 1; $f6_2 = $f6 << 1; $f7_2 = $f7 << 1; $f5_38 = self::mul($f5, 38, 6); /* 1.959375*2^30 */ $f6_19 = self::mul($f6, 19, 5); /* 1.959375*2^30 */ $f7_38 = self::mul($f7, 38, 6); /* 1.959375*2^30 */ $f8_19 = self::mul($f8, 19, 5); /* 1.959375*2^30 */ $f9_38 = self::mul($f9, 38, 6); /* 1.959375*2^30 */ $f0f0 = self::mul($f0, $f0, 24); $f0f1_2 = self::mul($f0_2, $f1, 24); $f0f2_2 = self::mul($f0_2, $f2, 24); $f0f3_2 = self::mul($f0_2, $f3, 24); $f0f4_2 = self::mul($f0_2, $f4, 24); $f0f5_2 = self::mul($f0_2, $f5, 24); $f0f6_2 = self::mul($f0_2, $f6, 24); $f0f7_2 = self::mul($f0_2, $f7, 24); $f0f8_2 = self::mul($f0_2, $f8, 24); $f0f9_2 = self::mul($f0_2, $f9, 24); $f1f1_2 = self::mul($f1_2, $f1, 24); $f1f2_2 = self::mul($f1_2, $f2, 24); $f1f3_4 = self::mul($f1_2, $f3_2, 24); $f1f4_2 = self::mul($f1_2, $f4, 24); $f1f5_4 = self::mul($f1_2, $f5_2, 24); $f1f6_2 = self::mul($f1_2, $f6, 24); $f1f7_4 = self::mul($f1_2, $f7_2, 24); $f1f8_2 = self::mul($f1_2, $f8, 24); $f1f9_76 = self::mul($f9_38, $f1_2, 24); $f2f2 = self::mul($f2, $f2, 24); $f2f3_2 = self::mul($f2_2, $f3, 24); $f2f4_2 = self::mul($f2_2, $f4, 24); $f2f5_2 = self::mul($f2_2, $f5, 24); $f2f6_2 = self::mul($f2_2, $f6, 24); $f2f7_2 = self::mul($f2_2, $f7, 24); $f2f8_38 = self::mul($f8_19, $f2_2, 25); $f2f9_38 = self::mul($f9_38, $f2, 24); $f3f3_2 = self::mul($f3_2, $f3, 24); $f3f4_2 = self::mul($f3_2, $f4, 24); $f3f5_4 = self::mul($f3_2, $f5_2, 24); $f3f6_2 = self::mul($f3_2, $f6, 24); $f3f7_76 = self::mul($f7_38, $f3_2, 24); $f3f8_38 = self::mul($f8_19, $f3_2, 24); $f3f9_76 = self::mul($f9_38, $f3_2, 24); $f4f4 = self::mul($f4, $f4, 24); $f4f5_2 = self::mul($f4_2, $f5, 24); $f4f6_38 = self::mul($f6_19, $f4_2, 25); $f4f7_38 = self::mul($f7_38, $f4, 24); $f4f8_38 = self::mul($f8_19, $f4_2, 25); $f4f9_38 = self::mul($f9_38, $f4, 24); $f5f5_38 = self::mul($f5_38, $f5, 24); $f5f6_38 = self::mul($f6_19, $f5_2, 24); $f5f7_76 = self::mul($f7_38, $f5_2, 24); $f5f8_38 = self::mul($f8_19, $f5_2, 24); $f5f9_76 = self::mul($f9_38, $f5_2, 24); $f6f6_19 = self::mul($f6_19, $f6, 24); $f6f7_38 = self::mul($f7_38, $f6, 24); $f6f8_38 = self::mul($f8_19, $f6_2, 25); $f6f9_38 = self::mul($f9_38, $f6, 24); $f7f7_38 = self::mul($f7_38, $f7, 24); $f7f8_38 = self::mul($f8_19, $f7_2, 24); $f7f9_76 = self::mul($f9_38, $f7_2, 24); $f8f8_19 = self::mul($f8_19, $f8, 24); $f8f9_38 = self::mul($f9_38, $f8, 24); $f9f9_38 = self::mul($f9_38, $f9, 24); $h0 = (int) ($f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38) << 1; $h1 = (int) ($f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38) << 1; $h2 = (int) ($f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19) << 1; $h3 = (int) ($f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38) << 1; $h4 = (int) ($f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38) << 1; $h5 = (int) ($f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38) << 1; $h6 = (int) ($f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19) << 1; $h7 = (int) ($f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38) << 1; $h8 = (int) ($f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38) << 1; $h9 = (int) ($f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2) << 1; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; return self::fe_normalize( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) $h0, (int) $h1, (int) $h2, (int) $h3, (int) $h4, (int) $h5, (int) $h6, (int) $h7, (int) $h8, (int) $h9 ) ) ); } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $Z * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_invert(ParagonIE_Sodium_Core_Curve25519_Fe $Z) { $z = clone $Z; $t0 = self::fe_sq($z); $t1 = self::fe_sq($t0); $t1 = self::fe_sq($t1); $t1 = self::fe_mul($z, $t1); $t0 = self::fe_mul($t0, $t1); $t2 = self::fe_sq($t0); $t1 = self::fe_mul($t1, $t2); $t2 = self::fe_sq($t1); for ($i = 1; $i < 5; ++$i) { $t2 = self::fe_sq($t2); } $t1 = self::fe_mul($t2, $t1); $t2 = self::fe_sq($t1); for ($i = 1; $i < 10; ++$i) { $t2 = self::fe_sq($t2); } $t2 = self::fe_mul($t2, $t1); $t3 = self::fe_sq($t2); for ($i = 1; $i < 20; ++$i) { $t3 = self::fe_sq($t3); } $t2 = self::fe_mul($t3, $t2); $t2 = self::fe_sq($t2); for ($i = 1; $i < 10; ++$i) { $t2 = self::fe_sq($t2); } $t1 = self::fe_mul($t2, $t1); $t2 = self::fe_sq($t1); for ($i = 1; $i < 50; ++$i) { $t2 = self::fe_sq($t2); } $t2 = self::fe_mul($t2, $t1); $t3 = self::fe_sq($t2); for ($i = 1; $i < 100; ++$i) { $t3 = self::fe_sq($t3); } $t2 = self::fe_mul($t3, $t2); $t2 = self::fe_sq($t2); for ($i = 1; $i < 50; ++$i) { $t2 = self::fe_sq($t2); } $t1 = self::fe_mul($t2, $t1); $t1 = self::fe_sq($t1); for ($i = 1; $i < 5; ++$i) { $t1 = self::fe_sq($t1); } return self::fe_mul($t1, $t0); } /** * @internal You should not use this directly from another application * * @ref https://github.com/jedisct1/libsodium/blob/68564326e1e9dc57ef03746f85734232d20ca6fb/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1054-L1106 * * @param ParagonIE_Sodium_Core_Curve25519_Fe $z * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_pow22523(ParagonIE_Sodium_Core_Curve25519_Fe $z) { $z = self::fe_normalize($z); # fe_sq(t0, z); # fe_sq(t1, t0); # fe_sq(t1, t1); # fe_mul(t1, z, t1); # fe_mul(t0, t0, t1); # fe_sq(t0, t0); # fe_mul(t0, t1, t0); # fe_sq(t1, t0); $t0 = self::fe_sq($z); $t1 = self::fe_sq($t0); $t1 = self::fe_sq($t1); $t1 = self::fe_mul($z, $t1); $t0 = self::fe_mul($t0, $t1); $t0 = self::fe_sq($t0); $t0 = self::fe_mul($t1, $t0); $t1 = self::fe_sq($t0); # for (i = 1; i < 5; ++i) { # fe_sq(t1, t1); # } for ($i = 1; $i < 5; ++$i) { $t1 = self::fe_sq($t1); } # fe_mul(t0, t1, t0); # fe_sq(t1, t0); $t0 = self::fe_mul($t1, $t0); $t1 = self::fe_sq($t0); # for (i = 1; i < 10; ++i) { # fe_sq(t1, t1); # } for ($i = 1; $i < 10; ++$i) { $t1 = self::fe_sq($t1); } # fe_mul(t1, t1, t0); # fe_sq(t2, t1); $t1 = self::fe_mul($t1, $t0); $t2 = self::fe_sq($t1); # for (i = 1; i < 20; ++i) { # fe_sq(t2, t2); # } for ($i = 1; $i < 20; ++$i) { $t2 = self::fe_sq($t2); } # fe_mul(t1, t2, t1); # fe_sq(t1, t1); $t1 = self::fe_mul($t2, $t1); $t1 = self::fe_sq($t1); # for (i = 1; i < 10; ++i) { # fe_sq(t1, t1); # } for ($i = 1; $i < 10; ++$i) { $t1 = self::fe_sq($t1); } # fe_mul(t0, t1, t0); # fe_sq(t1, t0); $t0 = self::fe_mul($t1, $t0); $t1 = self::fe_sq($t0); # for (i = 1; i < 50; ++i) { # fe_sq(t1, t1); # } for ($i = 1; $i < 50; ++$i) { $t1 = self::fe_sq($t1); } # fe_mul(t1, t1, t0); # fe_sq(t2, t1); $t1 = self::fe_mul($t1, $t0); $t2 = self::fe_sq($t1); # for (i = 1; i < 100; ++i) { # fe_sq(t2, t2); # } for ($i = 1; $i < 100; ++$i) { $t2 = self::fe_sq($t2); } # fe_mul(t1, t2, t1); # fe_sq(t1, t1); $t1 = self::fe_mul($t2, $t1); $t1 = self::fe_sq($t1); # for (i = 1; i < 50; ++i) { # fe_sq(t1, t1); # } for ($i = 1; $i < 50; ++$i) { $t1 = self::fe_sq($t1); } # fe_mul(t0, t1, t0); # fe_sq(t0, t0); # fe_sq(t0, t0); # fe_mul(out, t0, z); $t0 = self::fe_mul($t1, $t0); $t0 = self::fe_sq($t0); $t0 = self::fe_sq($t0); return self::fe_mul($t0, $z); } /** * Subtract two field elements. * * h = f - g * * Preconditions: * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. * * Postconditions: * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @param ParagonIE_Sodium_Core_Curve25519_Fe $g * @return ParagonIE_Sodium_Core_Curve25519_Fe * @psalm-suppress MixedOperand */ public static function fe_sub(ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g) { return self::fe_normalize( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) ($f[0] - $g[0]), (int) ($f[1] - $g[1]), (int) ($f[2] - $g[2]), (int) ($f[3] - $g[3]), (int) ($f[4] - $g[4]), (int) ($f[5] - $g[5]), (int) ($f[6] - $g[6]), (int) ($f[7] - $g[7]), (int) ($f[8] - $g[8]), (int) ($f[9] - $g[9]) ) ) ); } /** * Add two group elements. * * r = p + q * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_add( ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q ) { $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); $r->X = self::fe_add($p->Y, $p->X); $r->Y = self::fe_sub($p->Y, $p->X); $r->Z = self::fe_mul($r->X, $q->YplusX); $r->Y = self::fe_mul($r->Y, $q->YminusX); $r->T = self::fe_mul($q->T2d, $p->T); $r->X = self::fe_mul($p->Z, $q->Z); $t0 = self::fe_add($r->X, $r->X); $r->X = self::fe_sub($r->Z, $r->Y); $r->Y = self::fe_add($r->Z, $r->Y); $r->Z = self::fe_add($t0, $r->T); $r->T = self::fe_sub($t0, $r->T); return $r; } /** * @internal You should not use this directly from another application * * @ref https://github.com/jedisct1/libsodium/blob/157c4a80c13b117608aeae12178b2d38825f9f8f/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1185-L1215 * @param string $a * @return array<int, mixed> * @throws SodiumException * @throws TypeError */ public static function slide($a) { if (self::strlen($a) < 256) { if (self::strlen($a) < 16) { $a = str_pad($a, 256, '0', STR_PAD_RIGHT); } } /** @var array<int, int> $r */ $r = array(); /** @var int $i */ for ($i = 0; $i < 256; ++$i) { $r[$i] = (int) ( 1 & ( self::chrToInt($a[(int) ($i >> 3)]) >> ($i & 7) ) ); } for ($i = 0;$i < 256;++$i) { if ($r[$i]) { for ($b = 1;$b <= 6 && $i + $b < 256;++$b) { if ($r[$i + $b]) { if ($r[$i] + ($r[$i + $b] << $b) <= 15) { $r[$i] += $r[$i + $b] << $b; $r[$i + $b] = 0; } elseif ($r[$i] - ($r[$i + $b] << $b) >= -15) { $r[$i] -= $r[$i + $b] << $b; for ($k = $i + $b; $k < 256; ++$k) { if (!$r[$k]) { $r[$k] = 1; break; } $r[$k] = 0; } } else { break; } } } } } return $r; } /** * @internal You should not use this directly from another application * * @param string $s * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 * @throws SodiumException * @throws TypeError */ public static function ge_frombytes_negate_vartime($s) { static $d = null; if (!$d) { $d = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d); } # fe_frombytes(h->Y,s); # fe_1(h->Z); $h = new ParagonIE_Sodium_Core_Curve25519_Ge_P3( self::fe_0(), self::fe_frombytes($s), self::fe_1() ); # fe_sq(u,h->Y); # fe_mul(v,u,d); # fe_sub(u,u,h->Z); /* u = y^2-1 */ # fe_add(v,v,h->Z); /* v = dy^2+1 */ $u = self::fe_sq($h->Y); /** @var ParagonIE_Sodium_Core_Curve25519_Fe $d */ $v = self::fe_mul($u, $d); $u = self::fe_sub($u, $h->Z); /* u = y^2 - 1 */ $v = self::fe_add($v, $h->Z); /* v = dy^2 + 1 */ # fe_sq(v3,v); # fe_mul(v3,v3,v); /* v3 = v^3 */ # fe_sq(h->X,v3); # fe_mul(h->X,h->X,v); # fe_mul(h->X,h->X,u); /* x = uv^7 */ $v3 = self::fe_sq($v); $v3 = self::fe_mul($v3, $v); /* v3 = v^3 */ $h->X = self::fe_sq($v3); $h->X = self::fe_mul($h->X, $v); $h->X = self::fe_mul($h->X, $u); /* x = uv^7 */ # fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */ # fe_mul(h->X,h->X,v3); # fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */ $h->X = self::fe_pow22523($h->X); /* x = (uv^7)^((q-5)/8) */ $h->X = self::fe_mul($h->X, $v3); $h->X = self::fe_mul($h->X, $u); /* x = uv^3(uv^7)^((q-5)/8) */ # fe_sq(vxx,h->X); # fe_mul(vxx,vxx,v); # fe_sub(check,vxx,u); /* vx^2-u */ $vxx = self::fe_sq($h->X); $vxx = self::fe_mul($vxx, $v); $check = self::fe_sub($vxx, $u); /* vx^2 - u */ # if (fe_isnonzero(check)) { # fe_add(check,vxx,u); /* vx^2+u */ # if (fe_isnonzero(check)) { # return -1; # } # fe_mul(h->X,h->X,sqrtm1); # } if (self::fe_isnonzero($check)) { $check = self::fe_add($vxx, $u); /* vx^2 + u */ if (self::fe_isnonzero($check)) { throw new RangeException('Internal check failed.'); } $h->X = self::fe_mul( $h->X, ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1) ); } # if (fe_isnegative(h->X) == (s[31] >> 7)) { # fe_neg(h->X,h->X); # } $i = self::chrToInt($s[31]); if (self::fe_isnegative($h->X) === ($i >> 7)) { $h->X = self::fe_neg($h->X); } # fe_mul(h->T,h->X,h->Y); $h->T = self::fe_mul($h->X, $h->Y); return $h; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_madd( ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R, ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q ) { $r = clone $R; $r->X = self::fe_add($p->Y, $p->X); $r->Y = self::fe_sub($p->Y, $p->X); $r->Z = self::fe_mul($r->X, $q->yplusx); $r->Y = self::fe_mul($r->Y, $q->yminusx); $r->T = self::fe_mul($q->xy2d, $p->T); $t0 = self::fe_add(clone $p->Z, clone $p->Z); $r->X = self::fe_sub($r->Z, $r->Y); $r->Y = self::fe_add($r->Z, $r->Y); $r->Z = self::fe_add($t0, $r->T); $r->T = self::fe_sub($t0, $r->T); return $r; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_msub( ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R, ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q ) { $r = clone $R; $r->X = self::fe_add($p->Y, $p->X); $r->Y = self::fe_sub($p->Y, $p->X); $r->Z = self::fe_mul($r->X, $q->yminusx); $r->Y = self::fe_mul($r->Y, $q->yplusx); $r->T = self::fe_mul($q->xy2d, $p->T); $t0 = self::fe_add($p->Z, $p->Z); $r->X = self::fe_sub($r->Z, $r->Y); $r->Y = self::fe_add($r->Z, $r->Y); $r->Z = self::fe_sub($t0, $r->T); $r->T = self::fe_add($t0, $r->T); return $r; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 */ public static function ge_p1p1_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p) { $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P2(); $r->X = self::fe_mul($p->X, $p->T); $r->Y = self::fe_mul($p->Y, $p->Z); $r->Z = self::fe_mul($p->Z, $p->T); return $r; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 */ public static function ge_p1p1_to_p3(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p) { $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P3(); $r->X = self::fe_mul($p->X, $p->T); $r->Y = self::fe_mul($p->Y, $p->Z); $r->Z = self::fe_mul($p->Z, $p->T); $r->T = self::fe_mul($p->X, $p->Y); return $r; } /** * @internal You should not use this directly from another application * * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 */ public static function ge_p2_0() { return new ParagonIE_Sodium_Core_Curve25519_Ge_P2( self::fe_0(), self::fe_1(), self::fe_1() ); } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_p2_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p) { $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); $r->X = self::fe_sq($p->X); $r->Z = self::fe_sq($p->Y); $r->T = self::fe_sq2($p->Z); $r->Y = self::fe_add($p->X, $p->Y); $t0 = self::fe_sq($r->Y); $r->Y = self::fe_add($r->Z, $r->X); $r->Z = self::fe_sub($r->Z, $r->X); $r->X = self::fe_sub($t0, $r->Y); $r->T = self::fe_sub($r->T, $r->Z); return $r; } /** * @internal You should not use this directly from another application * * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 */ public static function ge_p3_0() { return new ParagonIE_Sodium_Core_Curve25519_Ge_P3( self::fe_0(), self::fe_1(), self::fe_1(), self::fe_0() ); } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached */ public static function ge_p3_to_cached(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) { static $d2 = null; if ($d2 === null) { $d2 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d2); } /** @var ParagonIE_Sodium_Core_Curve25519_Fe $d2 */ $r = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(); $r->YplusX = self::fe_add($p->Y, $p->X); $r->YminusX = self::fe_sub($p->Y, $p->X); $r->Z = self::fe_copy($p->Z); $r->T2d = self::fe_mul($p->T, $d2); return $r; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 */ public static function ge_p3_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) { return new ParagonIE_Sodium_Core_Curve25519_Ge_P2( self::fe_copy($p->X), self::fe_copy($p->Y), self::fe_copy($p->Z) ); } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h * @return string * @throws SodiumException * @throws TypeError */ public static function ge_p3_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h) { $recip = self::fe_invert($h->Z); $x = self::fe_mul($h->X, $recip); $y = self::fe_mul($h->Y, $recip); $s = self::fe_tobytes($y); $s[31] = self::intToChr( self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7) ); return $s; } /** * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_p3_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) { $q = self::ge_p3_to_p2($p); return self::ge_p2_dbl($q); } /** * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp */ public static function ge_precomp_0() { return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( self::fe_1(), self::fe_1(), self::fe_0() ); } /** * @internal You should not use this directly from another application * * @param int $b * @param int $c * @return int */ public static function equal($b, $c) { return (int) ((($b ^ $c) - 1) >> 31) & 1; } /** * @internal You should not use this directly from another application * * @param int|string $char * @return int (1 = yes, 0 = no) * @throws SodiumException * @throws TypeError */ public static function negative($char) { if (is_int($char)) { return ($char >> 63) & 1; } $x = self::chrToInt(self::substr($char, 0, 1)); return (int) ($x >> 63); } /** * Conditional move * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u * @param int $b * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp */ public static function cmov( ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u, $b ) { if (!is_int($b)) { throw new InvalidArgumentException('Expected an integer.'); } return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( self::fe_cmov($t->yplusx, $u->yplusx, $b), self::fe_cmov($t->yminusx, $u->yminusx, $b), self::fe_cmov($t->xy2d, $u->xy2d, $b) ); } /** * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u * @param int $b * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached */ public static function ge_cmov_cached( ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t, ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u, $b ) { $b &= 1; $ret = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(); $ret->YplusX = self::fe_cmov($t->YplusX, $u->YplusX, $b); $ret->YminusX = self::fe_cmov($t->YminusX, $u->YminusX, $b); $ret->Z = self::fe_cmov($t->Z, $u->Z, $b); $ret->T2d = self::fe_cmov($t->T2d, $u->T2d, $b); return $ret; } /** * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $cached * @param int $b * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached * @throws SodiumException */ public static function ge_cmov8_cached(array $cached, $b) { // const unsigned char bnegative = negative(b); // const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); $bnegative = self::negative($b); $babs = $b - (((-$bnegative) & $b) << 1); // ge25519_cached_0(t); $t = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( self::fe_1(), self::fe_1(), self::fe_1(), self::fe_0() ); // ge25519_cmov_cached(t, &cached[0], equal(babs, 1)); // ge25519_cmov_cached(t, &cached[1], equal(babs, 2)); // ge25519_cmov_cached(t, &cached[2], equal(babs, 3)); // ge25519_cmov_cached(t, &cached[3], equal(babs, 4)); // ge25519_cmov_cached(t, &cached[4], equal(babs, 5)); // ge25519_cmov_cached(t, &cached[5], equal(babs, 6)); // ge25519_cmov_cached(t, &cached[6], equal(babs, 7)); // ge25519_cmov_cached(t, &cached[7], equal(babs, 8)); for ($x = 0; $x < 8; ++$x) { $t = self::ge_cmov_cached($t, $cached[$x], self::equal($babs, $x + 1)); } // fe25519_copy(minust.YplusX, t->YminusX); // fe25519_copy(minust.YminusX, t->YplusX); // fe25519_copy(minust.Z, t->Z); // fe25519_neg(minust.T2d, t->T2d); $minust = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( self::fe_copy($t->YminusX), self::fe_copy($t->YplusX), self::fe_copy($t->Z), self::fe_neg($t->T2d) ); return self::ge_cmov_cached($t, $minust, $bnegative); } /** * @internal You should not use this directly from another application * * @param int $pos * @param int $b * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp * @throws SodiumException * @throws TypeError * @psalm-suppress MixedArgument * @psalm-suppress MixedArrayAccess * @psalm-suppress MixedArrayOffset */ public static function ge_select($pos = 0, $b = 0) { static $base = null; if ($base === null) { $base = array(); /** @var int $i */ foreach (self::$base as $i => $bas) { for ($j = 0; $j < 8; ++$j) { $base[$i][$j] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][0]), ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][1]), ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][2]) ); } } } /** @var array<int, array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp>> $base */ if (!is_int($pos)) { throw new InvalidArgumentException('Position must be an integer'); } if ($pos < 0 || $pos > 31) { throw new RangeException('Position is out of range [0, 31]'); } $bnegative = self::negative($b); $babs = $b - (((-$bnegative) & $b) << 1); $t = self::ge_precomp_0(); for ($i = 0; $i < 8; ++$i) { $t = self::cmov( $t, $base[$pos][$i], self::equal($babs, $i + 1) ); } $minusT = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( self::fe_copy($t->yminusx), self::fe_copy($t->yplusx), self::fe_neg($t->xy2d) ); return self::cmov($t, $minusT, $bnegative); } /** * Subtract two group elements. * * r = p - q * * @internal You should not use this directly from another application * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 */ public static function ge_sub( ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q ) { $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); $r->X = self::fe_add($p->Y, $p->X); $r->Y = self::fe_sub($p->Y, $p->X); $r->Z = self::fe_mul($r->X, $q->YminusX); $r->Y = self::fe_mul($r->Y, $q->YplusX); $r->T = self::fe_mul($q->T2d, $p->T); $r->X = self::fe_mul($p->Z, $q->Z); $t0 = self::fe_add($r->X, $r->X); $r->X = self::fe_sub($r->Z, $r->Y); $r->Y = self::fe_add($r->Z, $r->Y); $r->Z = self::fe_sub($t0, $r->T); $r->T = self::fe_add($t0, $r->T); return $r; } /** * Convert a group element to a byte string. * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h * @return string * @throws SodiumException * @throws TypeError */ public static function ge_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h) { $recip = self::fe_invert($h->Z); $x = self::fe_mul($h->X, $recip); $y = self::fe_mul($h->Y, $recip); $s = self::fe_tobytes($y); $s[31] = self::intToChr( self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7) ); return $s; } /** * @internal You should not use this directly from another application * * @param string $a * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A * @param string $b * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 * @throws SodiumException * @throws TypeError * @psalm-suppress MixedArgument * @psalm-suppress MixedArrayAccess */ public static function ge_double_scalarmult_vartime( $a, ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A, $b ) { /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai */ $Ai = array(); /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp> $Bi */ static $Bi = array(); if (!$Bi) { for ($i = 0; $i < 8; ++$i) { $Bi[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][0]), ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][1]), ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][2]) ); } } for ($i = 0; $i < 8; ++$i) { $Ai[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( self::fe_0(), self::fe_0(), self::fe_0(), self::fe_0() ); } # slide(aslide,a); # slide(bslide,b); /** @var array<int, int> $aslide */ $aslide = self::slide($a); /** @var array<int, int> $bslide */ $bslide = self::slide($b); # ge_p3_to_cached(&Ai[0],A); # ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); $Ai[0] = self::ge_p3_to_cached($A); $t = self::ge_p3_dbl($A); $A2 = self::ge_p1p1_to_p3($t); # ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); # ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); # ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); # ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); # ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); # ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); # ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); for ($i = 0; $i < 7; ++$i) { $t = self::ge_add($A2, $Ai[$i]); $u = self::ge_p1p1_to_p3($t); $Ai[$i + 1] = self::ge_p3_to_cached($u); } # ge_p2_0(r); $r = self::ge_p2_0(); # for (i = 255;i >= 0;--i) { # if (aslide[i] || bslide[i]) break; # } $i = 255; for (; $i >= 0; --$i) { if ($aslide[$i] || $bslide[$i]) { break; } } # for (;i >= 0;--i) { for (; $i >= 0; --$i) { # ge_p2_dbl(&t,r); $t = self::ge_p2_dbl($r); # if (aslide[i] > 0) { if ($aslide[$i] > 0) { # ge_p1p1_to_p3(&u,&t); # ge_add(&t,&u,&Ai[aslide[i]/2]); $u = self::ge_p1p1_to_p3($t); $t = self::ge_add( $u, $Ai[(int) floor($aslide[$i] / 2)] ); # } else if (aslide[i] < 0) { } elseif ($aslide[$i] < 0) { # ge_p1p1_to_p3(&u,&t); # ge_sub(&t,&u,&Ai[(-aslide[i])/2]); $u = self::ge_p1p1_to_p3($t); $t = self::ge_sub( $u, $Ai[(int) floor(-$aslide[$i] / 2)] ); } # if (bslide[i] > 0) { if ($bslide[$i] > 0) { /** @var int $index */ $index = (int) floor($bslide[$i] / 2); # ge_p1p1_to_p3(&u,&t); # ge_madd(&t,&u,&Bi[bslide[i]/2]); $u = self::ge_p1p1_to_p3($t); $t = self::ge_madd($t, $u, $Bi[$index]); # } else if (bslide[i] < 0) { } elseif ($bslide[$i] < 0) { /** @var int $index */ $index = (int) floor(-$bslide[$i] / 2); # ge_p1p1_to_p3(&u,&t); # ge_msub(&t,&u,&Bi[(-bslide[i])/2]); $u = self::ge_p1p1_to_p3($t); $t = self::ge_msub($t, $u, $Bi[$index]); } # ge_p1p1_to_p2(r,&t); $r = self::ge_p1p1_to_p2($t); } return $r; } /** * @internal You should not use this directly from another application * * @param string $a * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 * @throws SodiumException * @throws TypeError * @psalm-suppress MixedAssignment * @psalm-suppress MixedOperand */ public static function ge_scalarmult($a, $p) { $e = array_fill(0, 64, 0); /** @var ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $pi */ $pi = array(); // ge25519_p3_to_cached(&pi[1 - 1], p); /* p */ $pi[0] = self::ge_p3_to_cached($p); // ge25519_p3_dbl(&t2, p); // ge25519_p1p1_to_p3(&p2, &t2); // ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */ $t2 = self::ge_p3_dbl($p); $p2 = self::ge_p1p1_to_p3($t2); $pi[1] = self::ge_p3_to_cached($p2); // ge25519_add_cached(&t3, p, &pi[2 - 1]); // ge25519_p1p1_to_p3(&p3, &t3); // ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */ $t3 = self::ge_add($p, $pi[1]); $p3 = self::ge_p1p1_to_p3($t3); $pi[2] = self::ge_p3_to_cached($p3); // ge25519_p3_dbl(&t4, &p2); // ge25519_p1p1_to_p3(&p4, &t4); // ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */ $t4 = self::ge_p3_dbl($p2); $p4 = self::ge_p1p1_to_p3($t4); $pi[3] = self::ge_p3_to_cached($p4); // ge25519_add_cached(&t5, p, &pi[4 - 1]); // ge25519_p1p1_to_p3(&p5, &t5); // ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */ $t5 = self::ge_add($p, $pi[3]); $p5 = self::ge_p1p1_to_p3($t5); $pi[4] = self::ge_p3_to_cached($p5); // ge25519_p3_dbl(&t6, &p3); // ge25519_p1p1_to_p3(&p6, &t6); // ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */ $t6 = self::ge_p3_dbl($p3); $p6 = self::ge_p1p1_to_p3($t6); $pi[5] = self::ge_p3_to_cached($p6); // ge25519_add_cached(&t7, p, &pi[6 - 1]); // ge25519_p1p1_to_p3(&p7, &t7); // ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */ $t7 = self::ge_add($p, $pi[5]); $p7 = self::ge_p1p1_to_p3($t7); $pi[6] = self::ge_p3_to_cached($p7); // ge25519_p3_dbl(&t8, &p4); // ge25519_p1p1_to_p3(&p8, &t8); // ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */ $t8 = self::ge_p3_dbl($p4); $p8 = self::ge_p1p1_to_p3($t8); $pi[7] = self::ge_p3_to_cached($p8); // for (i = 0; i < 32; ++i) { // e[2 * i + 0] = (a[i] >> 0) & 15; // e[2 * i + 1] = (a[i] >> 4) & 15; // } for ($i = 0; $i < 32; ++$i) { $e[($i << 1) ] = self::chrToInt($a[$i]) & 15; $e[($i << 1) + 1] = (self::chrToInt($a[$i]) >> 4) & 15; } // /* each e[i] is between 0 and 15 */ // /* e[63] is between 0 and 7 */ // carry = 0; // for (i = 0; i < 63; ++i) { // e[i] += carry; // carry = e[i] + 8; // carry >>= 4; // e[i] -= carry * ((signed char) 1 << 4); // } $carry = 0; for ($i = 0; $i < 63; ++$i) { $e[$i] += $carry; $carry = $e[$i] + 8; $carry >>= 4; $e[$i] -= $carry << 4; } // e[63] += carry; // /* each e[i] is between -8 and 8 */ $e[63] += $carry; // ge25519_p3_0(h); $h = self::ge_p3_0(); // for (i = 63; i != 0; i--) { for ($i = 63; $i != 0; --$i) { // ge25519_cmov8_cached(&t, pi, e[i]); $t = self::ge_cmov8_cached($pi, $e[$i]); // ge25519_add_cached(&r, h, &t); $r = self::ge_add($h, $t); // ge25519_p1p1_to_p2(&s, &r); // ge25519_p2_dbl(&r, &s); // ge25519_p1p1_to_p2(&s, &r); // ge25519_p2_dbl(&r, &s); // ge25519_p1p1_to_p2(&s, &r); // ge25519_p2_dbl(&r, &s); // ge25519_p1p1_to_p2(&s, &r); // ge25519_p2_dbl(&r, &s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); // ge25519_p1p1_to_p3(h, &r); /* *16 */ $h = self::ge_p1p1_to_p3($r); /* *16 */ } // ge25519_cmov8_cached(&t, pi, e[i]); // ge25519_add_cached(&r, h, &t); // ge25519_p1p1_to_p3(h, &r); $t = self::ge_cmov8_cached($pi, $e[0]); $r = self::ge_add($h, $t); return self::ge_p1p1_to_p3($r); } /** * @internal You should not use this directly from another application * * @param string $a * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 * @throws SodiumException * @throws TypeError * @psalm-suppress MixedAssignment * @psalm-suppress MixedOperand */ public static function ge_scalarmult_base($a) { /** @var array<int, int> $e */ $e = array(); $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); for ($i = 0; $i < 32; ++$i) { $dbl = (int) $i << 1; $e[$dbl] = (int) self::chrToInt($a[$i]) & 15; $e[$dbl + 1] = (int) (self::chrToInt($a[$i]) >> 4) & 15; } $carry = 0; for ($i = 0; $i < 63; ++$i) { $e[$i] += $carry; $carry = $e[$i] + 8; $carry >>= 4; $e[$i] -= $carry << 4; } $e[63] += (int) $carry; $h = self::ge_p3_0(); for ($i = 1; $i < 64; $i += 2) { $t = self::ge_select((int) floor($i / 2), (int) $e[$i]); $r = self::ge_madd($r, $h, $t); $h = self::ge_p1p1_to_p3($r); } $r = self::ge_p3_dbl($h); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $s = self::ge_p1p1_to_p2($r); $r = self::ge_p2_dbl($s); $h = self::ge_p1p1_to_p3($r); for ($i = 0; $i < 64; $i += 2) { $t = self::ge_select($i >> 1, (int) $e[$i]); $r = self::ge_madd($r, $h, $t); $h = self::ge_p1p1_to_p3($r); } return $h; } /** * Calculates (ab + c) mod l * where l = 2^252 + 27742317777372353535851937790883648493 * * @internal You should not use this directly from another application * * @param string $a * @param string $b * @param string $c * @return string * @throws TypeError */ public static function sc_muladd($a, $b, $c) { $a0 = 2097151 & self::load_3(self::substr($a, 0, 3)); $a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5); $a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2); $a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7); $a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4); $a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1); $a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6); $a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3); $a8 = 2097151 & self::load_3(self::substr($a, 21, 3)); $a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5); $a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2); $a11 = (self::load_4(self::substr($a, 28, 4)) >> 7); $b0 = 2097151 & self::load_3(self::substr($b, 0, 3)); $b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5); $b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2); $b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7); $b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4); $b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1); $b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6); $b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3); $b8 = 2097151 & self::load_3(self::substr($b, 21, 3)); $b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5); $b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2); $b11 = (self::load_4(self::substr($b, 28, 4)) >> 7); $c0 = 2097151 & self::load_3(self::substr($c, 0, 3)); $c1 = 2097151 & (self::load_4(self::substr($c, 2, 4)) >> 5); $c2 = 2097151 & (self::load_3(self::substr($c, 5, 3)) >> 2); $c3 = 2097151 & (self::load_4(self::substr($c, 7, 4)) >> 7); $c4 = 2097151 & (self::load_4(self::substr($c, 10, 4)) >> 4); $c5 = 2097151 & (self::load_3(self::substr($c, 13, 3)) >> 1); $c6 = 2097151 & (self::load_4(self::substr($c, 15, 4)) >> 6); $c7 = 2097151 & (self::load_3(self::substr($c, 18, 3)) >> 3); $c8 = 2097151 & self::load_3(self::substr($c, 21, 3)); $c9 = 2097151 & (self::load_4(self::substr($c, 23, 4)) >> 5); $c10 = 2097151 & (self::load_3(self::substr($c, 26, 3)) >> 2); $c11 = (self::load_4(self::substr($c, 28, 4)) >> 7); /* Can't really avoid the pyramid here: */ $s0 = $c0 + self::mul($a0, $b0, 24); $s1 = $c1 + self::mul($a0, $b1, 24) + self::mul($a1, $b0, 24); $s2 = $c2 + self::mul($a0, $b2, 24) + self::mul($a1, $b1, 24) + self::mul($a2, $b0, 24); $s3 = $c3 + self::mul($a0, $b3, 24) + self::mul($a1, $b2, 24) + self::mul($a2, $b1, 24) + self::mul($a3, $b0, 24); $s4 = $c4 + self::mul($a0, $b4, 24) + self::mul($a1, $b3, 24) + self::mul($a2, $b2, 24) + self::mul($a3, $b1, 24) + self::mul($a4, $b0, 24); $s5 = $c5 + self::mul($a0, $b5, 24) + self::mul($a1, $b4, 24) + self::mul($a2, $b3, 24) + self::mul($a3, $b2, 24) + self::mul($a4, $b1, 24) + self::mul($a5, $b0, 24); $s6 = $c6 + self::mul($a0, $b6, 24) + self::mul($a1, $b5, 24) + self::mul($a2, $b4, 24) + self::mul($a3, $b3, 24) + self::mul($a4, $b2, 24) + self::mul($a5, $b1, 24) + self::mul($a6, $b0, 24); $s7 = $c7 + self::mul($a0, $b7, 24) + self::mul($a1, $b6, 24) + self::mul($a2, $b5, 24) + self::mul($a3, $b4, 24) + self::mul($a4, $b3, 24) + self::mul($a5, $b2, 24) + self::mul($a6, $b1, 24) + self::mul($a7, $b0, 24); $s8 = $c8 + self::mul($a0, $b8, 24) + self::mul($a1, $b7, 24) + self::mul($a2, $b6, 24) + self::mul($a3, $b5, 24) + self::mul($a4, $b4, 24) + self::mul($a5, $b3, 24) + self::mul($a6, $b2, 24) + self::mul($a7, $b1, 24) + self::mul($a8, $b0, 24); $s9 = $c9 + self::mul($a0, $b9, 24) + self::mul($a1, $b8, 24) + self::mul($a2, $b7, 24) + self::mul($a3, $b6, 24) + self::mul($a4, $b5, 24) + self::mul($a5, $b4, 24) + self::mul($a6, $b3, 24) + self::mul($a7, $b2, 24) + self::mul($a8, $b1, 24) + self::mul($a9, $b0, 24); $s10 = $c10 + self::mul($a0, $b10, 24) + self::mul($a1, $b9, 24) + self::mul($a2, $b8, 24) + self::mul($a3, $b7, 24) + self::mul($a4, $b6, 24) + self::mul($a5, $b5, 24) + self::mul($a6, $b4, 24) + self::mul($a7, $b3, 24) + self::mul($a8, $b2, 24) + self::mul($a9, $b1, 24) + self::mul($a10, $b0, 24); $s11 = $c11 + self::mul($a0, $b11, 24) + self::mul($a1, $b10, 24) + self::mul($a2, $b9, 24) + self::mul($a3, $b8, 24) + self::mul($a4, $b7, 24) + self::mul($a5, $b6, 24) + self::mul($a6, $b5, 24) + self::mul($a7, $b4, 24) + self::mul($a8, $b3, 24) + self::mul($a9, $b2, 24) + self::mul($a10, $b1, 24) + self::mul($a11, $b0, 24); $s12 = self::mul($a1, $b11, 24) + self::mul($a2, $b10, 24) + self::mul($a3, $b9, 24) + self::mul($a4, $b8, 24) + self::mul($a5, $b7, 24) + self::mul($a6, $b6, 24) + self::mul($a7, $b5, 24) + self::mul($a8, $b4, 24) + self::mul($a9, $b3, 24) + self::mul($a10, $b2, 24) + self::mul($a11, $b1, 24); $s13 = self::mul($a2, $b11, 24) + self::mul($a3, $b10, 24) + self::mul($a4, $b9, 24) + self::mul($a5, $b8, 24) + self::mul($a6, $b7, 24) + self::mul($a7, $b6, 24) + self::mul($a8, $b5, 24) + self::mul($a9, $b4, 24) + self::mul($a10, $b3, 24) + self::mul($a11, $b2, 24); $s14 = self::mul($a3, $b11, 24) + self::mul($a4, $b10, 24) + self::mul($a5, $b9, 24) + self::mul($a6, $b8, 24) + self::mul($a7, $b7, 24) + self::mul($a8, $b6, 24) + self::mul($a9, $b5, 24) + self::mul($a10, $b4, 24) + self::mul($a11, $b3, 24); $s15 = self::mul($a4, $b11, 24) + self::mul($a5, $b10, 24) + self::mul($a6, $b9, 24) + self::mul($a7, $b8, 24) + self::mul($a8, $b7, 24) + self::mul($a9, $b6, 24) + self::mul($a10, $b5, 24) + self::mul($a11, $b4, 24); $s16 = self::mul($a5, $b11, 24) + self::mul($a6, $b10, 24) + self::mul($a7, $b9, 24) + self::mul($a8, $b8, 24) + self::mul($a9, $b7, 24) + self::mul($a10, $b6, 24) + self::mul($a11, $b5, 24); $s17 = self::mul($a6, $b11, 24) + self::mul($a7, $b10, 24) + self::mul($a8, $b9, 24) + self::mul($a9, $b8, 24) + self::mul($a10, $b7, 24) + self::mul($a11, $b6, 24); $s18 = self::mul($a7, $b11, 24) + self::mul($a8, $b10, 24) + self::mul($a9, $b9, 24) + self::mul($a10, $b8, 24) + self::mul($a11, $b7, 24); $s19 = self::mul($a8, $b11, 24) + self::mul($a9, $b10, 24) + self::mul($a10, $b9, 24) + self::mul($a11, $b8, 24); $s20 = self::mul($a9, $b11, 24) + self::mul($a10, $b10, 24) + self::mul($a11, $b9, 24); $s21 = self::mul($a10, $b11, 24) + self::mul($a11, $b10, 24); $s22 = self::mul($a11, $b11, 24); $s23 = 0; $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; $carry18 = ($s18 + (1 << 20)) >> 21; $s19 += $carry18; $s18 -= $carry18 << 21; $carry20 = ($s20 + (1 << 20)) >> 21; $s21 += $carry20; $s20 -= $carry20 << 21; $carry22 = ($s22 + (1 << 20)) >> 21; $s23 += $carry22; $s22 -= $carry22 << 21; $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; $carry17 = ($s17 + (1 << 20)) >> 21; $s18 += $carry17; $s17 -= $carry17 << 21; $carry19 = ($s19 + (1 << 20)) >> 21; $s20 += $carry19; $s19 -= $carry19 << 21; $carry21 = ($s21 + (1 << 20)) >> 21; $s22 += $carry21; $s21 -= $carry21 << 21; $s11 += self::mul($s23, 666643, 20); $s12 += self::mul($s23, 470296, 19); $s13 += self::mul($s23, 654183, 20); $s14 -= self::mul($s23, 997805, 20); $s15 += self::mul($s23, 136657, 18); $s16 -= self::mul($s23, 683901, 20); $s10 += self::mul($s22, 666643, 20); $s11 += self::mul($s22, 470296, 19); $s12 += self::mul($s22, 654183, 20); $s13 -= self::mul($s22, 997805, 20); $s14 += self::mul($s22, 136657, 18); $s15 -= self::mul($s22, 683901, 20); $s9 += self::mul($s21, 666643, 20); $s10 += self::mul($s21, 470296, 19); $s11 += self::mul($s21, 654183, 20); $s12 -= self::mul($s21, 997805, 20); $s13 += self::mul($s21, 136657, 18); $s14 -= self::mul($s21, 683901, 20); $s8 += self::mul($s20, 666643, 20); $s9 += self::mul($s20, 470296, 19); $s10 += self::mul($s20, 654183, 20); $s11 -= self::mul($s20, 997805, 20); $s12 += self::mul($s20, 136657, 18); $s13 -= self::mul($s20, 683901, 20); $s7 += self::mul($s19, 666643, 20); $s8 += self::mul($s19, 470296, 19); $s9 += self::mul($s19, 654183, 20); $s10 -= self::mul($s19, 997805, 20); $s11 += self::mul($s19, 136657, 18); $s12 -= self::mul($s19, 683901, 20); $s6 += self::mul($s18, 666643, 20); $s7 += self::mul($s18, 470296, 19); $s8 += self::mul($s18, 654183, 20); $s9 -= self::mul($s18, 997805, 20); $s10 += self::mul($s18, 136657, 18); $s11 -= self::mul($s18, 683901, 20); $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; $s5 += self::mul($s17, 666643, 20); $s6 += self::mul($s17, 470296, 19); $s7 += self::mul($s17, 654183, 20); $s8 -= self::mul($s17, 997805, 20); $s9 += self::mul($s17, 136657, 18); $s10 -= self::mul($s17, 683901, 20); $s4 += self::mul($s16, 666643, 20); $s5 += self::mul($s16, 470296, 19); $s6 += self::mul($s16, 654183, 20); $s7 -= self::mul($s16, 997805, 20); $s8 += self::mul($s16, 136657, 18); $s9 -= self::mul($s16, 683901, 20); $s3 += self::mul($s15, 666643, 20); $s4 += self::mul($s15, 470296, 19); $s5 += self::mul($s15, 654183, 20); $s6 -= self::mul($s15, 997805, 20); $s7 += self::mul($s15, 136657, 18); $s8 -= self::mul($s15, 683901, 20); $s2 += self::mul($s14, 666643, 20); $s3 += self::mul($s14, 470296, 19); $s4 += self::mul($s14, 654183, 20); $s5 -= self::mul($s14, 997805, 20); $s6 += self::mul($s14, 136657, 18); $s7 -= self::mul($s14, 683901, 20); $s1 += self::mul($s13, 666643, 20); $s2 += self::mul($s13, 470296, 19); $s3 += self::mul($s13, 654183, 20); $s4 -= self::mul($s13, 997805, 20); $s5 += self::mul($s13, 136657, 18); $s6 -= self::mul($s13, 683901, 20); $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry11 = $s11 >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** * @var array<int, int> */ $arr = array( (int) (0xff & ($s0 >> 0)), (int) (0xff & ($s0 >> 8)), (int) (0xff & (($s0 >> 16) | $s1 << 5)), (int) (0xff & ($s1 >> 3)), (int) (0xff & ($s1 >> 11)), (int) (0xff & (($s1 >> 19) | $s2 << 2)), (int) (0xff & ($s2 >> 6)), (int) (0xff & (($s2 >> 14) | $s3 << 7)), (int) (0xff & ($s3 >> 1)), (int) (0xff & ($s3 >> 9)), (int) (0xff & (($s3 >> 17) | $s4 << 4)), (int) (0xff & ($s4 >> 4)), (int) (0xff & ($s4 >> 12)), (int) (0xff & (($s4 >> 20) | $s5 << 1)), (int) (0xff & ($s5 >> 7)), (int) (0xff & (($s5 >> 15) | $s6 << 6)), (int) (0xff & ($s6 >> 2)), (int) (0xff & ($s6 >> 10)), (int) (0xff & (($s6 >> 18) | $s7 << 3)), (int) (0xff & ($s7 >> 5)), (int) (0xff & ($s7 >> 13)), (int) (0xff & ($s8 >> 0)), (int) (0xff & ($s8 >> 8)), (int) (0xff & (($s8 >> 16) | $s9 << 5)), (int) (0xff & ($s9 >> 3)), (int) (0xff & ($s9 >> 11)), (int) (0xff & (($s9 >> 19) | $s10 << 2)), (int) (0xff & ($s10 >> 6)), (int) (0xff & (($s10 >> 14) | $s11 << 7)), (int) (0xff & ($s11 >> 1)), (int) (0xff & ($s11 >> 9)), 0xff & ($s11 >> 17) ); return self::intArrayToString($arr); } /** * @internal You should not use this directly from another application * * @param string $s * @return string * @throws TypeError */ public static function sc_reduce($s) { $s0 = 2097151 & self::load_3(self::substr($s, 0, 3)); $s1 = 2097151 & (self::load_4(self::substr($s, 2, 4)) >> 5); $s2 = 2097151 & (self::load_3(self::substr($s, 5, 3)) >> 2); $s3 = 2097151 & (self::load_4(self::substr($s, 7, 4)) >> 7); $s4 = 2097151 & (self::load_4(self::substr($s, 10, 4)) >> 4); $s5 = 2097151 & (self::load_3(self::substr($s, 13, 3)) >> 1); $s6 = 2097151 & (self::load_4(self::substr($s, 15, 4)) >> 6); $s7 = 2097151 & (self::load_3(self::substr($s, 18, 4)) >> 3); $s8 = 2097151 & self::load_3(self::substr($s, 21, 3)); $s9 = 2097151 & (self::load_4(self::substr($s, 23, 4)) >> 5); $s10 = 2097151 & (self::load_3(self::substr($s, 26, 3)) >> 2); $s11 = 2097151 & (self::load_4(self::substr($s, 28, 4)) >> 7); $s12 = 2097151 & (self::load_4(self::substr($s, 31, 4)) >> 4); $s13 = 2097151 & (self::load_3(self::substr($s, 34, 3)) >> 1); $s14 = 2097151 & (self::load_4(self::substr($s, 36, 4)) >> 6); $s15 = 2097151 & (self::load_3(self::substr($s, 39, 4)) >> 3); $s16 = 2097151 & self::load_3(self::substr($s, 42, 3)); $s17 = 2097151 & (self::load_4(self::substr($s, 44, 4)) >> 5); $s18 = 2097151 & (self::load_3(self::substr($s, 47, 3)) >> 2); $s19 = 2097151 & (self::load_4(self::substr($s, 49, 4)) >> 7); $s20 = 2097151 & (self::load_4(self::substr($s, 52, 4)) >> 4); $s21 = 2097151 & (self::load_3(self::substr($s, 55, 3)) >> 1); $s22 = 2097151 & (self::load_4(self::substr($s, 57, 4)) >> 6); $s23 = 0x1fffffff & (self::load_4(self::substr($s, 60, 4)) >> 3); $s11 += self::mul($s23, 666643, 20); $s12 += self::mul($s23, 470296, 19); $s13 += self::mul($s23, 654183, 20); $s14 -= self::mul($s23, 997805, 20); $s15 += self::mul($s23, 136657, 18); $s16 -= self::mul($s23, 683901, 20); $s10 += self::mul($s22, 666643, 20); $s11 += self::mul($s22, 470296, 19); $s12 += self::mul($s22, 654183, 20); $s13 -= self::mul($s22, 997805, 20); $s14 += self::mul($s22, 136657, 18); $s15 -= self::mul($s22, 683901, 20); $s9 += self::mul($s21, 666643, 20); $s10 += self::mul($s21, 470296, 19); $s11 += self::mul($s21, 654183, 20); $s12 -= self::mul($s21, 997805, 20); $s13 += self::mul($s21, 136657, 18); $s14 -= self::mul($s21, 683901, 20); $s8 += self::mul($s20, 666643, 20); $s9 += self::mul($s20, 470296, 19); $s10 += self::mul($s20, 654183, 20); $s11 -= self::mul($s20, 997805, 20); $s12 += self::mul($s20, 136657, 18); $s13 -= self::mul($s20, 683901, 20); $s7 += self::mul($s19, 666643, 20); $s8 += self::mul($s19, 470296, 19); $s9 += self::mul($s19, 654183, 20); $s10 -= self::mul($s19, 997805, 20); $s11 += self::mul($s19, 136657, 18); $s12 -= self::mul($s19, 683901, 20); $s6 += self::mul($s18, 666643, 20); $s7 += self::mul($s18, 470296, 19); $s8 += self::mul($s18, 654183, 20); $s9 -= self::mul($s18, 997805, 20); $s10 += self::mul($s18, 136657, 18); $s11 -= self::mul($s18, 683901, 20); $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; $s5 += self::mul($s17, 666643, 20); $s6 += self::mul($s17, 470296, 19); $s7 += self::mul($s17, 654183, 20); $s8 -= self::mul($s17, 997805, 20); $s9 += self::mul($s17, 136657, 18); $s10 -= self::mul($s17, 683901, 20); $s4 += self::mul($s16, 666643, 20); $s5 += self::mul($s16, 470296, 19); $s6 += self::mul($s16, 654183, 20); $s7 -= self::mul($s16, 997805, 20); $s8 += self::mul($s16, 136657, 18); $s9 -= self::mul($s16, 683901, 20); $s3 += self::mul($s15, 666643, 20); $s4 += self::mul($s15, 470296, 19); $s5 += self::mul($s15, 654183, 20); $s6 -= self::mul($s15, 997805, 20); $s7 += self::mul($s15, 136657, 18); $s8 -= self::mul($s15, 683901, 20); $s2 += self::mul($s14, 666643, 20); $s3 += self::mul($s14, 470296, 19); $s4 += self::mul($s14, 654183, 20); $s5 -= self::mul($s14, 997805, 20); $s6 += self::mul($s14, 136657, 18); $s7 -= self::mul($s14, 683901, 20); $s1 += self::mul($s13, 666643, 20); $s2 += self::mul($s13, 470296, 19); $s3 += self::mul($s13, 654183, 20); $s4 -= self::mul($s13, 997805, 20); $s5 += self::mul($s13, 136657, 18); $s6 -= self::mul($s13, 683901, 20); $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $carry11 = $s11 >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** * @var array<int, int> */ $arr = array( (int) ($s0 >> 0), (int) ($s0 >> 8), (int) (($s0 >> 16) | $s1 << 5), (int) ($s1 >> 3), (int) ($s1 >> 11), (int) (($s1 >> 19) | $s2 << 2), (int) ($s2 >> 6), (int) (($s2 >> 14) | $s3 << 7), (int) ($s3 >> 1), (int) ($s3 >> 9), (int) (($s3 >> 17) | $s4 << 4), (int) ($s4 >> 4), (int) ($s4 >> 12), (int) (($s4 >> 20) | $s5 << 1), (int) ($s5 >> 7), (int) (($s5 >> 15) | $s6 << 6), (int) ($s6 >> 2), (int) ($s6 >> 10), (int) (($s6 >> 18) | $s7 << 3), (int) ($s7 >> 5), (int) ($s7 >> 13), (int) ($s8 >> 0), (int) ($s8 >> 8), (int) (($s8 >> 16) | $s9 << 5), (int) ($s9 >> 3), (int) ($s9 >> 11), (int) (($s9 >> 19) | $s10 << 2), (int) ($s10 >> 6), (int) (($s10 >> 14) | $s11 << 7), (int) ($s11 >> 1), (int) ($s11 >> 9), (int) $s11 >> 17 ); return self::intArrayToString($arr); } /** * multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 * * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 */ public static function ge_mul_l(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A) { $aslide = array( 13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ); /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai size 8 */ $Ai = array(); # ge_p3_to_cached(&Ai[0], A); $Ai[0] = self::ge_p3_to_cached($A); # ge_p3_dbl(&t, A); $t = self::ge_p3_dbl($A); # ge_p1p1_to_p3(&A2, &t); $A2 = self::ge_p1p1_to_p3($t); for ($i = 1; $i < 8; ++$i) { # ge_add(&t, &A2, &Ai[0]); $t = self::ge_add($A2, $Ai[$i - 1]); # ge_p1p1_to_p3(&u, &t); $u = self::ge_p1p1_to_p3($t); # ge_p3_to_cached(&Ai[i], &u); $Ai[$i] = self::ge_p3_to_cached($u); } $r = self::ge_p3_0(); for ($i = 252; $i >= 0; --$i) { $t = self::ge_p3_dbl($r); if ($aslide[$i] > 0) { # ge_p1p1_to_p3(&u, &t); $u = self::ge_p1p1_to_p3($t); # ge_add(&t, &u, &Ai[aslide[i] / 2]); $t = self::ge_add($u, $Ai[(int)($aslide[$i] / 2)]); } elseif ($aslide[$i] < 0) { # ge_p1p1_to_p3(&u, &t); $u = self::ge_p1p1_to_p3($t); # ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); $t = self::ge_sub($u, $Ai[(int)(-$aslide[$i] / 2)]); } } # ge_p1p1_to_p3(r, &t); return self::ge_p1p1_to_p3($t); } /** * @param string $a * @param string $b * @return string */ public static function sc25519_mul($a, $b) { // int64_t a0 = 2097151 & load_3(a); // int64_t a1 = 2097151 & (load_4(a + 2) >> 5); // int64_t a2 = 2097151 & (load_3(a + 5) >> 2); // int64_t a3 = 2097151 & (load_4(a + 7) >> 7); // int64_t a4 = 2097151 & (load_4(a + 10) >> 4); // int64_t a5 = 2097151 & (load_3(a + 13) >> 1); // int64_t a6 = 2097151 & (load_4(a + 15) >> 6); // int64_t a7 = 2097151 & (load_3(a + 18) >> 3); // int64_t a8 = 2097151 & load_3(a + 21); // int64_t a9 = 2097151 & (load_4(a + 23) >> 5); // int64_t a10 = 2097151 & (load_3(a + 26) >> 2); // int64_t a11 = (load_4(a + 28) >> 7); $a0 = 2097151 & self::load_3(self::substr($a, 0, 3)); $a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5); $a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2); $a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7); $a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4); $a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1); $a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6); $a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3); $a8 = 2097151 & self::load_3(self::substr($a, 21, 3)); $a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5); $a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2); $a11 = (self::load_4(self::substr($a, 28, 4)) >> 7); // int64_t b0 = 2097151 & load_3(b); // int64_t b1 = 2097151 & (load_4(b + 2) >> 5); // int64_t b2 = 2097151 & (load_3(b + 5) >> 2); // int64_t b3 = 2097151 & (load_4(b + 7) >> 7); // int64_t b4 = 2097151 & (load_4(b + 10) >> 4); // int64_t b5 = 2097151 & (load_3(b + 13) >> 1); // int64_t b6 = 2097151 & (load_4(b + 15) >> 6); // int64_t b7 = 2097151 & (load_3(b + 18) >> 3); // int64_t b8 = 2097151 & load_3(b + 21); // int64_t b9 = 2097151 & (load_4(b + 23) >> 5); // int64_t b10 = 2097151 & (load_3(b + 26) >> 2); // int64_t b11 = (load_4(b + 28) >> 7); $b0 = 2097151 & self::load_3(self::substr($b, 0, 3)); $b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5); $b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2); $b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7); $b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4); $b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1); $b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6); $b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3); $b8 = 2097151 & self::load_3(self::substr($b, 21, 3)); $b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5); $b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2); $b11 = (self::load_4(self::substr($b, 28, 4)) >> 7); // s0 = a0 * b0; // s1 = a0 * b1 + a1 * b0; // s2 = a0 * b2 + a1 * b1 + a2 * b0; // s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; // s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; // s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; // s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; // s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + // a6 * b1 + a7 * b0; // s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + // a6 * b2 + a7 * b1 + a8 * b0; // s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + // a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; // s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + // a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; // s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + // a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; // s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + // a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; // s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + // a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; // s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + // a9 * b5 + a10 * b4 + a11 * b3; // s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + // a10 * b5 + a11 * b4; // s16 = // a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; // s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; // s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; // s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; // s20 = a9 * b11 + a10 * b10 + a11 * b9; // s21 = a10 * b11 + a11 * b10; // s22 = a11 * b11; // s23 = 0; $s0 = self::mul($a0, $b0, 22); $s1 = self::mul($a0, $b1, 22) + self::mul($a1, $b0, 22); $s2 = self::mul($a0, $b2, 22) + self::mul($a1, $b1, 22) + self::mul($a2, $b0, 22); $s3 = self::mul($a0, $b3, 22) + self::mul($a1, $b2, 22) + self::mul($a2, $b1, 22) + self::mul($a3, $b0, 22); $s4 = self::mul($a0, $b4, 22) + self::mul($a1, $b3, 22) + self::mul($a2, $b2, 22) + self::mul($a3, $b1, 22) + self::mul($a4, $b0, 22); $s5 = self::mul($a0, $b5, 22) + self::mul($a1, $b4, 22) + self::mul($a2, $b3, 22) + self::mul($a3, $b2, 22) + self::mul($a4, $b1, 22) + self::mul($a5, $b0, 22); $s6 = self::mul($a0, $b6, 22) + self::mul($a1, $b5, 22) + self::mul($a2, $b4, 22) + self::mul($a3, $b3, 22) + self::mul($a4, $b2, 22) + self::mul($a5, $b1, 22) + self::mul($a6, $b0, 22); $s7 = self::mul($a0, $b7, 22) + self::mul($a1, $b6, 22) + self::mul($a2, $b5, 22) + self::mul($a3, $b4, 22) + self::mul($a4, $b3, 22) + self::mul($a5, $b2, 22) + self::mul($a6, $b1, 22) + self::mul($a7, $b0, 22); $s8 = self::mul($a0, $b8, 22) + self::mul($a1, $b7, 22) + self::mul($a2, $b6, 22) + self::mul($a3, $b5, 22) + self::mul($a4, $b4, 22) + self::mul($a5, $b3, 22) + self::mul($a6, $b2, 22) + self::mul($a7, $b1, 22) + self::mul($a8, $b0, 22); $s9 = self::mul($a0, $b9, 22) + self::mul($a1, $b8, 22) + self::mul($a2, $b7, 22) + self::mul($a3, $b6, 22) + self::mul($a4, $b5, 22) + self::mul($a5, $b4, 22) + self::mul($a6, $b3, 22) + self::mul($a7, $b2, 22) + self::mul($a8, $b1, 22) + self::mul($a9, $b0, 22); $s10 = self::mul($a0, $b10, 22) + self::mul($a1, $b9, 22) + self::mul($a2, $b8, 22) + self::mul($a3, $b7, 22) + self::mul($a4, $b6, 22) + self::mul($a5, $b5, 22) + self::mul($a6, $b4, 22) + self::mul($a7, $b3, 22) + self::mul($a8, $b2, 22) + self::mul($a9, $b1, 22) + self::mul($a10, $b0, 22); $s11 = self::mul($a0, $b11, 22) + self::mul($a1, $b10, 22) + self::mul($a2, $b9, 22) + self::mul($a3, $b8, 22) + self::mul($a4, $b7, 22) + self::mul($a5, $b6, 22) + self::mul($a6, $b5, 22) + self::mul($a7, $b4, 22) + self::mul($a8, $b3, 22) + self::mul($a9, $b2, 22) + self::mul($a10, $b1, 22) + self::mul($a11, $b0, 22); $s12 = self::mul($a1, $b11, 22) + self::mul($a2, $b10, 22) + self::mul($a3, $b9, 22) + self::mul($a4, $b8, 22) + self::mul($a5, $b7, 22) + self::mul($a6, $b6, 22) + self::mul($a7, $b5, 22) + self::mul($a8, $b4, 22) + self::mul($a9, $b3, 22) + self::mul($a10, $b2, 22) + self::mul($a11, $b1, 22); $s13 = self::mul($a2, $b11, 22) + self::mul($a3, $b10, 22) + self::mul($a4, $b9, 22) + self::mul($a5, $b8, 22) + self::mul($a6, $b7, 22) + self::mul($a7, $b6, 22) + self::mul($a8, $b5, 22) + self::mul($a9, $b4, 22) + self::mul($a10, $b3, 22) + self::mul($a11, $b2, 22); $s14 = self::mul($a3, $b11, 22) + self::mul($a4, $b10, 22) + self::mul($a5, $b9, 22) + self::mul($a6, $b8, 22) + self::mul($a7, $b7, 22) + self::mul($a8, $b6, 22) + self::mul($a9, $b5, 22) + self::mul($a10, $b4, 22) + self::mul($a11, $b3, 22); $s15 = self::mul($a4, $b11, 22) + self::mul($a5, $b10, 22) + self::mul($a6, $b9, 22) + self::mul($a7, $b8, 22) + self::mul($a8, $b7, 22) + self::mul($a9, $b6, 22) + self::mul($a10, $b5, 22) + self::mul($a11, $b4, 22); $s16 = self::mul($a5, $b11, 22) + self::mul($a6, $b10, 22) + self::mul($a7, $b9, 22) + self::mul($a8, $b8, 22) + self::mul($a9, $b7, 22) + self::mul($a10, $b6, 22) + self::mul($a11, $b5, 22); $s17 = self::mul($a6, $b11, 22) + self::mul($a7, $b10, 22) + self::mul($a8, $b9, 22) + self::mul($a9, $b8, 22) + self::mul($a10, $b7, 22) + self::mul($a11, $b6, 22); $s18 = self::mul($a7, $b11, 22) + self::mul($a8, $b10, 22) + self::mul($a9, $b9, 22) + self::mul($a10, $b8, 22) + self::mul($a11, $b7, 22); $s19 = self::mul($a8, $b11, 22) + self::mul($a9, $b10, 22) + self::mul($a10, $b9, 22) + self::mul($a11, $b8, 22); $s20 = self::mul($a9, $b11, 22) + self::mul($a10, $b10, 22) + self::mul($a11, $b9, 22); $s21 = self::mul($a10, $b11, 22) + self::mul($a11, $b10, 22); $s22 = self::mul($a11, $b11, 22); $s23 = 0; // carry0 = (s0 + (int64_t) (1L << 20)) >> 21; // s1 += carry0; // s0 -= carry0 * ((uint64_t) 1L << 21); $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; // carry2 = (s2 + (int64_t) (1L << 20)) >> 21; // s3 += carry2; // s2 -= carry2 * ((uint64_t) 1L << 21); $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; // carry4 = (s4 + (int64_t) (1L << 20)) >> 21; // s5 += carry4; // s4 -= carry4 * ((uint64_t) 1L << 21); $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; // s7 += carry6; // s6 -= carry6 * ((uint64_t) 1L << 21); $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; // s9 += carry8; // s8 -= carry8 * ((uint64_t) 1L << 21); $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; // s11 += carry10; // s10 -= carry10 * ((uint64_t) 1L << 21); $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; // carry12 = (s12 + (int64_t) (1L << 20)) >> 21; // s13 += carry12; // s12 -= carry12 * ((uint64_t) 1L << 21); $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; // carry14 = (s14 + (int64_t) (1L << 20)) >> 21; // s15 += carry14; // s14 -= carry14 * ((uint64_t) 1L << 21); $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; // carry16 = (s16 + (int64_t) (1L << 20)) >> 21; // s17 += carry16; // s16 -= carry16 * ((uint64_t) 1L << 21); $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; // carry18 = (s18 + (int64_t) (1L << 20)) >> 21; // s19 += carry18; // s18 -= carry18 * ((uint64_t) 1L << 21); $carry18 = ($s18 + (1 << 20)) >> 21; $s19 += $carry18; $s18 -= $carry18 << 21; // carry20 = (s20 + (int64_t) (1L << 20)) >> 21; // s21 += carry20; // s20 -= carry20 * ((uint64_t) 1L << 21); $carry20 = ($s20 + (1 << 20)) >> 21; $s21 += $carry20; $s20 -= $carry20 << 21; // carry22 = (s22 + (int64_t) (1L << 20)) >> 21; // s23 += carry22; // s22 -= carry22 * ((uint64_t) 1L << 21); $carry22 = ($s22 + (1 << 20)) >> 21; $s23 += $carry22; $s22 -= $carry22 << 21; // carry1 = (s1 + (int64_t) (1L << 20)) >> 21; // s2 += carry1; // s1 -= carry1 * ((uint64_t) 1L << 21); $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; // carry3 = (s3 + (int64_t) (1L << 20)) >> 21; // s4 += carry3; // s3 -= carry3 * ((uint64_t) 1L << 21); $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; // carry5 = (s5 + (int64_t) (1L << 20)) >> 21; // s6 += carry5; // s5 -= carry5 * ((uint64_t) 1L << 21); $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; // s8 += carry7; // s7 -= carry7 * ((uint64_t) 1L << 21); $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; // s10 += carry9; // s9 -= carry9 * ((uint64_t) 1L << 21); $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; // s12 += carry11; // s11 -= carry11 * ((uint64_t) 1L << 21); $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; // carry13 = (s13 + (int64_t) (1L << 20)) >> 21; // s14 += carry13; // s13 -= carry13 * ((uint64_t) 1L << 21); $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; // carry15 = (s15 + (int64_t) (1L << 20)) >> 21; // s16 += carry15; // s15 -= carry15 * ((uint64_t) 1L << 21); $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; // carry17 = (s17 + (int64_t) (1L << 20)) >> 21; // s18 += carry17; // s17 -= carry17 * ((uint64_t) 1L << 21); $carry17 = ($s17 + (1 << 20)) >> 21; $s18 += $carry17; $s17 -= $carry17 << 21; // carry19 = (s19 + (int64_t) (1L << 20)) >> 21; // s20 += carry19; // s19 -= carry19 * ((uint64_t) 1L << 21); $carry19 = ($s19 + (1 << 20)) >> 21; $s20 += $carry19; $s19 -= $carry19 << 21; // carry21 = (s21 + (int64_t) (1L << 20)) >> 21; // s22 += carry21; // s21 -= carry21 * ((uint64_t) 1L << 21); $carry21 = ($s21 + (1 << 20)) >> 21; $s22 += $carry21; $s21 -= $carry21 << 21; // s11 += s23 * 666643; // s12 += s23 * 470296; // s13 += s23 * 654183; // s14 -= s23 * 997805; // s15 += s23 * 136657; // s16 -= s23 * 683901; $s11 += self::mul($s23, 666643, 20); $s12 += self::mul($s23, 470296, 19); $s13 += self::mul($s23, 654183, 20); $s14 -= self::mul($s23, 997805, 20); $s15 += self::mul($s23, 136657, 18); $s16 -= self::mul($s23, 683901, 20); // s10 += s22 * 666643; // s11 += s22 * 470296; // s12 += s22 * 654183; // s13 -= s22 * 997805; // s14 += s22 * 136657; // s15 -= s22 * 683901; $s10 += self::mul($s22, 666643, 20); $s11 += self::mul($s22, 470296, 19); $s12 += self::mul($s22, 654183, 20); $s13 -= self::mul($s22, 997805, 20); $s14 += self::mul($s22, 136657, 18); $s15 -= self::mul($s22, 683901, 20); // s9 += s21 * 666643; // s10 += s21 * 470296; // s11 += s21 * 654183; // s12 -= s21 * 997805; // s13 += s21 * 136657; // s14 -= s21 * 683901; $s9 += self::mul($s21, 666643, 20); $s10 += self::mul($s21, 470296, 19); $s11 += self::mul($s21, 654183, 20); $s12 -= self::mul($s21, 997805, 20); $s13 += self::mul($s21, 136657, 18); $s14 -= self::mul($s21, 683901, 20); // s8 += s20 * 666643; // s9 += s20 * 470296; // s10 += s20 * 654183; // s11 -= s20 * 997805; // s12 += s20 * 136657; // s13 -= s20 * 683901; $s8 += self::mul($s20, 666643, 20); $s9 += self::mul($s20, 470296, 19); $s10 += self::mul($s20, 654183, 20); $s11 -= self::mul($s20, 997805, 20); $s12 += self::mul($s20, 136657, 18); $s13 -= self::mul($s20, 683901, 20); // s7 += s19 * 666643; // s8 += s19 * 470296; // s9 += s19 * 654183; // s10 -= s19 * 997805; // s11 += s19 * 136657; // s12 -= s19 * 683901; $s7 += self::mul($s19, 666643, 20); $s8 += self::mul($s19, 470296, 19); $s9 += self::mul($s19, 654183, 20); $s10 -= self::mul($s19, 997805, 20); $s11 += self::mul($s19, 136657, 18); $s12 -= self::mul($s19, 683901, 20); // s6 += s18 * 666643; // s7 += s18 * 470296; // s8 += s18 * 654183; // s9 -= s18 * 997805; // s10 += s18 * 136657; // s11 -= s18 * 683901; $s6 += self::mul($s18, 666643, 20); $s7 += self::mul($s18, 470296, 19); $s8 += self::mul($s18, 654183, 20); $s9 -= self::mul($s18, 997805, 20); $s10 += self::mul($s18, 136657, 18); $s11 -= self::mul($s18, 683901, 20); // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; // s7 += carry6; // s6 -= carry6 * ((uint64_t) 1L << 21); $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; // s9 += carry8; // s8 -= carry8 * ((uint64_t) 1L << 21); $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; // s11 += carry10; // s10 -= carry10 * ((uint64_t) 1L << 21); $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; // carry12 = (s12 + (int64_t) (1L << 20)) >> 21; // s13 += carry12; // s12 -= carry12 * ((uint64_t) 1L << 21); $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; // carry14 = (s14 + (int64_t) (1L << 20)) >> 21; // s15 += carry14; // s14 -= carry14 * ((uint64_t) 1L << 21); $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; // carry16 = (s16 + (int64_t) (1L << 20)) >> 21; // s17 += carry16; // s16 -= carry16 * ((uint64_t) 1L << 21); $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; // s8 += carry7; // s7 -= carry7 * ((uint64_t) 1L << 21); $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; // s10 += carry9; // s9 -= carry9 * ((uint64_t) 1L << 21); $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; // s12 += carry11; // s11 -= carry11 * ((uint64_t) 1L << 21); $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; // carry13 = (s13 + (int64_t) (1L << 20)) >> 21; // s14 += carry13; // s13 -= carry13 * ((uint64_t) 1L << 21); $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; // carry15 = (s15 + (int64_t) (1L << 20)) >> 21; // s16 += carry15; // s15 -= carry15 * ((uint64_t) 1L << 21); $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; // s5 += s17 * 666643; // s6 += s17 * 470296; // s7 += s17 * 654183; // s8 -= s17 * 997805; // s9 += s17 * 136657; // s10 -= s17 * 683901; $s5 += self::mul($s17, 666643, 20); $s6 += self::mul($s17, 470296, 19); $s7 += self::mul($s17, 654183, 20); $s8 -= self::mul($s17, 997805, 20); $s9 += self::mul($s17, 136657, 18); $s10 -= self::mul($s17, 683901, 20); // s4 += s16 * 666643; // s5 += s16 * 470296; // s6 += s16 * 654183; // s7 -= s16 * 997805; // s8 += s16 * 136657; // s9 -= s16 * 683901; $s4 += self::mul($s16, 666643, 20); $s5 += self::mul($s16, 470296, 19); $s6 += self::mul($s16, 654183, 20); $s7 -= self::mul($s16, 997805, 20); $s8 += self::mul($s16, 136657, 18); $s9 -= self::mul($s16, 683901, 20); // s3 += s15 * 666643; // s4 += s15 * 470296; // s5 += s15 * 654183; // s6 -= s15 * 997805; // s7 += s15 * 136657; // s8 -= s15 * 683901; $s3 += self::mul($s15, 666643, 20); $s4 += self::mul($s15, 470296, 19); $s5 += self::mul($s15, 654183, 20); $s6 -= self::mul($s15, 997805, 20); $s7 += self::mul($s15, 136657, 18); $s8 -= self::mul($s15, 683901, 20); // s2 += s14 * 666643; // s3 += s14 * 470296; // s4 += s14 * 654183; // s5 -= s14 * 997805; // s6 += s14 * 136657; // s7 -= s14 * 683901; $s2 += self::mul($s14, 666643, 20); $s3 += self::mul($s14, 470296, 19); $s4 += self::mul($s14, 654183, 20); $s5 -= self::mul($s14, 997805, 20); $s6 += self::mul($s14, 136657, 18); $s7 -= self::mul($s14, 683901, 20); // s1 += s13 * 666643; // s2 += s13 * 470296; // s3 += s13 * 654183; // s4 -= s13 * 997805; // s5 += s13 * 136657; // s6 -= s13 * 683901; $s1 += self::mul($s13, 666643, 20); $s2 += self::mul($s13, 470296, 19); $s3 += self::mul($s13, 654183, 20); $s4 -= self::mul($s13, 997805, 20); $s5 += self::mul($s13, 136657, 18); $s6 -= self::mul($s13, 683901, 20); // s0 += s12 * 666643; // s1 += s12 * 470296; // s2 += s12 * 654183; // s3 -= s12 * 997805; // s4 += s12 * 136657; // s5 -= s12 * 683901; // s12 = 0; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; // carry0 = (s0 + (int64_t) (1L << 20)) >> 21; // s1 += carry0; // s0 -= carry0 * ((uint64_t) 1L << 21); $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; // carry2 = (s2 + (int64_t) (1L << 20)) >> 21; // s3 += carry2; // s2 -= carry2 * ((uint64_t) 1L << 21); $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; // carry4 = (s4 + (int64_t) (1L << 20)) >> 21; // s5 += carry4; // s4 -= carry4 * ((uint64_t) 1L << 21); $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; // s7 += carry6; // s6 -= carry6 * ((uint64_t) 1L << 21); $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; // s9 += carry8; // s8 -= carry8 * ((uint64_t) 1L << 21); $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; // s11 += carry10; // s10 -= carry10 * ((uint64_t) 1L << 21); $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; // carry1 = (s1 + (int64_t) (1L << 20)) >> 21; // s2 += carry1; // s1 -= carry1 * ((uint64_t) 1L << 21); $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; // carry3 = (s3 + (int64_t) (1L << 20)) >> 21; // s4 += carry3; // s3 -= carry3 * ((uint64_t) 1L << 21); $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; // carry5 = (s5 + (int64_t) (1L << 20)) >> 21; // s6 += carry5; // s5 -= carry5 * ((uint64_t) 1L << 21); $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; // s8 += carry7; // s7 -= carry7 * ((uint64_t) 1L << 21); $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; // s10 += carry9; // s9 -= carry9 * ((uint64_t) 1L << 21); $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; // s12 += carry11; // s11 -= carry11 * ((uint64_t) 1L << 21); $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; // s0 += s12 * 666643; // s1 += s12 * 470296; // s2 += s12 * 654183; // s3 -= s12 * 997805; // s4 += s12 * 136657; // s5 -= s12 * 683901; // s12 = 0; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); $s12 = 0; // carry0 = s0 >> 21; // s1 += carry0; // s0 -= carry0 * ((uint64_t) 1L << 21); $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; // carry1 = s1 >> 21; // s2 += carry1; // s1 -= carry1 * ((uint64_t) 1L << 21); $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; // carry2 = s2 >> 21; // s3 += carry2; // s2 -= carry2 * ((uint64_t) 1L << 21); $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; // carry3 = s3 >> 21; // s4 += carry3; // s3 -= carry3 * ((uint64_t) 1L << 21); $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; // carry4 = s4 >> 21; // s5 += carry4; // s4 -= carry4 * ((uint64_t) 1L << 21); $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; // carry5 = s5 >> 21; // s6 += carry5; // s5 -= carry5 * ((uint64_t) 1L << 21); $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; // carry6 = s6 >> 21; // s7 += carry6; // s6 -= carry6 * ((uint64_t) 1L << 21); $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; // carry7 = s7 >> 21; // s8 += carry7; // s7 -= carry7 * ((uint64_t) 1L << 21); $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; // carry8 = s8 >> 21; // s9 += carry8; // s8 -= carry8 * ((uint64_t) 1L << 21); $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; // carry9 = s9 >> 21; // s10 += carry9; // s9 -= carry9 * ((uint64_t) 1L << 21); $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; // carry10 = s10 >> 21; // s11 += carry10; // s10 -= carry10 * ((uint64_t) 1L << 21); $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; // carry11 = s11 >> 21; // s12 += carry11; // s11 -= carry11 * ((uint64_t) 1L << 21); $carry11 = $s11 >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; // s0 += s12 * 666643; // s1 += s12 * 470296; // s2 += s12 * 654183; // s3 -= s12 * 997805; // s4 += s12 * 136657; // s5 -= s12 * 683901; $s0 += self::mul($s12, 666643, 20); $s1 += self::mul($s12, 470296, 19); $s2 += self::mul($s12, 654183, 20); $s3 -= self::mul($s12, 997805, 20); $s4 += self::mul($s12, 136657, 18); $s5 -= self::mul($s12, 683901, 20); // carry0 = s0 >> 21; // s1 += carry0; // s0 -= carry0 * ((uint64_t) 1L << 21); $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; // carry1 = s1 >> 21; // s2 += carry1; // s1 -= carry1 * ((uint64_t) 1L << 21); $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; // carry2 = s2 >> 21; // s3 += carry2; // s2 -= carry2 * ((uint64_t) 1L << 21); $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; // carry3 = s3 >> 21; // s4 += carry3; // s3 -= carry3 * ((uint64_t) 1L << 21); $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; // carry4 = s4 >> 21; // s5 += carry4; // s4 -= carry4 * ((uint64_t) 1L << 21); $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; // carry5 = s5 >> 21; // s6 += carry5; // s5 -= carry5 * ((uint64_t) 1L << 21); $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; // carry6 = s6 >> 21; // s7 += carry6; // s6 -= carry6 * ((uint64_t) 1L << 21); $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; // carry7 = s7 >> 21; // s8 += carry7; // s7 -= carry7 * ((uint64_t) 1L << 21); $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; // carry8 = s8 >> 21; // s9 += carry8; // s8 -= carry8 * ((uint64_t) 1L << 21); $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; // carry9 = s9 >> 21; // s10 += carry9; // s9 -= carry9 * ((uint64_t) 1L << 21); $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; // carry10 = s10 >> 21; // s11 += carry10; // s10 -= carry10 * ((uint64_t) 1L << 21); $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; $s = array_fill(0, 32, 0); // s[0] = s0 >> 0; $s[0] = $s0 >> 0; // s[1] = s0 >> 8; $s[1] = $s0 >> 8; // s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); $s[2] = ($s0 >> 16) | ($s1 << 5); // s[3] = s1 >> 3; $s[3] = $s1 >> 3; // s[4] = s1 >> 11; $s[4] = $s1 >> 11; // s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); $s[5] = ($s1 >> 19) | ($s2 << 2); // s[6] = s2 >> 6; $s[6] = $s2 >> 6; // s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); $s[7] = ($s2 >> 14) | ($s3 << 7); // s[8] = s3 >> 1; $s[8] = $s3 >> 1; // s[9] = s3 >> 9; $s[9] = $s3 >> 9; // s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); $s[10] = ($s3 >> 17) | ($s4 << 4); // s[11] = s4 >> 4; $s[11] = $s4 >> 4; // s[12] = s4 >> 12; $s[12] = $s4 >> 12; // s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); $s[13] = ($s4 >> 20) | ($s5 << 1); // s[14] = s5 >> 7; $s[14] = $s5 >> 7; // s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); $s[15] = ($s5 >> 15) | ($s6 << 6); // s[16] = s6 >> 2; $s[16] = $s6 >> 2; // s[17] = s6 >> 10; $s[17] = $s6 >> 10; // s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); $s[18] = ($s6 >> 18) | ($s7 << 3); // s[19] = s7 >> 5; $s[19] = $s7 >> 5; // s[20] = s7 >> 13; $s[20] = $s7 >> 13; // s[21] = s8 >> 0; $s[21] = $s8 >> 0; // s[22] = s8 >> 8; $s[22] = $s8 >> 8; // s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); $s[23] = ($s8 >> 16) | ($s9 << 5); // s[24] = s9 >> 3; $s[24] = $s9 >> 3; // s[25] = s9 >> 11; $s[25] = $s9 >> 11; // s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); $s[26] = ($s9 >> 19) | ($s10 << 2); // s[27] = s10 >> 6; $s[27] = $s10 >> 6; // s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); $s[28] = ($s10 >> 14) | ($s11 << 7); // s[29] = s11 >> 1; $s[29] = $s11 >> 1; // s[30] = s11 >> 9; $s[30] = $s11 >> 9; // s[31] = s11 >> 17; $s[31] = $s11 >> 17; return self::intArrayToString($s); } /** * @param string $s * @return string */ public static function sc25519_sq($s) { return self::sc25519_mul($s, $s); } /** * @param string $s * @param int $n * @param string $a * @return string */ public static function sc25519_sqmul($s, $n, $a) { for ($i = 0; $i < $n; ++$i) { $s = self::sc25519_sq($s); } return self::sc25519_mul($s, $a); } /** * @param string $s * @return string */ public static function sc25519_invert($s) { $_10 = self::sc25519_sq($s); $_11 = self::sc25519_mul($s, $_10); $_100 = self::sc25519_mul($s, $_11); $_1000 = self::sc25519_sq($_100); $_1010 = self::sc25519_mul($_10, $_1000); $_1011 = self::sc25519_mul($s, $_1010); $_10000 = self::sc25519_sq($_1000); $_10110 = self::sc25519_sq($_1011); $_100000 = self::sc25519_mul($_1010, $_10110); $_100110 = self::sc25519_mul($_10000, $_10110); $_1000000 = self::sc25519_sq($_100000); $_1010000 = self::sc25519_mul($_10000, $_1000000); $_1010011 = self::sc25519_mul($_11, $_1010000); $_1100011 = self::sc25519_mul($_10000, $_1010011); $_1100111 = self::sc25519_mul($_100, $_1100011); $_1101011 = self::sc25519_mul($_100, $_1100111); $_10010011 = self::sc25519_mul($_1000000, $_1010011); $_10010111 = self::sc25519_mul($_100, $_10010011); $_10111101 = self::sc25519_mul($_100110, $_10010111); $_11010011 = self::sc25519_mul($_10110, $_10111101); $_11100111 = self::sc25519_mul($_1010000, $_10010111); $_11101011 = self::sc25519_mul($_100, $_11100111); $_11110101 = self::sc25519_mul($_1010, $_11101011); $recip = self::sc25519_mul($_1011, $_11110101); $recip = self::sc25519_sqmul($recip, 126, $_1010011); $recip = self::sc25519_sqmul($recip, 9, $_10); $recip = self::sc25519_mul($recip, $_11110101); $recip = self::sc25519_sqmul($recip, 7, $_1100111); $recip = self::sc25519_sqmul($recip, 9, $_11110101); $recip = self::sc25519_sqmul($recip, 11, $_10111101); $recip = self::sc25519_sqmul($recip, 8, $_11100111); $recip = self::sc25519_sqmul($recip, 9, $_1101011); $recip = self::sc25519_sqmul($recip, 6, $_1011); $recip = self::sc25519_sqmul($recip, 14, $_10010011); $recip = self::sc25519_sqmul($recip, 10, $_1100011); $recip = self::sc25519_sqmul($recip, 9, $_10010111); $recip = self::sc25519_sqmul($recip, 10, $_11110101); $recip = self::sc25519_sqmul($recip, 8, $_11010011); return self::sc25519_sqmul($recip, 8, $_11101011); } /** * @param string $s * @return string */ public static function clamp($s) { $s_ = self::stringToIntArray($s); $s_[0] &= 248; $s_[31] |= 64; $s_[31] &= 128; return self::intArrayToString($s_); } /** * Ensure limbs are less than 28 bits long to prevent float promotion. * * This uses a constant-time conditional swap under the hood. * * @param ParagonIE_Sodium_Core_Curve25519_Fe $f * @return ParagonIE_Sodium_Core_Curve25519_Fe */ public static function fe_normalize(ParagonIE_Sodium_Core_Curve25519_Fe $f) { $x = (PHP_INT_SIZE << 3) - 1; // 31 or 63 $g = self::fe_copy($f); for ($i = 0; $i < 10; ++$i) { $mask = -(($g[$i] >> $x) & 1); /* * Get two candidate normalized values for $g[$i], depending on the sign of $g[$i]: */ $a = $g[$i] & 0x7ffffff; $b = -((-$g[$i]) & 0x7ffffff); /* * Return the appropriate candidate value, based on the sign of the original input: * * The following is equivalent to this ternary: * * $g[$i] = (($g[$i] >> $x) & 1) ? $a : $b; * * Except what's written doesn't contain timing leaks. */ $g[$i] = ($a ^ (($a ^ $b) & $mask)); } return $g; } }

Es la eliminación del sarro y la placa adherida a la superficie de los dientes mediante un equipo de ultrasonidos que garantiza la integridad de las piezas dentales a la vez que elimina en profundidad cualquier resto de suciedad.

A continuación se procede al pulido de los dientes mediante una fresa especial que elimina la placa bacteriana y devuelve a los dientes el aspecto sano que deben tener.

Una vez terminado todo el proceso, se mantiene al perro en observación hasta que se despierta de la anestesia, bajo la atenta supervisión de un veterinario.

¿Cada cuánto tiempo tengo que hacerle una limpieza dental a mi perro?

A partir de cierta edad, los perros pueden necesitar una limpieza dental anual o bianual. Depende de cada caso. En líneas generales, puede decirse que los perros de razas pequeñas suelen acumular más sarro y suelen necesitar una atención mayor en cuanto a higiene dental.

Riesgos de una mala higiene

Los riesgos más evidentes de una mala higiene dental en los perros son los siguientes:

Cuando la acumulación de sarro no se trata, se puede producir una inflamación y retracción de las encías que puede descalzar el diente y provocar caídas.
Mal aliento (halitosis).
Sarro perros
Puede ir a más
Las bacterias de la placa pueden trasladarse a través del torrente circulatorio a órganos vitales como el corazón ocasionando problemas de endocarditis en las válvulas. Las bacterias pueden incluso acantonarse en huesos (La osteomielitis es la infección ósea, tanto cortical como medular) provocando mucho dolor y una artritis séptica).

¿Cómo se forma el sarro?

El sarro es la calcificación de la placa dental. Los restos de alimentos, junto con las bacterias presentes en la boca, van a formar la placa bacteriana o placa dental. Si la placa no se retira, al mezclarse con la saliva y los minerales presentes en ella, reaccionará formando una costra. La placa se calcifica y se forma el sarro.

El sarro, cuando se forma, es de color blanquecino pero a medida que pasa el tiempo se va poniendo amarillo y luego marrón.

Síntomas de una pobre higiene dental
La señal más obvia de una mala salud dental canina es el mal aliento.

Sin embargo, a veces no es tan fácil de detectar
Y hay perros que no se dejan abrir la boca por su dueño. Por ejemplo…

Recientemente nos trajeron a la clínica a un perro que parpadeaba de un ojo y decía su dueño que le picaba un lado de la cara. Tenía molestias y dificultad para comer, lo que había llevado a sus dueños a comprarle comida blanda (que suele ser un poco más cara y llevar más contenido en grasa) durante medio año. Después de una exploración oftalmológica, nos dimos cuenta de que el ojo tenía una úlcera en la córnea probablemente de rascarse . Además, el canto lateral del ojo estaba inflamado. Tenía lo que en humanos llamamos flemón pero como era un perro de pelo largo, no se le notaba a simple vista. Al abrirle la boca nos llamó la atención el ver una muela llena de sarro. Le realizamos una radiografía y encontramos una fístula que llegaba hasta la parte inferior del ojo.

Le tuvimos que extraer la muela. Tras esto, el ojo se curó completamente con unos colirios y una lentilla protectora de úlcera. Afortunadamente, la úlcera no profundizó y no perforó el ojo. Ahora el perro come perfectamente a pesar de haber perdido una muela.

¿Cómo mantener la higiene dental de tu perro?
Hay varias maneras de prevenir problemas derivados de la salud dental de tu perro.

Limpiezas de dientes en casa
Es recomendable limpiar los dientes de tu perro semanal o diariamente si se puede. Existe una gran variedad de productos que se pueden utilizar:

Pastas de dientes.
Cepillos de dientes o dedales para el dedo índice, que hacen más fácil la limpieza.
Colutorios para echar en agua de bebida o directamente sobre el diente en líquido o en spray.

En la Clínica Tus Veterinarios enseñamos a nuestros clientes a tomar el hábito de limpiar los dientes de sus perros desde que son cachorros. Esto responde a nuestro compromiso con la prevención de enfermedades caninas.

Hoy en día tenemos muchos clientes que limpian los dientes todos los días a su mascota, y como resultado, se ahorran el dinero de hacer limpiezas dentales profesionales y consiguen una mejor salud de su perro.

Limpiezas dentales profesionales de perros y gatos

Recomendamos hacer una limpieza dental especializada anualmente. La realizamos con un aparato de ultrasonidos que utiliza agua para quitar el sarro. Después, procedemos a pulir los dientes con un cepillo de alta velocidad y una pasta especial. Hacemos esto para proteger el esmalte.

La frecuencia de limpiezas dentales necesaria varía mucho entre razas. En general, las razas grandes tienen buena calidad de esmalte, por lo que no necesitan hacerlo tan a menudo e incluso pueden pasarse la vida sin requerir una limpieza. Sin embargo, razas pequeñas como el Yorkshire o el Maltés, deben hacérselas todos los años desde cachorros si se quiere conservar sus piezas dentales.

Otro factor fundamental es la calidad del pienso. Algunas marcas han diseñado croquetas que limpian la superficie del diente y de la muela al masticarse.

Ultrasonido para perros

¿Se necesita anestesia para las limpiezas dentales de perros y gatos?

La limpieza dental en perros no es una técnica que pueda practicarse sin anestesia general , aunque hay veces que los propietarios no quieren anestesiar y si tiene poco sarro y el perro es muy bueno se puede intentar…… , pero no se va a poder pulir ni acceder a todas la zona de la boca …. Además los limpiadores dentales van a irrigar agua y hay riesgo de aspiración a vías respiratorias si no se realiza una anestesia correcta con intubación traqueal . En resumen , sin anestesia no se va hacer una correcta limpieza dental.

Tampoco sirve la sedación ya que necesitamos que el animal esté totalmente quieto, y el veterinario tenga un acceso completo a todas sus piezas dentales y encías.

Alimentos para la limpieza dental

Hay que tener cierto cuidado a la hora de comprar determinados alimentos porque no todos son saludables. Algunos tienen demasiado contenido graso, que en exceso puede causar problemas cardiovasculares y obesidad.

Los mejores alimentos para los dientes son aquellos que están elaborados por empresas farmacéuticas y llevan componentes químicos con tratamientos específicos para el diente del perro. Esto implica no solo limpieza a través de la acción mecánica de morder sino también un tratamiento antibacteriano para prevenir el sarro.

Conclusión

Si eres como la mayoría de dueños, por falta de tiempo , es probable que no estés prestando la suficiente atención a la limpieza dental de tu perro. Por eso te animamos a que comiences a limpiar los dientes de tu perro y consideres atender a su higiene bucal con frecuencia.

Estas simples medidas pueden conllevar a que tu perro tenga una vida más larga y mucho más saludable.

Si te resulta imposible introducir un cepillo de dientes a tu perro en la boca, pásate con él por clínica Tus Veterinarios y te explicamos cómo hacerlo.

Necesitas hacer una limpieza dental profesional a tu mascota?
Llámanos al 622575274 o contacta con nosotros

¿Cada cuánto tiempo tengo que hacerle una limpieza dental a mi perro?

Riesgos de una mala higiene

¿Cómo se forma el sarro?

Limpiezas dentales profesionales de perros y gatos

Ultrasonido para perros

Alimentos para la limpieza dental

Conclusión

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