芝麻web文件管理V1.00

编辑当前文件:/home2/sdektunc/.trash/libraries.5/vendor/paragonie/sodium_compat/src/Core/Curve25519.php
<?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) { /** @var int $x */ $x = (($f[$i] ^ $g[$i]) & $b); $h[$i] = (int) ((int) ($f[$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.'); } /** @var int $h0 */ $h0 = self::load_4($s); /** @var int $h1 */ $h1 = self::load_3(self::substr($s, 4, 3)) << 6; /** @var int $h2 */ $h2 = self::load_3(self::substr($s, 7, 3)) << 5; /** @var int $h3 */ $h3 = self::load_3(self::substr($s, 10, 3)) << 3; /** @var int $h4 */ $h4 = self::load_3(self::substr($s, 13, 3)) << 2; /** @var int $h5 */ $h5 = self::load_4(self::substr($s, 16, 4)); /** @var int $h6 */ $h6 = self::load_3(self::substr($s, 20, 3)) << 7; /** @var int $h7 */ $h7 = self::load_3(self::substr($s, 23, 3)) << 5; /** @var int $h8 */ $h8 = self::load_3(self::substr($s, 26, 3)) << 4; /** @var int $h9 */ $h9 = (self::load_3(self::substr($s, 29, 3)) & 8388607) << 2; /** @var int $carry9 */ $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; /** @var int $carry1 */ $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; /** @var int $carry3 */ $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; /** @var int $carry5 */ $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; /** @var int $carry7 */ $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; /** @var int $carry2 */ $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry6 */ $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; /** @var int $carry8 */ $carry8 = ($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) { /** @var int $h0 */ $h0 = (int) $h[0]; /** @var int $h1 */ $h1 = (int) $h[1]; /** @var int $h2 */ $h2 = (int) $h[2]; /** @var int $h3 */ $h3 = (int) $h[3]; /** @var int $h4 */ $h4 = (int) $h[4]; /** @var int $h5 */ $h5 = (int) $h[5]; /** @var int $h6 */ $h6 = (int) $h[6]; /** @var int $h7 */ $h7 = (int) $h[7]; /** @var int $h8 */ $h8 = (int) $h[8]; /** @var int $h9 */ $h9 = (int) $h[9]; /** @var int $q */ $q = (self::mul($h9, 19, 5) + (1 << 24)) >> 25; /** @var int $q */ $q = ($h0 + $q) >> 26; /** @var int $q */ $q = ($h1 + $q) >> 25; /** @var int $q */ $q = ($h2 + $q) >> 26; /** @var int $q */ $q = ($h3 + $q) >> 25; /** @var int $q */ $q = ($h4 + $q) >> 26; /** @var int $q */ $q = ($h5 + $q) >> 25; /** @var int $q */ $q = ($h6 + $q) >> 26; /** @var int $q */ $q = ($h7 + $q) >> 25; /** @var int $q */ $q = ($h8 + $q) >> 26; /** @var int $q */ $q = ($h9 + $q) >> 25; $h0 += self::mul($q, 19, 5); /** @var int $carry0 */ $carry0 = $h0 >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; /** @var int $carry1 */ $carry1 = $h1 >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; /** @var int $carry2 */ $carry2 = $h2 >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; /** @var int $carry3 */ $carry3 = $h3 >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; /** @var int $carry4 */ $carry4 = $h4 >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry5 */ $carry5 = $h5 >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; /** @var int $carry6 */ $carry6 = $h6 >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; /** @var int $carry7 */ $carry7 = $h7 >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; /** @var int $carry8 */ $carry8 = $h8 >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; /** @var int $carry9 */ $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 ) { /** @var int $f0 */ $f0 = $f[0]; /** @var int $f1 */ $f1 = $f[1]; /** @var int $f2 */ $f2 = $f[2]; /** @var int $f3 */ $f3 = $f[3]; /** @var int $f4 */ $f4 = $f[4]; /** @var int $f5 */ $f5 = $f[5]; /** @var int $f6 */ $f6 = $f[6]; /** @var int $f7 */ $f7 = $f[7]; /** @var int $f8 */ $f8 = $f[8]; /** @var int $f9 */ $f9 = $f[9]; /** @var int $g0 */ $g0 = $g[0]; /** @var int $g1 */ $g1 = $g[1]; /** @var int $g2 */ $g2 = $g[2]; /** @var int $g3 */ $g3 = $g[3]; /** @var int $g4 */ $g4 = $g[4]; /** @var int $g5 */ $g5 = $g[5]; /** @var int $g6 */ $g6 = $g[6]; /** @var int $g7 */ $g7 = $g[7]; /** @var int $g8 */ $g8 = $g[8]; /** @var int $g9 */ $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); /** @var int $f1_2 */ $f1_2 = $f1 << 1; /** @var int $f3_2 */ $f3_2 = $f3 << 1; /** @var int $f5_2 */ $f5_2 = $f5 << 1; /** @var int $f7_2 */ $f7_2 = $f7 << 1; /** @var int $f9_2 */ $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 ; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry1 */ $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; /** @var int $carry5 */ $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; /** @var int $carry2 */ $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; /** @var int $carry6 */ $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; /** @var int $carry3 */ $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; /** @var int $carry7 */ $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry8 */ $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; /** @var int $carry9 */ $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 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 ) ); } /** * 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 $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) { $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]; /** @var int $f0_2 */ $f0_2 = $f0 << 1; /** @var int $f1_2 */ $f1_2 = $f1 << 1; /** @var int $f2_2 */ $f2_2 = $f2 << 1; /** @var int $f3_2 */ $f3_2 = $f3 << 1; /** @var int $f4_2 */ $f4_2 = $f4 << 1; /** @var int $f5_2 */ $f5_2 = $f5 << 1; /** @var int $f6_2 */ $f6_2 = $f6 << 1; /** @var int $f7_2 */ $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, 25); $f0f1_2 = self::mul($f0_2, $f1, 24); $f0f2_2 = self::mul($f0_2, $f2, 25); $f0f3_2 = self::mul($f0_2, $f3, 24); $f0f4_2 = self::mul($f0_2, $f4, 25); $f0f5_2 = self::mul($f0_2, $f5, 25); $f0f6_2 = self::mul($f0_2, $f6, 25); $f0f7_2 = self::mul($f0_2, $f7, 24); $f0f8_2 = self::mul($f0_2, $f8, 25); $f0f9_2 = self::mul($f0_2, $f9, 25); $f1f1_2 = self::mul($f1_2, $f1, 24); $f1f2_2 = self::mul($f1_2, $f2, 25); $f1f3_4 = self::mul($f1_2, $f3_2, 25); $f1f4_2 = self::mul($f1_2, $f4, 25); $f1f5_4 = self::mul($f1_2, $f5_2, 26); $f1f6_2 = self::mul($f1_2, $f6, 25); $f1f7_4 = self::mul($f1_2, $f7_2, 25); $f1f8_2 = self::mul($f1_2, $f8, 25); $f1f9_76 = self::mul($f9_38, $f1_2, 25); $f2f2 = self::mul($f2, $f2, 25); $f2f3_2 = self::mul($f2_2, $f3, 24); $f2f4_2 = self::mul($f2_2, $f4, 25); $f2f5_2 = self::mul($f2_2, $f5, 25); $f2f6_2 = self::mul($f2_2, $f6, 25); $f2f7_2 = self::mul($f2_2, $f7, 24); $f2f8_38 = self::mul($f8_19, $f2_2, 26); $f2f9_38 = self::mul($f9_38, $f2, 25); $f3f3_2 = self::mul($f3_2, $f3, 24); $f3f4_2 = self::mul($f3_2, $f4, 25); $f3f5_4 = self::mul($f3_2, $f5_2, 26); $f3f6_2 = self::mul($f3_2, $f6, 25); $f3f7_76 = self::mul($f7_38, $f3_2, 25); $f3f8_38 = self::mul($f8_19, $f3_2, 25); $f3f9_76 = self::mul($f9_38, $f3_2, 25); $f4f4 = self::mul($f4, $f4, 25); $f4f5_2 = self::mul($f4_2, $f5, 25); $f4f6_38 = self::mul($f6_19, $f4_2, 26); $f4f7_38 = self::mul($f7_38, $f4, 25); $f4f8_38 = self::mul($f8_19, $f4_2, 26); $f4f9_38 = self::mul($f9_38, $f4, 25); $f5f5_38 = self::mul($f5_38, $f5, 25); $f5f6_38 = self::mul($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, 25); $f6f7_38 = self::mul($f7_38, $f6, 25); $f6f8_38 = self::mul($f8_19, $f6_2, 26); $f6f9_38 = self::mul($f9_38, $f6, 25); $f7f7_38 = self::mul($f7_38, $f7, 24); $f7f8_38 = self::mul($f8_19, $f7_2, 25); $f7f9_76 = self::mul($f9_38, $f7_2, 25); $f8f8_19 = self::mul($f8_19, $f8, 25); $f8f9_38 = self::mul($f9_38, $f8, 25); $f9f9_38 = self::mul($f9_38, $f9, 25); $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; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry1 */ $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; /** @var int $carry5 */ $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; /** @var int $carry2 */ $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; /** @var int $carry6 */ $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; /** @var int $carry3 */ $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; /** @var int $carry7 */ $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry8 */ $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; /** @var int $carry9 */ $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 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 ) ); } /** * 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) { $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]; /** @var int $f0_2 */ $f0_2 = $f0 << 1; /** @var int $f1_2 */ $f1_2 = $f1 << 1; /** @var int $f2_2 */ $f2_2 = $f2 << 1; /** @var int $f3_2 */ $f3_2 = $f3 << 1; /** @var int $f4_2 */ $f4_2 = $f4 << 1; /** @var int $f5_2 */ $f5_2 = $f5 << 1; /** @var int $f6_2 */ $f6_2 = $f6 << 1; /** @var int $f7_2 */ $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); /** @var int $h0 */ $h0 = (int) ($f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38) << 1; /** @var int $h1 */ $h1 = (int) ($f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38) << 1; /** @var int $h2 */ $h2 = (int) ($f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19) << 1; /** @var int $h3 */ $h3 = (int) ($f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38) << 1; /** @var int $h4 */ $h4 = (int) ($f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38) << 1; /** @var int $h5 */ $h5 = (int) ($f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38) << 1; /** @var int $h6 */ $h6 = (int) ($f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19) << 1; /** @var int $h7 */ $h7 = (int) ($f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38) << 1; /** @var int $h8 */ $h8 = (int) ($f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38) << 1; /** @var int $h9 */ $h9 = (int) ($f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2) << 1; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 26; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry1 */ $carry1 = ($h1 + (1 << 24)) >> 25; $h2 += $carry1; $h1 -= $carry1 << 25; /** @var int $carry5 */ $carry5 = ($h5 + (1 << 24)) >> 25; $h6 += $carry5; $h5 -= $carry5 << 25; /** @var int $carry2 */ $carry2 = ($h2 + (1 << 25)) >> 26; $h3 += $carry2; $h2 -= $carry2 << 26; /** @var int $carry6 */ $carry6 = ($h6 + (1 << 25)) >> 26; $h7 += $carry6; $h6 -= $carry6 << 26; /** @var int $carry3 */ $carry3 = ($h3 + (1 << 24)) >> 25; $h4 += $carry3; $h3 -= $carry3 << 25; /** @var int $carry7 */ $carry7 = ($h7 + (1 << 24)) >> 25; $h8 += $carry7; $h7 -= $carry7 << 25; /** @var int $carry4 */ $carry4 = ($h4 + (1 << 25)) >> 26; $h5 += $carry4; $h4 -= $carry4 << 26; /** @var int $carry8 */ $carry8 = ($h8 + (1 << 25)) >> 26; $h9 += $carry8; $h8 -= $carry8 << 26; /** @var int $carry9 */ $carry9 = ($h9 + (1 << 24)) >> 25; $h0 += self::mul($carry9, 19, 5); $h9 -= $carry9 << 25; /** @var int $carry0 */ $carry0 = ($h0 + (1 << 25)) >> 26; $h1 += $carry0; $h0 -= $carry0 << 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 ) ); } /** * @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) { # 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 $g) { return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray( array( (int) ($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( $p->X, $p->Y, $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 & 0xffffffff) >> 31); } /** * @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 < 0 ? 1 : 0; } $x = self::chrToInt(self::substr($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) ); } /** * @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]'); } /** @var int $bnegative */ $bnegative = self::negative($b); /** @var int $babs */ $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 $a * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 * @throws SodiumException * @throws TypeError * @psalm-suppress MixedAssignment * @psalm-suppress MixedOperand */ public static function ge_scalarmult_base($a) { /** @var array<int, int> $e */ $e = array(); $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); for ($i = 0; $i < 32; ++$i) { /** @var int $dbl */ $dbl = (int) $i << 1; $e[$dbl] = (int) self::chrToInt($a[$i]) & 15; $e[$dbl + 1] = (int) (self::chrToInt($a[$i]) >> 4) & 15; } /** @var int $carry */ $carry = 0; for ($i = 0; $i < 63; ++$i) { $e[$i] += $carry; /** @var int $carry */ $carry = $e[$i] + 8; /** @var int $carry */ $carry >>= 4; $e[$i] -= $carry << 4; } /** @var array<int, int> $e */ $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) { /** @var int $a0 */ $a0 = 2097151 & self::load_3(self::substr($a, 0, 3)); /** @var int $a1 */ $a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5); /** @var int $a2 */ $a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2); /** @var int $a3 */ $a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7); /** @var int $a4 */ $a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4); /** @var int $a5 */ $a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1); /** @var int $a6 */ $a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6); /** @var int $a7 */ $a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3); /** @var int $a8 */ $a8 = 2097151 & self::load_3(self::substr($a, 21, 3)); /** @var int $a9 */ $a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5); /** @var int $a10 */ $a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2); /** @var int $a11 */ $a11 = (self::load_4(self::substr($a, 28, 4)) >> 7); /** @var int $b0 */ $b0 = 2097151 & self::load_3(self::substr($b, 0, 3)); /** @var int $b1 */ $b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5); /** @var int $b2 */ $b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2); /** @var int $b3 */ $b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7); /** @var int $b4 */ $b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4); /** @var int $b5 */ $b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1); /** @var int $b6 */ $b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6); /** @var int $b7 */ $b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3); /** @var int $b8 */ $b8 = 2097151 & self::load_3(self::substr($b, 21, 3)); /** @var int $b9 */ $b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5); /** @var int $b10 */ $b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2); /** @var int $b11 */ $b11 = (self::load_4(self::substr($b, 28, 4)) >> 7); /** @var int $c0 */ $c0 = 2097151 & self::load_3(self::substr($c, 0, 3)); /** @var int $c1 */ $c1 = 2097151 & (self::load_4(self::substr($c, 2, 4)) >> 5); /** @var int $c2 */ $c2 = 2097151 & (self::load_3(self::substr($c, 5, 3)) >> 2); /** @var int $c3 */ $c3 = 2097151 & (self::load_4(self::substr($c, 7, 4)) >> 7); /** @var int $c4 */ $c4 = 2097151 & (self::load_4(self::substr($c, 10, 4)) >> 4); /** @var int $c5 */ $c5 = 2097151 & (self::load_3(self::substr($c, 13, 3)) >> 1); /** @var int $c6 */ $c6 = 2097151 & (self::load_4(self::substr($c, 15, 4)) >> 6); /** @var int $c7 */ $c7 = 2097151 & (self::load_3(self::substr($c, 18, 3)) >> 3); /** @var int $c8 */ $c8 = 2097151 & self::load_3(self::substr($c, 21, 3)); /** @var int $c9 */ $c9 = 2097151 & (self::load_4(self::substr($c, 23, 4)) >> 5); /** @var int $c10 */ $c10 = 2097151 & (self::load_3(self::substr($c, 26, 3)) >> 2); /** @var int $c11 */ $c11 = (self::load_4(self::substr($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; /** @var int $carry0 */ $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry2 */ $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry4 */ $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry6 */ $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry8 */ $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry10 */ $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry12 */ $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; /** @var int $carry14 */ $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; /** @var int $carry16 */ $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; /** @var int $carry18 */ $carry18 = ($s18 + (1 << 20)) >> 21; $s19 += $carry18; $s18 -= $carry18 << 21; /** @var int $carry20 */ $carry20 = ($s20 + (1 << 20)) >> 21; $s21 += $carry20; $s20 -= $carry20 << 21; /** @var int $carry22 */ $carry22 = ($s22 + (1 << 20)) >> 21; $s23 += $carry22; $s22 -= $carry22 << 21; /** @var int $carry1 */ $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry3 */ $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry5 */ $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry7 */ $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry9 */ $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry11 */ $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; /** @var int $carry13 */ $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; /** @var int $carry15 */ $carry15 = ($s15 + (1 << 20)) >> 21; $s16 += $carry15; $s15 -= $carry15 << 21; /** @var int $carry17 */ $carry17 = ($s17 + (1 << 20)) >> 21; $s18 += $carry17; $s17 -= $carry17 << 21; /** @var int $carry19 */ $carry19 = ($s19 + (1 << 20)) >> 21; $s20 += $carry19; $s19 -= $carry19 << 21; /** @var int $carry21 */ $carry21 = ($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); /** @var int $carry6 */ $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry8 */ $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry10 */ $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry12 */ $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; /** @var int $carry14 */ $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; /** @var int $carry16 */ $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; /** @var int $carry7 */ $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry9 */ $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry11 */ $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; /** @var int $carry13 */ $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; /** @var int $carry15 */ $carry15 = ($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; /** @var int $carry0 */ $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry2 */ $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry4 */ $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry6 */ $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry8 */ $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry10 */ $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry1 */ $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry3 */ $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry5 */ $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry7 */ $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry9 */ $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry11 */ $carry11 = ($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; /** @var int $carry0 */ $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry1 */ $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry2 */ $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry3 */ $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry4 */ $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry5 */ $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry6 */ $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry7 */ $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry8 */ $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry9 */ $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry10 */ $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry11 */ $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); /** @var int $carry0 */ $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry1 */ $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry2 */ $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry3 */ $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry4 */ $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry5 */ $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry6 */ $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry7 */ $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry8 */ $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry9 */ $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry10 */ $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) { /** @var int $s0 */ $s0 = 2097151 & self::load_3(self::substr($s, 0, 3)); /** @var int $s1 */ $s1 = 2097151 & (self::load_4(self::substr($s, 2, 4)) >> 5); /** @var int $s2 */ $s2 = 2097151 & (self::load_3(self::substr($s, 5, 3)) >> 2); /** @var int $s3 */ $s3 = 2097151 & (self::load_4(self::substr($s, 7, 4)) >> 7); /** @var int $s4 */ $s4 = 2097151 & (self::load_4(self::substr($s, 10, 4)) >> 4); /** @var int $s5 */ $s5 = 2097151 & (self::load_3(self::substr($s, 13, 3)) >> 1); /** @var int $s6 */ $s6 = 2097151 & (self::load_4(self::substr($s, 15, 4)) >> 6); /** @var int $s7 */ $s7 = 2097151 & (self::load_3(self::substr($s, 18, 4)) >> 3); /** @var int $s8 */ $s8 = 2097151 & self::load_3(self::substr($s, 21, 3)); /** @var int $s9 */ $s9 = 2097151 & (self::load_4(self::substr($s, 23, 4)) >> 5); /** @var int $s10 */ $s10 = 2097151 & (self::load_3(self::substr($s, 26, 3)) >> 2); /** @var int $s11 */ $s11 = 2097151 & (self::load_4(self::substr($s, 28, 4)) >> 7); /** @var int $s12 */ $s12 = 2097151 & (self::load_4(self::substr($s, 31, 4)) >> 4); /** @var int $s13 */ $s13 = 2097151 & (self::load_3(self::substr($s, 34, 3)) >> 1); /** @var int $s14 */ $s14 = 2097151 & (self::load_4(self::substr($s, 36, 4)) >> 6); /** @var int $s15 */ $s15 = 2097151 & (self::load_3(self::substr($s, 39, 4)) >> 3); /** @var int $s16 */ $s16 = 2097151 & self::load_3(self::substr($s, 42, 3)); /** @var int $s17 */ $s17 = 2097151 & (self::load_4(self::substr($s, 44, 4)) >> 5); /** @var int $s18 */ $s18 = 2097151 & (self::load_3(self::substr($s, 47, 3)) >> 2); /** @var int $s19 */ $s19 = 2097151 & (self::load_4(self::substr($s, 49, 4)) >> 7); /** @var int $s20 */ $s20 = 2097151 & (self::load_4(self::substr($s, 52, 4)) >> 4); /** @var int $s21 */ $s21 = 2097151 & (self::load_3(self::substr($s, 55, 3)) >> 1); /** @var int $s22 */ $s22 = 2097151 & (self::load_4(self::substr($s, 57, 4)) >> 6); /** @var int $s23 */ $s23 = (self::load_4(self::substr($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); /** @var int $carry6 */ $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry8 */ $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry10 */ $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry12 */ $carry12 = ($s12 + (1 << 20)) >> 21; $s13 += $carry12; $s12 -= $carry12 << 21; /** @var int $carry14 */ $carry14 = ($s14 + (1 << 20)) >> 21; $s15 += $carry14; $s14 -= $carry14 << 21; /** @var int $carry16 */ $carry16 = ($s16 + (1 << 20)) >> 21; $s17 += $carry16; $s16 -= $carry16 << 21; /** @var int $carry7 */ $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry9 */ $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry11 */ $carry11 = ($s11 + (1 << 20)) >> 21; $s12 += $carry11; $s11 -= $carry11 << 21; /** @var int $carry13 */ $carry13 = ($s13 + (1 << 20)) >> 21; $s14 += $carry13; $s13 -= $carry13 << 21; /** @var int $carry15 */ $carry15 = ($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; /** @var int $carry0 */ $carry0 = ($s0 + (1 << 20)) >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry2 */ $carry2 = ($s2 + (1 << 20)) >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry4 */ $carry4 = ($s4 + (1 << 20)) >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry6 */ $carry6 = ($s6 + (1 << 20)) >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry8 */ $carry8 = ($s8 + (1 << 20)) >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry10 */ $carry10 = ($s10 + (1 << 20)) >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry1 */ $carry1 = ($s1 + (1 << 20)) >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry3 */ $carry3 = ($s3 + (1 << 20)) >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry5 */ $carry5 = ($s5 + (1 << 20)) >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry7 */ $carry7 = ($s7 + (1 << 20)) >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry9 */ $carry9 = ($s9 + (1 << 20)) >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry11 */ $carry11 = ($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; /** @var int $carry0 */ $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry1 */ $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry2 */ $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry3 */ $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry4 */ $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry5 */ $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry6 */ $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry7 */ $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry8 */ $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry9 */ $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry10 */ $carry10 = $s10 >> 21; $s11 += $carry10; $s10 -= $carry10 << 21; /** @var int $carry11 */ $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); /** @var int $carry0 */ $carry0 = $s0 >> 21; $s1 += $carry0; $s0 -= $carry0 << 21; /** @var int $carry1 */ $carry1 = $s1 >> 21; $s2 += $carry1; $s1 -= $carry1 << 21; /** @var int $carry2 */ $carry2 = $s2 >> 21; $s3 += $carry2; $s2 -= $carry2 << 21; /** @var int $carry3 */ $carry3 = $s3 >> 21; $s4 += $carry3; $s3 -= $carry3 << 21; /** @var int $carry4 */ $carry4 = $s4 >> 21; $s5 += $carry4; $s4 -= $carry4 << 21; /** @var int $carry5 */ $carry5 = $s5 >> 21; $s6 += $carry5; $s5 -= $carry5 << 21; /** @var int $carry6 */ $carry6 = $s6 >> 21; $s7 += $carry6; $s6 -= $carry6 << 21; /** @var int $carry7 */ $carry7 = $s7 >> 21; $s8 += $carry7; $s7 -= $carry7 << 21; /** @var int $carry8 */ $carry8 = $s8 >> 21; $s9 += $carry8; $s8 -= $carry8 << 21; /** @var int $carry9 */ $carry9 = $s9 >> 21; $s10 += $carry9; $s9 -= $carry9 << 21; /** @var int $carry10 */ $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) { /** @var array<int, int> $aslide */ $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); } }