<?php
declare(strict_types=1);
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(): ParagonIE_Sodium_Core_Curve25519_Fe
{
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[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(): ParagonIE_Sodium_Core_Curve25519_Fe
{
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[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
*/
public static function fe_add(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g
): ParagonIE_Sodium_Core_Curve25519_Fe {
/** @var array<int, int> $arr */
$arr = array();
for ($i = 0; $i < 10; ++$i) {
$arr[$i] = ($f[$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
*/
public static function fe_cmov(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g,
int $b = 0
): ParagonIE_Sodium_Core_Curve25519_Fe {
/** @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);
}
/**
* 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(
#[SensitiveParameter]
string $s
): ParagonIE_Sodium_Core_Curve25519_Fe {
if (self::strlen($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 -= $carry8 << 26;
return ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[$h0, $h1, $h2, $h3, $h4, $h5, $h6, $h7, $h8, $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): string
{
$h0 = $h[0];
$h1 = $h[1];
$h2 = $h[2];
$h3 = $h[3];
$h4 = $h[4];
$h5 = $h[5];
$h6 = $h[6];
$h7 = $h[7];
$h8 = $h[8];
$h9 = $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 -= $carry9 << 25;
return self::intArrayToString([
(($h0 >> 0) & 0xff),
(($h0 >> 8) & 0xff),
(($h0 >> 16) & 0xff),
((($h0 >> 24) | ($h1 << 2)) & 0xff),
(($h1 >> 6) & 0xff),
(($h1 >> 14) & 0xff),
((($h1 >> 22) | ($h2 << 3)) & 0xff),
(($h2 >> 5) & 0xff),
(($h2 >> 13) & 0xff),
((($h2 >> 21) | ($h3 << 5)) & 0xff),
(($h3 >> 3) & 0xff),
(($h3 >> 11) & 0xff),
((($h3 >> 19) | ($h4 << 6)) & 0xff),
(($h4 >> 2) & 0xff),
(($h4 >> 10) & 0xff),
(($h4 >> 18) & 0xff),
(($h5 >> 0) & 0xff),
(($h5 >> 8) & 0xff),
(($h5 >> 16) & 0xff),
((($h5 >> 24) | ($h6 << 1)) & 0xff),
(($h6 >> 7) & 0xff),
(($h6 >> 15) & 0xff),
((($h6 >> 23) | ($h7 << 3)) & 0xff),
(($h7 >> 5) & 0xff),
(($h7 >> 13) & 0xff),
((($h7 >> 21) | ($h8 << 4)) & 0xff),
(($h8 >> 4) & 0xff),
(($h8 >> 12) & 0xff),
((($h8 >> 20) | ($h9 << 6)) & 0xff),
(($h9 >> 2) & 0xff),
(($h9 >> 10) & 0xff),
(($h9 >> 18) & 0xff)
]);
}
/**
* 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): int
{
$str = self::fe_tobytes($f);
return (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): bool
{
static $zero;
if ($zero === null) {
$zero = str_repeat("\x00", 32);
}
$str = self::fe_tobytes($f);
return !self::verify_32($str, $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
): ParagonIE_Sodium_Core_Curve25519_Fe {
// Ensure limbs aren't oversized.
$f = self::fe_normalize($f);
$g = self::fe_normalize($g);
$g1_19 = self::mul($g[1], 19, 5);
$g2_19 = self::mul($g[2], 19, 5);
$g3_19 = self::mul($g[3], 19, 5);
$g4_19 = self::mul($g[4], 19, 5);
$g5_19 = self::mul($g[5], 19, 5);
$g6_19 = self::mul($g[6], 19, 5);
$g7_19 = self::mul($g[7], 19, 5);
$g8_19 = self::mul($g[8], 19, 5);
$g9_19 = self::mul($g[9], 19, 5);
$f1_2 = $f[1] << 1;
$f3_2 = $f[3] << 1;
$f5_2 = $f[5] << 1;
$f7_2 = $f[7] << 1;
$f9_2 = $f[9] << 1;
$f0g0 = self::mul($f[0], $g[0], 26);
$f0g1 = self::mul($f[0], $g[1], 25);
$f0g2 = self::mul($f[0], $g[2], 26);
$f0g3 = self::mul($f[0], $g[3], 25);
$f0g4 = self::mul($f[0], $g[4], 26);
$f0g5 = self::mul($f[0], $g[5], 25);
$f0g6 = self::mul($f[0], $g[6], 26);
$f0g7 = self::mul($f[0], $g[7], 25);
$f0g8 = self::mul($f[0], $g[8], 26);
$f0g9 = self::mul($f[0], $g[9], 26);
$f1g0 = self::mul($f[1], $g[0], 26);
$f1g1_2 = self::mul($f1_2, $g[1], 25);
$f1g2 = self::mul($f[1], $g[2], 26);
$f1g3_2 = self::mul($f1_2, $g[3], 25);
$f1g4 = self::mul($f[1], $g[4], 26);
$f1g5_2 = self::mul($f1_2, $g[5], 25);
$f1g6 = self::mul($f[1], $g[6], 26);
$f1g7_2 = self::mul($f1_2, $g[7], 25);
$f1g8 = self::mul($f[1], $g[8], 26);
$f1g9_38 = self::mul($g9_19, $f1_2, 26);
$f2g0 = self::mul($f[2], $g[0], 26);
$f2g1 = self::mul($f[2], $g[1], 25);
$f2g2 = self::mul($f[2], $g[2], 26);
$f2g3 = self::mul($f[2], $g[3], 25);
$f2g4 = self::mul($f[2], $g[4], 26);
$f2g5 = self::mul($f[2], $g[5], 25);
$f2g6 = self::mul($f[2], $g[6], 26);
$f2g7 = self::mul($f[2], $g[7], 25);
$f2g8_19 = self::mul($g8_19, $f[2], 26);
$f2g9_19 = self::mul($g9_19, $f[2], 26);
$f3g0 = self::mul($f[3], $g[0], 26);
$f3g1_2 = self::mul($f3_2, $g[1], 25);
$f3g2 = self::mul($f[3], $g[2], 26);
$f3g3_2 = self::mul($f3_2, $g[3], 25);
$f3g4 = self::mul($f[3], $g[4], 26);
$f3g5_2 = self::mul($f3_2, $g[5], 25);
$f3g6 = self::mul($f[3], $g[6], 26);
$f3g7_38 = self::mul($g7_19, $f3_2, 26);
$f3g8_19 = self::mul($g8_19, $f[3], 25);
$f3g9_38 = self::mul($g9_19, $f3_2, 26);
$f4g0 = self::mul($f[4], $g[0], 26);
$f4g1 = self::mul($f[4], $g[1], 25);
$f4g2 = self::mul($f[4], $g[2], 26);
$f4g3 = self::mul($f[4], $g[3], 25);
$f4g4 = self::mul($f[4], $g[4], 26);
$f4g5 = self::mul($f[4], $g[5], 25);
$f4g6_19 = self::mul($g6_19, $f[4], 26);
$f4g7_19 = self::mul($g7_19, $f[4], 26);
$f4g8_19 = self::mul($g8_19, $f[4], 26);
$f4g9_19 = self::mul($g9_19, $f[4], 26);
$f5g0 = self::mul($f[5], $g[0], 26);
$f5g1_2 = self::mul($f5_2, $g[1], 25);
$f5g2 = self::mul($f[5], $g[2], 26);
$f5g3_2 = self::mul($f5_2, $g[3], 25);
$f5g4 = self::mul($f[5], $g[4], 26);
$f5g5_38 = self::mul($g5_19, $f5_2, 26);
$f5g6_19 = self::mul($g6_19, $f[5], 25);
$f5g7_38 = self::mul($g7_19, $f5_2, 26);
$f5g8_19 = self::mul($g8_19, $f[5], 25);
$f5g9_38 = self::mul($g9_19, $f5_2, 26);
$f6g0 = self::mul($f[6], $g[0], 26);
$f6g1 = self::mul($f[6], $g[1], 25);
$f6g2 = self::mul($f[6], $g[2], 26);
$f6g3 = self::mul($f[6], $g[3], 25);
$f6g4_19 = self::mul($g4_19, $f[6], 26);
$f6g5_19 = self::mul($g5_19, $f[6], 26);
$f6g6_19 = self::mul($g6_19, $f[6], 26);
$f6g7_19 = self::mul($g7_19, $f[6], 26);
$f6g8_19 = self::mul($g8_19, $f[6], 26);
$f6g9_19 = self::mul($g9_19, $f[6], 26);
$f7g0 = self::mul($f[7], $g[0], 26);
$f7g1_2 = self::mul($f7_2, $g[1], 25);
$f7g2 = self::mul($f[7], $g[2], 26);
$f7g3_38 = self::mul($g3_19, $f7_2, 26);
$f7g4_19 = self::mul($g4_19, $f[7], 26);
$f7g5_38 = self::mul($g5_19, $f7_2, 26);
$f7g6_19 = self::mul($g6_19, $f[7], 25);
$f7g7_38 = self::mul($g7_19, $f7_2, 26);
$f7g8_19 = self::mul($g8_19, $f[7], 25);
$f7g9_38 = self::mul($g9_19,$f7_2, 26);
$f8g0 = self::mul($f[8], $g[0], 26);
$f8g1 = self::mul($f[8], $g[1], 25);
$f8g2_19 = self::mul($g2_19, $f[8], 26);
$f8g3_19 = self::mul($g3_19, $f[8], 26);
$f8g4_19 = self::mul($g4_19, $f[8], 26);
$f8g5_19 = self::mul($g5_19, $f[8], 26);
$f8g6_19 = self::mul($g6_19, $f[8], 26);
$f8g7_19 = self::mul($g7_19, $f[8], 26);
$f8g8_19 = self::mul($g8_19, $f[8], 26);
$f8g9_19 = self::mul($g9_19, $f[8], 26);
$f9g0 = self::mul($f[9], $g[0], 26);
$f9g1_38 = self::mul($g1_19, $f9_2, 26);
$f9g2_19 = self::mul($g2_19, $f[9], 25);
$f9g3_38 = self::mul($g3_19, $f9_2, 26);
$f9g4_19 = self::mul($g4_19, $f[9], 25);
$f9g5_38 = self::mul($g5_19, $f9_2, 26);
$f9g6_19 = self::mul($g6_19, $f[9], 25);
$f9g7_38 = self::mul($g7_19, $f9_2, 26);
$f9g8_19 = self::mul($g8_19, $f[9], 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 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[$h0, $h1, $h2, $h3, $h4, $h5, $h6, $h7, $h8, $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
*/
public static function fe_neg(ParagonIE_Sodium_Core_Curve25519_Fe $f): ParagonIE_Sodium_Core_Curve25519_Fe
{
$h = new ParagonIE_Sodium_Core_Curve25519_Fe();
for ($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
): ParagonIE_Sodium_Core_Curve25519_Fe {
$f = self::fe_normalize($f);
$f0_2 = $f[0] << 1;
$f1_2 = $f[1] << 1;
$f2_2 = $f[2] << 1;
$f3_2 = $f[3] << 1;
$f4_2 = $f[4] << 1;
$f5_2 = $f[5] << 1;
$f6_2 = $f[6] << 1;
$f7_2 = $f[7] << 1;
$f5_38 = self::mul($f[5], 38, 6);
$f6_19 = self::mul($f[6], 19, 5);
$f7_38 = self::mul($f[7], 38, 6);
$f8_19 = self::mul($f[8], 19, 5);
$f9_38 = self::mul($f[9], 38, 6);
$f0f0 = self::mul($f[0], $f[0], 26);
$f0f1_2 = self::mul($f0_2, $f[1], 26);
$f0f2_2 = self::mul($f0_2, $f[2], 26);
$f0f3_2 = self::mul($f0_2, $f[3], 26);
$f0f4_2 = self::mul($f0_2, $f[4], 26);
$f0f5_2 = self::mul($f0_2, $f[5], 26);
$f0f6_2 = self::mul($f0_2, $f[6], 26);
$f0f7_2 = self::mul($f0_2, $f[7], 26);
$f0f8_2 = self::mul($f0_2, $f[8], 26);
$f0f9_2 = self::mul($f0_2, $f[9], 26);
$f1f1_2 = self::mul($f1_2, $f[1], 26);
$f1f2_2 = self::mul($f1_2, $f[2], 26);
$f1f3_4 = self::mul($f1_2, $f3_2, 26);
$f1f4_2 = self::mul($f1_2, $f[4], 26);
$f1f5_4 = self::mul($f1_2, $f5_2, 26);
$f1f6_2 = self::mul($f1_2, $f[6], 26);
$f1f7_4 = self::mul($f1_2, $f7_2, 26);
$f1f8_2 = self::mul($f1_2, $f[8], 26);
$f1f9_76 = self::mul($f9_38, $f1_2, 27);
$f2f2 = self::mul($f[2], $f[2], 27);
$f2f3_2 = self::mul($f2_2, $f[3], 27);
$f2f4_2 = self::mul($f2_2, $f[4], 27);
$f2f5_2 = self::mul($f2_2, $f[5], 27);
$f2f6_2 = self::mul($f2_2, $f[6], 27);
$f2f7_2 = self::mul($f2_2, $f[7], 27);
$f2f8_38 = self::mul($f8_19, $f2_2, 27);
$f2f9_38 = self::mul($f9_38, $f[2], 26);
$f3f3_2 = self::mul($f3_2, $f[3], 26);
$f3f4_2 = self::mul($f3_2, $f[4], 26);
$f3f5_4 = self::mul($f3_2, $f5_2, 26);
$f3f6_2 = self::mul($f3_2, $f[6], 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);
$f4f4 = self::mul($f[4], $f[4], 26);
$f4f5_2 = self::mul($f4_2, $f[5], 26);
$f4f6_38 = self::mul($f6_19, $f4_2, 27);
$f4f7_38 = self::mul($f7_38, $f[4], 26);
$f4f8_38 = self::mul($f8_19, $f4_2, 27);
$f4f9_38 = self::mul($f9_38, $f[4], 26);
$f5f5_38 = self::mul($f5_38, $f[5], 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, $f[6], 26);
$f6f7_38 = self::mul($f7_38, $f[6], 26);
$f6f8_38 = self::mul($f8_19, $f6_2, 27);
$f6f9_38 = self::mul($f9_38, $f[6], 26);
$f7f7_38 = self::mul($f7_38, $f[7], 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, $f[8], 26);
$f8f9_38 = self::mul($f9_38, $f[8], 26);
$f9f9_38 = self::mul($f9_38, $f[9], 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 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[$h0, $h1, $h2, $h3, $h4, $h5, $h6, $h7, $h8, $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): ParagonIE_Sodium_Core_Curve25519_Fe
{
$f = self::fe_normalize($f);
$f0_2 = $f[0] << 1;
$f1_2 = $f[1] << 1;
$f2_2 = $f[2] << 1;
$f3_2 = $f[3] << 1;
$f4_2 = $f[4] << 1;
$f5_2 = $f[5] << 1;
$f6_2 = $f[6] << 1;
$f7_2 = $f[7] << 1;
$f5_38 = self::mul($f[5], 38, 6); /* 1.959375*2^30 */
$f6_19 = self::mul($f[6], 19, 5); /* 1.959375*2^30 */
$f7_38 = self::mul($f[7], 38, 6); /* 1.959375*2^30 */
$f8_19 = self::mul($f[8], 19, 5); /* 1.959375*2^30 */
$f9_38 = self::mul($f[9], 38, 6); /* 1.959375*2^30 */
$f0f0 = self::mul($f[0], $f[0], 24);
$f0f1_2 = self::mul($f0_2, $f[1], 24);
$f0f2_2 = self::mul($f0_2, $f[2], 24);
$f0f3_2 = self::mul($f0_2, $f[3], 24);
$f0f4_2 = self::mul($f0_2, $f[4], 24);
$f0f5_2 = self::mul($f0_2, $f[5], 24);
$f0f6_2 = self::mul($f0_2, $f[6], 24);
$f0f7_2 = self::mul($f0_2, $f[7], 24);
$f0f8_2 = self::mul($f0_2, $f[8], 24);
$f0f9_2 = self::mul($f0_2, $f[9], 24);
$f1f1_2 = self::mul($f1_2, $f[1], 24);
$f1f2_2 = self::mul($f1_2, $f[2], 24);
$f1f3_4 = self::mul($f1_2, $f3_2, 24);
$f1f4_2 = self::mul($f1_2, $f[4], 24);
$f1f5_4 = self::mul($f1_2, $f5_2, 24);
$f1f6_2 = self::mul($f1_2, $f[6], 24);
$f1f7_4 = self::mul($f1_2, $f7_2, 24);
$f1f8_2 = self::mul($f1_2, $f[8], 24);
$f1f9_76 = self::mul($f9_38, $f1_2, 24);
$f2f2 = self::mul($f[2], $f[2], 24);
$f2f3_2 = self::mul($f2_2, $f[3], 24);
$f2f4_2 = self::mul($f2_2, $f[4], 24);
$f2f5_2 = self::mul($f2_2, $f[5], 24);
$f2f6_2 = self::mul($f2_2, $f[6], 24);
$f2f7_2 = self::mul($f2_2, $f[7], 24);
$f2f8_38 = self::mul($f8_19, $f2_2, 25);
$f2f9_38 = self::mul($f9_38, $f[2], 24);
$f3f3_2 = self::mul($f3_2, $f[3], 24);
$f3f4_2 = self::mul($f3_2, $f[4], 24);
$f3f5_4 = self::mul($f3_2, $f5_2, 24);
$f3f6_2 = self::mul($f3_2, $f[6], 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);
$f4f4 = self::mul($f[4], $f[4], 24);
$f4f5_2 = self::mul($f4_2, $f[5], 24);
$f4f6_38 = self::mul($f6_19, $f4_2, 25);
$f4f7_38 = self::mul($f7_38, $f[4], 24);
$f4f8_38 = self::mul($f8_19, $f4_2, 25);
$f4f9_38 = self::mul($f9_38, $f[4], 24);
$f5f5_38 = self::mul($f5_38, $f[5], 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, $f[6], 24);
$f6f7_38 = self::mul($f7_38, $f[6], 24);
$f6f8_38 = self::mul($f8_19, $f6_2, 25);
$f6f9_38 = self::mul($f9_38, $f[6], 24);
$f7f7_38 = self::mul($f7_38, $f[7], 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, $f[8], 24);
$f8f9_38 = self::mul($f9_38, $f[8], 24);
$f9f9_38 = self::mul($f9_38, $f[9], 24);
$h0 = ($f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38) << 1;
$h1 = ($f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38) << 1;
$h2 = ($f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19) << 1;
$h3 = ($f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38) << 1;
$h4 = ($f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38) << 1;
$h5 = ($f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38) << 1;
$h6 = ($f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19) << 1;
$h7 = ($f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38) << 1;
$h8 = ($f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38) << 1;
$h9 = ($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 -= $carry0 << 26;
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
[$h0, $h1, $h2, $h3, $h4, $h5, $h6, $h7, $h8, $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
): ParagonIE_Sodium_Core_Curve25519_Fe {
$t0 = self::fe_sq($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): ParagonIE_Sodium_Core_Curve25519_Fe
{
$z = self::fe_normalize($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);
$t0 = self::fe_sq($t0);
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
for ($i = 1; $i < 5; ++$i) {
$t1 = self::fe_sq($t1);
}
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_sq($t1);
}
$t1 = self::fe_mul($t1, $t0);
$t2 = self::fe_sq($t1);
for ($i = 1; $i < 20; ++$i) {
$t2 = self::fe_sq($t2);
}
$t1 = self::fe_mul($t2, $t1);
$t1 = self::fe_sq($t1);
for ($i = 1; $i < 10; ++$i) {
$t1 = self::fe_sq($t1);
}
$t0 = self::fe_mul($t1, $t0);
$t1 = self::fe_sq($t0);
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_sq($t1);
}
$t1 = self::fe_mul($t1, $t0);
$t2 = self::fe_sq($t1);
for ($i = 1; $i < 100; ++$i) {
$t2 = self::fe_sq($t2);
}
$t1 = self::fe_mul($t2, $t1);
$t1 = self::fe_sq($t1);
for ($i = 1; $i < 50; ++$i) {
$t1 = self::fe_sq($t1);
}
$t0 = self::fe_mul($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
*/
public static function fe_sub(
ParagonIE_Sodium_Core_Curve25519_Fe $f,
ParagonIE_Sodium_Core_Curve25519_Fe $g
): ParagonIE_Sodium_Core_Curve25519_Fe {
return self::fe_normalize(
ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(
array(
($f[0] - $g[0]),
($f[1] - $g[1]),
($f[2] - $g[2]),
($f[3] - $g[3]),
($f[4] - $g[4]),
($f[5] - $g[5]),
($f[6] - $g[6]),
($f[7] - $g[7]),
($f[8] - $g[8]),
($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
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
$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(string $a): array
{
if (self::strlen($a) < 256) {
if (self::strlen($a) < 16) {
$a = str_pad($a, 256, '0');
}
}
/** @var array<int, int> $r */
$r = array();
for ($i = 0; $i < 256; ++$i) {
$r[$i] = (
1 & (
self::chrToInt($a[($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(
string $s
): ParagonIE_Sodium_Core_Curve25519_Ge_P3 {
static $d = null;
if (!$d) {
$d = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::D);
}
$h = new ParagonIE_Sodium_Core_Curve25519_Ge_P3(
self::fe_0(),
self::fe_frombytes($s),
self::fe_1()
);
$u = self::fe_sq($h->Y);
$v = self::fe_mul($u, $d);
$u = self::fe_sub($u, $h->Z); /* u = y^2 - 1 */
$v = self::fe_add($v, $h->Z); /* v = dy^2 + 1 */
$v3 = self::fe_sq($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 */
$h->X = self::fe_pow22523($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) */
$vxx = self::fe_sq($h->X);
$vxx = self::fe_mul($vxx, $v);
$check = self::fe_sub($vxx, $u); /* vx^2 - u */
if (self::fe_isnonzero($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)
);
}
$i = self::chrToInt($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
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
$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
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
$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
): ParagonIE_Sodium_Core_Curve25519_Ge_P2{
$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
): ParagonIE_Sodium_Core_Curve25519_Ge_P3 {
$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(): ParagonIE_Sodium_Core_Curve25519_Ge_P2
{
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
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
$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(): ParagonIE_Sodium_Core_Curve25519_Ge_P3
{
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
): ParagonIE_Sodium_Core_Curve25519_Ge_Cached {
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 = clone $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
): ParagonIE_Sodium_Core_Curve25519_Ge_P2 {
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
): string {
$recip = self::fe_invert($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 $p
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
return self::ge_p2_dbl(self::ge_p3_to_p2($p));
}
/**
* @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
*/
public static function ge_precomp_0(): ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
{
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(int $b, int $c): int
{
return ((($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(int|string $char): int
{
if (is_int($char)) {
return ($char >> 63) & 1;
}
$x = self::chrToInt(self::substr($char, 0, 1));
return ($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,
#[SensitiveParameter]
int $b
): ParagonIE_Sodium_Core_Curve25519_Ge_Precomp {
return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp(
self::fe_cmov($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,
#[SensitiveParameter]
int $b
): ParagonIE_Sodium_Core_Curve25519_Ge_Cached {
$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,
#[SensitiveParameter]
int $b
): ParagonIE_Sodium_Core_Curve25519_Ge_Cached {
$bNegative = self::negative($b);
$babs = $b - (((-$bNegative) & $b) << 1);
$t = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(
self::fe_1(),
self::fe_1(),
self::fe_1(),
self::fe_0()
);
for ($x = 0; $x < 8; ++$x) {
$t = self::ge_cmov_cached($t, $cached[$x], self::equal($babs, $x + 1));
}
$minust = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(
$t->YminusX,
$t->YplusX,
$t->Z,
self::fe_neg($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
*/
public static function ge_select(int $pos = 0, int $b = 0): ParagonIE_Sodium_Core_Curve25519_Ge_Precomp
{
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>> $base */
if ($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(
$t->yminusx,
$t->yplusx,
self::fe_neg($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
): ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 {
$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): string
{
$recip = self::fe_invert($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
*/
public static function ge_double_scalarmult_vartime(
string $a,
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A,
string $b
): ParagonIE_Sodium_Core_Curve25519_Ge_P2 {
/** @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()
);
}
/** @var array<int, int> $aslide */
$aslide = self::slide($a);
/** @var array<int, int> $bslide */
$bslide = self::slide($b);
$Ai[0] = self::ge_p3_to_cached($A);
$t = self::ge_p3_dbl($A);
$A2 = self::ge_p1p1_to_p3($t);
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);
}
$r = self::ge_p2_0();
$i = 255;
for (; $i >= 0; --$i) {
if ($aslide[$i] || $bslide[$i]) {
break;
}
}
for (; $i >= 0; --$i) {
$t = self::ge_p2_dbl($r);
if ($aslide[$i] > 0) {
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_add(
$u,
$Ai[(int) floor($aslide[$i] / 2)]
);
} elseif ($aslide[$i] < 0) {
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_sub(
$u,
$Ai[(int) floor(-$aslide[$i] / 2)]
);
}
if ($bslide[$i] > 0) {
$index = (int) floor($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) {
$index = (int) floor(-$bslide[$i] / 2);
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_msub($t, $u, $Bi[$index]);
}
$r = self::ge_p1p1_to_p2($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
*/
public static function ge_scalarmult(
#[SensitiveParameter]
string $a,
ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p
): ParagonIE_Sodium_Core_Curve25519_Ge_P3 {
$e = array_fill(0, 64, 0);
/** @var ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $pi */
$pi = array();
$pi[0] = self::ge_p3_to_cached($p);
$t2 = self::ge_p3_dbl($p);
$p2 = self::ge_p1p1_to_p3($t2);
$pi[1] = self::ge_p3_to_cached($p2);
$t3 = self::ge_add($p, $pi[1]);
$p3 = self::ge_p1p1_to_p3($t3);
$pi[2] = self::ge_p3_to_cached($p3);
$t4 = self::ge_p3_dbl($p2);
$p4 = self::ge_p1p1_to_p3($t4);
$pi[3] = self::ge_p3_to_cached($p4);
$t5 = self::ge_add($p, $pi[3]);
$p5 = self::ge_p1p1_to_p3($t5);
$pi[4] = self::ge_p3_to_cached($p5);
$t6 = self::ge_p3_dbl($p3);
$p6 = self::ge_p1p1_to_p3($t6);
$pi[5] = self::ge_p3_to_cached($p6);
$t7 = self::ge_add($p, $pi[5]);
$p7 = self::ge_p1p1_to_p3($t7);
$pi[6] = self::ge_p3_to_cached($p7);
$t8 = self::ge_p3_dbl($p4);
$p8 = self::ge_p1p1_to_p3($t8);
$pi[7] = self::ge_p3_to_cached($p8);
for ($i = 0; $i < 32; ++$i) {
$e[($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 << 4;
}
$e[63] += $carry;
$h = self::ge_p3_0();
for ($i = 63; $i != 0; --$i) {
$t = self::ge_cmov8_cached($pi, $e[$i]);
$r = self::ge_add($h, $t);
$s = self::ge_p1p1_to_p2($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);
$h = self::ge_p1p1_to_p3($r); /* *16 */
}
$t = self::ge_cmov8_cached($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
*/
public static function ge_scalarmult_base(
#[SensitiveParameter]
string $a
): ParagonIE_Sodium_Core_Curve25519_Ge_P3 {
/** @var array<int, int> $e */
$e = array();
$r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1();
for ($i = 0; $i < 32; ++$i) {
$dbl = $i << 1;
$e[$dbl] = self::chrToInt($a[$i]) & 15;
$e[$dbl + 1] = (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] += $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(
#[SensitiveParameter]
string $a,
#[SensitiveParameter]
string $b,
#[SensitiveParameter]
string $c
): string {
$a0 = 2097151 & self::load_3(self::substr($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 -= $carry10 << 21;
return self::intArrayToString([
(0xff & ($s0 >> 0)),
(0xff & ($s0 >> 8)),
(0xff & (($s0 >> 16) | $s1 << 5)),
(0xff & ($s1 >> 3)),
(0xff & ($s1 >> 11)),
(0xff & (($s1 >> 19) | $s2 << 2)),
(0xff & ($s2 >> 6)),
(0xff & (($s2 >> 14) | $s3 << 7)),
(0xff & ($s3 >> 1)),
(0xff & ($s3 >> 9)),
(0xff & (($s3 >> 17) | $s4 << 4)),
(0xff & ($s4 >> 4)),
(0xff & ($s4 >> 12)),
(0xff & (($s4 >> 20) | $s5 << 1)),
(0xff & ($s5 >> 7)),
(0xff & (($s5 >> 15) | $s6 << 6)),
(0xff & ($s6 >> 2)),
(0xff & ($s6 >> 10)),
(0xff & (($s6 >> 18) | $s7 << 3)),
(0xff & ($s7 >> 5)),
(0xff & ($s7 >> 13)),
(0xff & ($s8 >> 0)),
(0xff & ($s8 >> 8)),
(0xff & (($s8 >> 16) | $s9 << 5)),
(0xff & ($s9 >> 3)),
(0xff & ($s9 >> 11)),
(0xff & (($s9 >> 19) | $s10 << 2)),
(0xff & ($s10 >> 6)),
(0xff & (($s10 >> 14) | $s11 << 7)),
(0xff & ($s11 >> 1)),
(0xff & ($s11 >> 9)),
0xff & ($s11 >> 17)
]);
}
/**
* @internal You should not use this directly from another application
*
* @param string $s
* @return string
* @throws TypeError
*/
public static function sc_reduce(
#[SensitiveParameter]
string $s
): string {
$s0 = 2097151 & self::load_3(self::substr($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 -= $carry10 << 21;
return self::intArrayToString([
($s0 >> 0),
($s0 >> 8),
(($s0 >> 16) | $s1 << 5),
($s1 >> 3),
($s1 >> 11),
(($s1 >> 19) | $s2 << 2),
($s2 >> 6),
(($s2 >> 14) | $s3 << 7),
($s3 >> 1),
($s3 >> 9),
(($s3 >> 17) | $s4 << 4),
($s4 >> 4),
($s4 >> 12),
(($s4 >> 20) | $s5 << 1),
($s5 >> 7),
(($s5 >> 15) | $s6 << 6),
($s6 >> 2),
($s6 >> 10),
(($s6 >> 18) | $s7 << 3),
($s7 >> 5),
($s7 >> 13),
($s8 >> 0),
($s8 >> 8),
(($s8 >> 16) | $s9 << 5),
($s9 >> 3),
($s9 >> 11),
(($s9 >> 19) | $s10 << 2),
($s10 >> 6),
(($s10 >> 14) | $s11 << 7),
($s11 >> 1),
($s11 >> 9),
$s11 >> 17
]);
}
/**
* 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
): ParagonIE_Sodium_Core_Curve25519_Ge_P3 {
$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();
$Ai[0] = self::ge_p3_to_cached($A);
$t = self::ge_p3_dbl($A);
$A2 = self::ge_p1p1_to_p3($t);
for ($i = 1; $i < 8; ++$i) {
$t = self::ge_add($A2, $Ai[$i - 1]);
$u = self::ge_p1p1_to_p3($t);
$Ai[$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) {
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_add($u, $Ai[(int)($aslide[$i] / 2)]);
} elseif ($aslide[$i] < 0) {
$u = self::ge_p1p1_to_p3($t);
$t = self::ge_sub($u, $Ai[(int)(-$aslide[$i] / 2)]);
}
}
return self::ge_p1p1_to_p3($t);
}
/**
* @param string $a
* @param string $b
* @return string
*/
public static function sc25519_mul(
#[SensitiveParameter]
string $a,
#[SensitiveParameter]
string $b
): string {
$a0 = 2097151 & self::load_3(self::substr($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);
$s0 = self::mul($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 + (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;
$s = array_fill(0, 32, 0);
$s[0] = $s0 >> 0;
$s[1] = $s0 >> 8;
$s[2] = ($s0 >> 16) | ($s1 << 5);
$s[3] = $s1 >> 3;
$s[4] = $s1 >> 11;
$s[5] = ($s1 >> 19) | ($s2 << 2);
$s[6] = $s2 >> 6;
$s[7] = ($s2 >> 14) | ($s3 << 7);
$s[8] = $s3 >> 1;
$s[9] = $s3 >> 9;
$s[10] = ($s3 >> 17) | ($s4 << 4);
$s[11] = $s4 >> 4;
$s[12] = $s4 >> 12;
$s[13] = ($s4 >> 20) | ($s5 << 1);
$s[14] = $s5 >> 7;
$s[15] = ($s5 >> 15) | ($s6 << 6);
$s[16] = $s6 >> 2;
$s[17] = $s6 >> 10;
$s[18] = ($s6 >> 18) | ($s7 << 3);
$s[19] = $s7 >> 5;
$s[20] = $s7 >> 13;
$s[21] = $s8 >> 0;
$s[22] = $s8 >> 8;
$s[23] = ($s8 >> 16) | ($s9 << 5);
$s[24] = $s9 >> 3;
$s[25] = $s9 >> 11;
$s[26] = ($s9 >> 19) | ($s10 << 2);
$s[27] = $s10 >> 6;
$s[28] = ($s10 >> 14) | ($s11 << 7);
$s[29] = $s11 >> 1;
$s[30] = $s11 >> 9;
$s[31] = $s11 >> 17;
return self::intArrayToString($s);
}
/**
* @param string $s
* @return string
*/
public static function sc25519_sq(
#[SensitiveParameter]
string $s
): string {
return self::sc25519_mul($s, $s);
}
/**
* @param string $s
* @param int $n
* @param string $a
* @return string
*/
public static function sc25519_sqmul(
#[SensitiveParameter]
string $s,
int $n,
#[SensitiveParameter]
string $a
): string {
for ($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(
#[SensitiveParameter]
string $s
): string {
$_10 = self::sc25519_sq($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);
}
/**
* 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
): ParagonIE_Sodium_Core_Curve25519_Fe {
$x = (PHP_INT_SIZE << 3) - 1; // 31 or 63
$g = $f;
for ($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;
}
}
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