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\ No newline at end of file diff --git a/composer.json b/composer.json index 8f552f4..4fe874d 100755 --- a/composer.json +++ b/composer.json @@ -21,7 +21,8 @@ "brick/math": "^0.14.2", "kornrunner/keccak": "^1.1", "protonlabs/bitcoin": "^1.0", - "simplito/elliptic-php": "^1.0" + "simplito/elliptic-php": "^1.0", + "ext-gmp": "*" }, "require-dev": { "friendsofphp/php-cs-fixer": "^3.59", diff --git a/src/BLS/Curves/G1.php b/src/BLS/Curves/G1.php new file mode 100644 index 0000000..ec78b98 --- /dev/null +++ b/src/BLS/Curves/G1.php @@ -0,0 +1,193 @@ +x = $x; + $this->y = $y; + $this->z = $z; + } + + public static function generator(): self + { + return new self(Fp::fromHex(self::GX), Fp::fromHex(self::GY), Fp::one()); + } + + public static function identity(): self + { + return new self(Fp::zero(), Fp::one(), Fp::zero()); + } + + public function isIdentity(): bool + { + return $this->z->isZero(); + } + + // ------------------------------------------------------------------------- + // Point doubling (dbl-2009-l, a=0) + // ------------------------------------------------------------------------- + + public function double(): self + { + if ($this->isIdentity()) { + return self::identity(); + } + + $X = $this->x; + $Y = $this->y; + $Z = $this->z; + + $A = $X->square(); + $B = $Y->square(); + $C = $B->square(); + $D = $X->add($B)->square()->sub($A)->sub($C)->mul(Fp::fromInt(2)); + $E = $A->mul(Fp::fromInt(3)); + $F = $E->square(); + $X3 = $F->sub($D->mul(Fp::fromInt(2))); + $Y3 = $E->mul($D->sub($X3))->sub($C->mul(Fp::fromInt(8))); + $Z3 = $Y->mul($Z)->mul(Fp::fromInt(2)); + + return new self($X3, $Y3, $Z3); + } + + // ------------------------------------------------------------------------- + // Point addition (add-2007-bl, handles mixed/projective) + // ------------------------------------------------------------------------- + + public function add(self $other): self + { + if ($this->isIdentity()) { + return $other; + } + if ($other->isIdentity()) { + return $this; + } + + $X1 = $this->x; + $Y1 = $this->y; + $Z1 = $this->z; + $X2 = $other->x; + $Y2 = $other->y; + $Z2 = $other->z; + + $Z1Z1 = $Z1->square(); + $Z2Z2 = $Z2->square(); + $U1 = $X1->mul($Z2Z2); + $U2 = $X2->mul($Z1Z1); + $S1 = $Y1->mul($Z2)->mul($Z2Z2); + $S2 = $Y2->mul($Z1)->mul($Z1Z1); + $H = $U2->sub($U1); + $r = $S2->sub($S1)->mul(Fp::fromInt(2)); + + // If H == 0 and r == 0: both points are equal, use double + if ($H->isZero()) { + if ($r->isZero()) { + return $this->double(); + } + + return self::identity(); // opposite points + } + + $I = $H->mul(Fp::fromInt(2))->square(); + $J = $H->mul($I); + $V = $U1->mul($I); + $X3 = $r->square()->sub($J)->sub($V->mul(Fp::fromInt(2))); + $Y3 = $r->mul($V->sub($X3))->sub($S1->mul($J)->mul(Fp::fromInt(2))); + $Z3 = $Z1->add($Z2)->square()->sub($Z1Z1)->sub($Z2Z2)->mul($H); + + return new self($X3, $Y3, $Z3); + } + + public function neg(): self + { + return new self($this->x, $this->y->neg(), $this->z); + } + + // ------------------------------------------------------------------------- + // Scalar multiplication (LSB double-and-add) + // ------------------------------------------------------------------------- + + public function scalarMul(\GMP $k): self + { + if (gmp_sign($k) === 0) { + return self::identity(); + } + + $result = self::identity(); + $addend = $this; + $n = gmp_abs($k); + + while (gmp_cmp($n, gmp_init(0)) > 0) { + if (gmp_testbit($n, 0)) { + $result = $result->add($addend); + } + $addend = $addend->double(); + $n = gmp_div($n, gmp_init(2)); + } + + if (gmp_sign($k) < 0) { + return $result->neg(); + } + + return $result; + } + + // ------------------------------------------------------------------------- + // Compressed serialization (ZCash encoding, 48 bytes) + // ------------------------------------------------------------------------- + + public function toCompressedBytes(): string + { + if ($this->isIdentity()) { + $bytes = str_repeat("\x00", 48); + $bytes[0] = chr(0xc0); // 0x80 (compressed) | 0x40 (infinity) + + return $bytes; + } + + // Convert to affine + $zinv = $this->z->inv(); + $zinv2 = $zinv->square(); + $zinv3 = $zinv2->mul($zinv); + $ax = $this->x->mul($zinv2); + $ay = $this->y->mul($zinv3); + + $bytes = $ax->toBytes(); // 48 bytes, top 3 bits of first byte are 0 + // Bit 7 (0x80): compressed flag + $bytes[0] = chr(ord($bytes[0]) | 0x80); + // Bit 5 (0x20): sort/sign flag, set if y > (p-1)/2 + if ($ay->isNegative()) { + $bytes[0] = chr(ord($bytes[0]) | 0x20); + } + + return $bytes; + } + + public function toHex(): string + { + return bin2hex($this->toCompressedBytes()); + } +} diff --git a/src/BLS/Curves/G2.php b/src/BLS/Curves/G2.php new file mode 100644 index 0000000..9cea68d --- /dev/null +++ b/src/BLS/Curves/G2.php @@ -0,0 +1,335 @@ +x = $x; + $this->y = $y; + $this->z = $z; + } + + public static function generator(): self + { + return new self( + Fp2::fromHex(self::GX_C0, self::GX_C1), + Fp2::fromHex(self::GY_C0, self::GY_C1), + Fp2::one() + ); + } + + public static function identity(): self + { + return new self(Fp2::zero(), Fp2::one(), Fp2::zero()); + } + + public function isIdentity(): bool + { + return $this->z->isZero(); + } + + // ------------------------------------------------------------------------- + // Point doubling (dbl-2009-l, a=0 for G2) + // ------------------------------------------------------------------------- + + public function double(): self + { + if ($this->isIdentity()) { + return self::identity(); + } + + $X = $this->x; + $Y = $this->y; + $Z = $this->z; + + $A = $X->square(); + $B = $Y->square(); + $C = $B->square(); + $D = $X->add($B)->square()->sub($A)->sub($C)->mulInt(2); + $E = $A->mulInt(3); + $F = $E->square(); + $X3 = $F->sub($D->mulInt(2)); + $Y3 = $E->mul($D->sub($X3))->sub($C->mulInt(8)); + $Z3 = $Y->mul($Z)->mulInt(2); + + return new self($X3, $Y3, $Z3); + } + + // ------------------------------------------------------------------------- + // Point addition + // ------------------------------------------------------------------------- + + public function add(self $other): self + { + if ($this->isIdentity()) { + return $other; + } + if ($other->isIdentity()) { + return $this; + } + + $X1 = $this->x; + $Y1 = $this->y; + $Z1 = $this->z; + $X2 = $other->x; + $Y2 = $other->y; + $Z2 = $other->z; + + $Z1Z1 = $Z1->square(); + $Z2Z2 = $Z2->square(); + $U1 = $X1->mul($Z2Z2); + $U2 = $X2->mul($Z1Z1); + $S1 = $Y1->mul($Z2)->mul($Z2Z2); + $S2 = $Y2->mul($Z1)->mul($Z1Z1); + $H = $U2->sub($U1); + $r = $S2->sub($S1)->mulInt(2); + + if ($H->isZero()) { + if ($r->isZero()) { + return $this->double(); + } + + return self::identity(); + } + + $I = $H->mulInt(2)->square(); + $J = $H->mul($I); + $V = $U1->mul($I); + $X3 = $r->square()->sub($J)->sub($V->mulInt(2)); + $Y3 = $r->mul($V->sub($X3))->sub($S1->mul($J)->mulInt(2)); + $Z3 = $Z1->add($Z2)->square()->sub($Z1Z1)->sub($Z2Z2)->mul($H); + + return new self($X3, $Y3, $Z3); + } + + public function neg(): self + { + return new self($this->x, $this->y->neg(), $this->z); + } + + // ------------------------------------------------------------------------- + // Scalar multiplication (LSB double-and-add) + // ------------------------------------------------------------------------- + + public function scalarMul(\GMP $k): self + { + if (gmp_sign($k) === 0) { + return self::identity(); + } + + $result = self::identity(); + $addend = $this; + $n = gmp_abs($k); + + while (gmp_cmp($n, gmp_init(0)) > 0) { + if (gmp_testbit($n, 0)) { + $result = $result->add($addend); + } + $addend = $addend->double(); + $n = gmp_div($n, gmp_init(2)); + } + + if (gmp_sign($k) < 0) { + return $result->neg(); + } + + return $result; + } + + /** + * ψ (psi) Frobenius endomorphism. + * ψ(x, y) = (conj(x) * PSI_X, conj(y) * PSI_Y) + * Applied to projective point (X:Y:Z): ψ(X:Y:Z) = (conj(X)*PSI_X : conj(Y)*PSI_Y : conj(Z)). + */ + public function psi(): self + { + if ($this->isIdentity()) { + return self::identity(); + } + $x2 = $this->x->conjugate()->mul(self::psiX()); + $y2 = $this->y->conjugate()->mul(self::psiY()); + $z2 = $this->z->conjugate(); + + return new self($x2, $y2, $z2); + } + + /** + * ψ² (psi squared) endomorphism. + * ψ²(x, y) = (x * PSI2_X, -y) + * In projective: (X*PSI2_X : -Y : Z) — no conjugation needed since PSI2_X ∈ Fp. + */ + public function psi2(): self + { + if ($this->isIdentity()) { + return self::identity(); + } + $x2 = $this->x->mul(self::psi2X()); + $y2 = $this->y->neg(); + + return new self($x2, $y2, $this->z); + } + + // ------------------------------------------------------------------------- + // Cofactor clearing via Bowe et al. efficient algorithm + // h_eff = (x² - x - 1)P + (x-1)ψ(P) + ψ²(2P) + // ------------------------------------------------------------------------- + + public function clearCofactor(): self + { + $x = gmp_init(self::BLS_X, 16); + + $t1 = $this->scalarMul($x)->neg(); // [-x]P + $t2 = $this->psi(); // ψ(P) + $t3 = $this->double(); // 2P + $t3 = $t3->psi2(); // ψ²(2P) + $t3 = $t3->sub($t2); // ψ²(2P) - ψ(P) + $t2 = $t1->add($t2); // [-x]P + ψ(P) + $t2 = $t2->scalarMul($x)->neg(); // -[x]([-x]P + ψ(P)) = [x²]P - [x]ψ(P) + $t3 = $t3->add($t2); // ψ²(2P) - ψ(P) + [x²]P - [x]ψ(P) + $t3 = $t3->sub($t1); // + [x]P (sub neg = add) + $Q = $t3->sub($this); // - P + + return $Q; + } + + // sub is just add(neg) + public function sub(self $other): self + { + return $this->add($other->neg()); + } + + // ------------------------------------------------------------------------- + // Convert to affine + // ------------------------------------------------------------------------- + + public function toAffine(): array // [Fp2 $x, Fp2 $y] + { + if ($this->isIdentity()) { + return [Fp2::zero(), Fp2::one()]; + } + $zinv = $this->z->inv(); + $zinv2 = $zinv->square(); + $zinv3 = $zinv2->mul($zinv); + + return [$this->x->mul($zinv2), $this->y->mul($zinv3)]; + } + + // ------------------------------------------------------------------------- + // Compressed serialization (ZCash encoding, 96 bytes) + // G2 x ∈ Fp2: encode as c1 || c0 (each 48 bytes), total 96 bytes + // ------------------------------------------------------------------------- + + public function toCompressedBytes(): string + { + if ($this->isIdentity()) { + $bytes = str_repeat("\x00", 96); + $bytes[0] = chr(0xc0); // 0x80 (compressed) | 0x40 (infinity) + + return $bytes; + } + + [$ax, $ay] = $this->toAffine(); + + // Fp2 serialization: c1 (high 48 bytes) then c0 (low 48 bytes) + $bytes = $ax->c1->toBytes().$ax->c0->toBytes(); // 96 bytes, top 3 bits of first byte are 0 + + // Bit 7 (0x80): compressed flag + $bytes[0] = chr(ord($bytes[0]) | 0x80); + + // Bit 5 (0x20): sort/sign flag — determined by y, not x + // ZCash: if y.c1 != 0 then sign = (y.c1 > (p-1)/2) else sign = (y.c0 > (p-1)/2) + $signFp = $ay->c1->isZero() ? $ay->c0 : $ay->c1; + if ($signFp->isNegative()) { + $bytes[0] = chr(ord($bytes[0]) | 0x20); + } + + return $bytes; + } + + /** + * Lazily compute and cache the three Frobenius constants. + * base = 1/(1+u) in Fp2 = ((p+1)/2, (p-1)/2) + * PSI_X = base^((p-1)/3) + * PSI_Y = base^((p-1)/2) + * PSI2_X = base^((p²-1)/3). + */ + private static function initPsiConstants(): void + { + if (self::$psiX !== null) { + return; + } + $p = Fp::prime(); + $inv2 = gmp_div(gmp_add($p, gmp_init(1)), gmp_init(2)); // (p+1)/2 = mod-inverse of 2 + $base = new Fp2(new Fp($inv2), new Fp(gmp_sub($p, $inv2))); + + $p1 = gmp_sub($p, gmp_init(1)); + self::$psiX = $base->pow(gmp_div($p1, gmp_init(3))); + self::$psiY = $base->pow(gmp_div($p1, gmp_init(2))); + + $p2 = gmp_mul($p, $p); + $p2m1 = gmp_sub($p2, gmp_init(1)); + self::$psi2X = $base->pow(gmp_div($p2m1, gmp_init(3))); + } + + private static function psiX(): Fp2 + { + self::initPsiConstants(); + + return self::$psiX; + } + + private static function psiY(): Fp2 + { + self::initPsiConstants(); + + return self::$psiY; + } + + private static function psi2X(): Fp2 + { + self::initPsiConstants(); + + return self::$psi2X; + } +} diff --git a/src/BLS/EIP2333.php b/src/BLS/EIP2333.php new file mode 100644 index 0000000..1ed8dad --- /dev/null +++ b/src/BLS/EIP2333.php @@ -0,0 +1,132 @@ + 0 + $this->value = $v; + } + + // ------------------------------------------------------------------------- + // Constructors + // ------------------------------------------------------------------------- + + public static function fromHex(string $hex): self + { + return new self(gmp_init($hex, 16)); + } + + public static function fromInt(int $n): self + { + return new self(gmp_init($n)); + } + + public static function zero(): self + { + return new self(gmp_init(0)); + } + + public static function one(): self + { + return new self(gmp_init(1)); + } + + public static function prime(): GMP + { + if (self::$prime === null) { + self::$prime = gmp_init(self::P_HEX, 16); + } + + return self::$prime; + } + + public static function order(): GMP + { + if (self::$order === null) { + self::$order = gmp_init(self::R_HEX, 16); + } + + return self::$order; + } + + // ------------------------------------------------------------------------- + // Arithmetic + // ------------------------------------------------------------------------- + + public function add(self $other): self + { + return new self(gmp_add($this->value, $other->value)); + } + + public function sub(self $other): self + { + $r = gmp_sub($this->value, $other->value); + if (gmp_sign($r) < 0) { + $r = gmp_add($r, self::prime()); + } + + return new self($r); + } + + public function mul(self $other): self + { + return new self(gmp_mul($this->value, $other->value)); + } + + public function square(): self + { + return new self(gmp_pow($this->value, 2)); + } + + public function neg(): self + { + if (gmp_sign($this->value) === 0) { + return self::zero(); + } + + return new self(gmp_sub(self::prime(), $this->value)); + } + + public function inv(): self + { + $inv = gmp_invert($this->value, self::prime()); + if ($inv === false) { + throw new \RuntimeException('Fp: element has no inverse (is zero)'); + } + + return new self($inv); + } + + public function pow(GMP $exp): self + { + return new self(gmp_powm($this->value, $exp, self::prime())); + } + + // ------------------------------------------------------------------------- + // Predicates + // ------------------------------------------------------------------------- + + public function isZero(): bool + { + return gmp_sign($this->value) === 0; + } + + public function equals(self $other): bool + { + return gmp_cmp($this->value, $other->value) === 0; + } + + /** sgn0: returns true if value is odd (used for hash-to-curve SWU) */ + public function isOdd(): bool + { + return gmp_testbit($this->value, 0); + } + + /** True if value > (p-1)/2 (used for ZCash compressed point sign bit) */ + public function isNegative(): bool + { + // p is odd, so (p-1)/2 = p >> 1 in integer arithmetic + return gmp_cmp($this->value, gmp_div(self::prime(), 2)) > 0; + } + + // ------------------------------------------------------------------------- + // Serialization + // ------------------------------------------------------------------------- + + /** Returns 48-byte big-endian representation */ + public function toBytes(): string + { + $hex = str_pad(gmp_strval($this->value, 16), 96, '0', STR_PAD_LEFT); + + return hex2bin($hex); + } +} diff --git a/src/BLS/Fields/Fp2.php b/src/BLS/Fields/Fp2.php new file mode 100644 index 0000000..94f53bd --- /dev/null +++ b/src/BLS/Fields/Fp2.php @@ -0,0 +1,176 @@ +c0 = $c0; + $this->c1 = $c1; + } + + // ------------------------------------------------------------------------- + // Constructors + // ------------------------------------------------------------------------- + + public static function fromInts(int $c0, int $c1): self + { + return new self(Fp::fromInt($c0), Fp::fromInt($c1)); + } + + public static function fromHex(string $c0hex, string $c1hex): self + { + return new self(Fp::fromHex($c0hex), Fp::fromHex($c1hex)); + } + + public static function zero(): self + { + return new self(Fp::zero(), Fp::zero()); + } + + public static function one(): self + { + return new self(Fp::one(), Fp::zero()); + } + + // ------------------------------------------------------------------------- + // Arithmetic + // ------------------------------------------------------------------------- + + public function add(self $other): self + { + return new self($this->c0->add($other->c0), $this->c1->add($other->c1)); + } + + public function sub(self $other): self + { + return new self($this->c0->sub($other->c0), $this->c1->sub($other->c1)); + } + + /** + * Karatsuba multiplication in Fp2. + * (a + b·u)(c + d·u) = (ac - bd) + (ad + bc)·u [since u²=-1]. + */ + public function mul(self $other): self + { + $ac = $this->c0->mul($other->c0); + $bd = $this->c1->mul($other->c1); + $c0 = $ac->sub($bd); + // (a+b)(c+d) - ac - bd = ad + bc + $c1 = $this->c0->add($this->c1)->mul($other->c0->add($other->c1))->sub($ac)->sub($bd); + + return new self($c0, $c1); + } + + public function mulInt(int $n): self + { + $s = Fp::fromInt($n); + + return new self($this->c0->mul($s), $this->c1->mul($s)); + } + + public function square(): self + { + // (a + b·u)² = (a²-b²) + 2ab·u + $a = $this->c0; + $b = $this->c1; + $c0 = $a->add($b)->mul($a->sub($b)); // (a+b)(a-b) = a²-b² + $c1 = $a->mul($b)->mul(Fp::fromInt(2)); + + return new self($c0, $c1); + } + + public function neg(): self + { + return new self($this->c0->neg(), $this->c1->neg()); + } + + /** Frobenius / conjugate: (a + b·u)* = a - b·u */ + public function conjugate(): self + { + return new self($this->c0, $this->c1->neg()); + } + + public function inv(): self + { + // 1/(a + b·u) = (a - b·u) / (a² + b²) + $norm = $this->c0->square()->add($this->c1->square()); // a² + b² + $invNorm = $norm->inv(); + + return new self($this->c0->mul($invNorm), $this->c1->neg()->mul($invNorm)); + } + + /** + * Exponentiation by a large GMP integer. + */ + public function pow(GMP $exp): self + { + $result = self::one(); + $base = $this; + $e = gmp_abs($exp); + while (gmp_cmp($e, gmp_init(0)) > 0) { + if (gmp_testbit($e, 0)) { + $result = $result->mul($base); + } + $base = $base->square(); + $e = gmp_div($e, gmp_init(2)); + } + + return $result; + } + + // ------------------------------------------------------------------------- + // Predicates + // ------------------------------------------------------------------------- + + public function isZero(): bool + { + return $this->c0->isZero() && $this->c1->isZero(); + } + + public function equals(self $other): bool + { + return $this->c0->equals($other->c0) && $this->c1->equals($other->c1); + } + + /** + * sgn0_m_eq_2 from RFC 9380: sign of Fp2 element. + * Returns c0's parity unless c0==0, then c1's parity. + */ + public function isOdd(): bool + { + if (! $this->c0->isZero()) { + return $this->c0->isOdd(); + } + + return $this->c1->isOdd(); + } + + public static function cmov(self $a, self $b, bool $condition): self + { + return $condition ? $b : $a; + } + + // ------------------------------------------------------------------------- + // Serialization (96 bytes: c1 first 48 bytes, c0 last 48 bytes) + // G2 compressed: 96 bytes per coordinate pair, two pairs = 192 bytes total + // ------------------------------------------------------------------------- + + public function toBytes(): string + { + return $this->c1->toBytes().$this->c0->toBytes(); + } +} diff --git a/src/BLS/HashToCurve/G2HashToCurve.php b/src/BLS/HashToCurve/G2HashToCurve.php new file mode 100644 index 0000000..9866d5b --- /dev/null +++ b/src/BLS/HashToCurve/G2HashToCurve.php @@ -0,0 +1,380 @@ +add($q1)->clearCofactor(); + } + + // ========================================================================= + // expand_message_xmd (RFC 9380 §5.3.1, SHA-256 variant) + // ========================================================================= + + private static function expandMessageXmd(string $msg, string $dst, int $lenInBytes): string + { + $ell = (int) ceil($lenInBytes / self::B_IN_BYTES); // = 8 for 256 bytes + $dstPrime = $dst.chr(strlen($dst)); + $zPad = str_repeat("\x00", self::R_IN_BYTES); + $libStr = chr(($lenInBytes >> 8) & 0xff).chr($lenInBytes & 0xff); + + $b0 = hash('sha256', $zPad.$msg.$libStr."\x00".$dstPrime, true); + $b = []; + $b[0] = hash('sha256', $b0."\x01".$dstPrime, true); + + for ($i = 1; $i < $ell; $i++) { + $b[$i] = hash('sha256', self::strxor($b0, $b[$i - 1]).chr($i + 1).$dstPrime, true); + } + + return substr(implode('', $b), 0, $lenInBytes); + } + + private static function strxor(string $a, string $b): string + { + $out = ''; + $len = strlen($a); + for ($i = 0; $i < $len; $i++) { + $out .= chr(ord($a[$i]) ^ ord($b[$i])); + } + + return $out; + } + + // ========================================================================= + // hash_to_field: 256 uniform bytes → two Fp2 elements + // Layout: [e0_c0 (64B), e0_c1 (64B), e1_c0 (64B), e1_c1 (64B)] + // ========================================================================= + + /** + * @return Fp2[] [u0, u1] + */ + private static function uniformBytesToFp2Pair(string $bytes, int $L): array + { + // m=2 extension, count=2 elements + // offset = L * (j + i * m) + // e0: j=0 → offset 0, j=1 → offset 64 + // e1: j=0 → offset 128, j=1 → offset 192 + $p = Fp::prime(); + $u0 = new Fp2( + new Fp(gmp_mod(gmp_init(bin2hex(substr($bytes, 0, $L)), 16), $p)), + new Fp(gmp_mod(gmp_init(bin2hex(substr($bytes, $L, $L)), 16), $p)) + ); + $u1 = new Fp2( + new Fp(gmp_mod(gmp_init(bin2hex(substr($bytes, 2 * $L, $L)), 16), $p)), + new Fp(gmp_mod(gmp_init(bin2hex(substr($bytes, 3 * $L, $L)), 16), $p)) + ); + + return [$u0, $u1]; + } + + // ========================================================================= + // SWU map: Fp2 element → affine point on isogenous E' + // Then apply the 3-isogeny to land on actual G2 curve E. + // ========================================================================= + + private static function mapToCurveG2(Fp2 $u): G2 + { + // SWU curve parameters + // A' = 240·u + $A = Fp2::fromInts(0, 240); + // B' = 1012 + 1012·u + $B = Fp2::fromInts(1012, 1012); + // Z = -(2 + u) = (p-2) + (p-1)·u + $p = Fp::prime(); + $Z = new Fp2(new Fp(gmp_sub($p, gmp_init(2))), new Fp(gmp_sub($p, gmp_init(1)))); + $F1 = Fp2::one(); + + // RFC 9380 §6.6.2 Simplified SWU, 25 steps (noble-curves numbering): + // prettier-ignore + $tv1 = $u->square(); // 1. tv1 = u² + $tv1 = $Z->mul($tv1); // 2. tv1 = Z * tv1 + $tv2 = $tv1->square(); // 3. tv2 = tv1² + $tv2 = $tv2->add($tv1); // 4. tv2 = tv2 + tv1 + $tv3 = $tv2->add($F1); // 5. tv3 = tv2 + 1 + $tv3 = $B->mul($tv3); // 6. tv3 = B * tv3 + // 7. tv4 = CMOV(Z, -tv2, tv2 != 0) + $tv4 = Fp2::cmov($Z, $tv2->neg(), ! $tv2->isZero()); + $tv4 = $A->mul($tv4); // 8. tv4 = A * tv4 + $tv2 = $tv3->square(); // 9. tv2 = tv3² + $tv6 = $tv4->square(); // 10. tv6 = tv4² + $tv5 = $A->mul($tv6); // 11. tv5 = A * tv6 + $tv2 = $tv2->add($tv5); // 12. tv2 = tv2 + tv5 + $tv2 = $tv2->mul($tv3); // 13. tv2 = tv2 * tv3 + $tv6 = $tv6->mul($tv4); // 14. tv6 = tv6 * tv4 + $tv5 = $B->mul($tv6); // 15. tv5 = B * tv6 + $tv2 = $tv2->add($tv5); // 16. tv2 = tv2 + tv5 + $x = $tv1->mul($tv3); // 17. x = tv1 * tv3 + + // 18. (is_gx1_square, y1) = sqrt_ratio(tv2, tv6) + ['isValid' => $isValid, 'value' => $y1] = self::sqrtRatio($tv2, $tv6); + + $y = $tv1->mul($u); // 19. y = tv1 * u (= Z·u³ * y_coeff) + $y = $y->mul($y1); // 20. y = y * y1 + + $x = Fp2::cmov($x, $tv3, $isValid); // 21. x = CMOV(x, tv3, is_gx1_square) + $y = Fp2::cmov($y, $y1, $isValid); // 22. y = CMOV(y, y1, is_gx1_square) + + // 23. e1 = (sgn0(u) == sgn0(y)) + $e1 = ($u->isOdd() === $y->isOdd()); + // 24. y = CMOV(-y, y, e1) + $y = Fp2::cmov($y->neg(), $y, $e1); + + // 25. x = x / tv4 + $x = $x->mul($tv4->inv()); + + // Apply 3-isogeny to get point on actual G2 curve + [$xi, $yi] = self::applyIsogeny($x, $y); + + // Return as Jacobian G2 point (Z=1) + return new G2($xi, $yi, Fp2::one()); + } + + // ========================================================================= + // RFC 9380 Appendix F.2.1.2 — sqrt_ratio for Fp2 (q ≡ 9 mod 16, c1=3) + // Returns { isValid, value } where value = sqrt(u/v) if QR, else sqrt(Z·u/v) + // ========================================================================= + + /** + * @return array{isValid: bool, value: Fp2} + */ + private static function sqrtRatio(Fp2 $u, Fp2 $v): array + { + [$c6, $c7] = self::swuPrecompute(); + + $c5 = gmp_init(4); // 2^(c1-1) = 4 + $c3 = self::swuC3(); + + // Steps 1-16 + $tv1 = $c6; // 1 + $tv2 = self::fp2Pow7($v); // 2. v^7 + $tv3 = $tv2->square()->mul($v); // 3-4. v^14 * v = v^15 + $tv5 = $u->mul($tv3); // 5. u * v^15 + $tv5 = $tv5->pow($c3); // 6. (u * v^15)^c3 + $tv5 = $tv5->mul($tv2); // 7. * v^7 + $tv2 = $tv5->mul($v); // 8. + $tv3 = $tv5->mul($u); // 9. + $tv4 = $tv3->mul($tv2); // 10. + $tv5 = $tv4->pow($c5); // 11. tv4^4 + $isQR = $tv5->equals(Fp2::one()); // 12. + $tv2 = $tv3->mul($c7); // 13. + $tv5 = $tv4->mul($tv1); // 14. tv4 * c6 + $tv3 = Fp2::cmov($tv2, $tv3, $isQR); // 15. + $tv4 = Fp2::cmov($tv5, $tv4, $isQR); // 16. + + // Steps 17-26: loop i = c1 downto 2 (i.e., i = 3 then i = 2) + for ($i = 3; $i >= 2; $i--) { + // tv5 = 2^(i-2): for i=3 → 2, for i=2 → 1 + $powExp = ($i === 3) ? 2 : 1; + $tvv5 = ($powExp === 2) ? $tv4->square() : $tv4; // tv4^powExp + $e1 = $tvv5->equals(Fp2::one()); // 21. + $tv2 = $tv3->mul($tv1); // 22. + $tv1 = $tv1->square(); // 23. + $tvv5 = $tv4->mul($tv1); // 24. + $tv3 = Fp2::cmov($tv2, $tv3, $e1); // 25. + $tv4 = Fp2::cmov($tvv5, $tv4, $e1); // 26. + } + + $isValid = ! $v->isZero() && ($isQR || $u->isZero()); + + return ['isValid' => $isValid, 'value' => $tv3]; + } + + /** Fp2^7 via binary method (3 squarings + 3 muls) */ + private static function fp2Pow7(Fp2 $v): Fp2 + { + $v2 = $v->square(); // v² + $v4 = $v2->square(); // v⁴ + + return $v4->mul($v2)->mul($v); // v⁶ * v = v⁷ + } + + // ========================================================================= + // Precomputation of sqrtRatio constants c6 and c7 (lazily cached) + // c1 = 3, q = p², c2 = (q-1)/8, c3 = (c2-1)/2 + // c6 = Z^c2, c7 = Z^((c2+1)/2) + // ========================================================================= + + /** @return Fp2[] [c6, c7] */ + private static function swuPrecompute(): array + { + if (self::$swuC6 !== null) { + return [self::$swuC6, self::$swuC7]; + } + + $p = Fp::prime(); + $q = gmp_mul($p, $p); // q = p² + $q1 = gmp_sub($q, gmp_init(1)); // q - 1 + $c2 = gmp_div($q1, gmp_init(8)); // (q-1) / 8 + + // Z = -(2 + u) = (p-2) + (p-1)·u + $Z = new Fp2(new Fp(gmp_sub($p, gmp_init(2))), new Fp(gmp_sub($p, gmp_init(1)))); + + self::$swuC6 = $Z->pow($c2); + self::$swuC7 = $Z->pow(gmp_div(gmp_add($c2, gmp_init(1)), gmp_init(2))); + + return [self::$swuC6, self::$swuC7]; + } + + private static function swuC3(): \GMP + { + static $c3 = null; + if ($c3 === null) { + $p = Fp::prime(); + $q = gmp_mul($p, $p); + $c2 = gmp_div(gmp_sub($q, gmp_init(1)), gmp_init(8)); + $c3 = gmp_div(gmp_sub($c2, gmp_init(1)), gmp_init(2)); + } + + return $c3; + } + + // ========================================================================= + // 3-isogeny: E' → G2 curve E (rational map via Horner evaluation) + // ========================================================================= + + /** @return Fp2[] [x, y] */ + private static function applyIsogeny(Fp2 $x, Fp2 $y): array + { + $xn = self::horner(self::ISO_XN, $x); + $xd = self::horner(self::ISO_XD, $x); + $yn = self::horner(self::ISO_YN, $x); + $yd = self::horner(self::ISO_YD, $x); + + $xi = $xn->mul($xd->inv()); + $yi = $y->mul($yn->mul($yd->inv())); + + return [$xi, $yi]; + } + + /** + * Horner evaluation of a polynomial at x. + * Coefficients in ascending order [k0, k1, ..., kd] are reversed for Horner. + * Result: k0 + k1*x + ... + kd*x^d = horner([kd,...,k1,k0], x). + */ + private static function horner(array $ascCoeffs, Fp2 $x): Fp2 + { + $coeffs = array_reverse( + array_map(function ($pair) { + // '0' is falsy in PHP so use explicit comparison + $c0 = ($pair[0] !== '' && $pair[0] !== null) ? $pair[0] : '0'; + $c1 = ($pair[1] !== '' && $pair[1] !== null) ? $pair[1] : '0'; + + return Fp2::fromHex($c0, $c1); + }, $ascCoeffs) + ); + $acc = $coeffs[0]; + for ($i = 1, $n = count($coeffs); $i < $n; $i++) { + $acc = $acc->mul($x)->add($coeffs[$i]); + } + + return $acc; + } +} diff --git a/src/BLS/ProofOfPossession.php b/src/BLS/ProofOfPossession.php new file mode 100644 index 0000000..2602315 --- /dev/null +++ b/src/BLS/ProofOfPossession.php @@ -0,0 +1,96 @@ +scalarMul($scalar)->toHex(); + } + + /** + * Builds the Proof of Possession for a given private key. + * + * PoP = Sign(sk, Hash_G2(pk)) where Hash_G2 hashes the G1 public key bytes + * to a G2 point under POP_DST, then the G2 point is "signed" by multiplying + * by the private key scalar. + * + * @param string $privateKeyBytes 32-byte raw private key + * @throws InvalidArgumentException if the key is not exactly 32 bytes or is the zero scalar + * @return array{pk: string, pop: string} hex-encoded G1 pk (96 chars) and G2 pop (192 chars) + */ + public static function buildProofOfPossession(string $privateKeyBytes): array + { + if (strlen($privateKeyBytes) !== 32) { + throw new InvalidArgumentException( + 'BLS secret key must be exactly 32 bytes, got '.strlen($privateKeyBytes) + ); + } + + $sk = gmp_init(bin2hex($privateKeyBytes), 16); + + if (gmp_sign($sk) === 0) { + throw new InvalidArgumentException('BLS secret key must not be zero'); + } + + // G1 public key: [sk] * G1 + $pk = G1::generator()->scalarMul($sk)->toCompressedBytes(); + + // Hash pk bytes to G2 under POP_DST + $messagePoint = G2HashToCurve::hashToG2($pk, self::POP_DST); + + // Sign: PoP = [sk] * hash(pk) + $pop = $messagePoint->scalarMul($sk)->toCompressedBytes(); + + return [ + 'pk' => bin2hex($pk), + 'pop' => bin2hex($pop), + ]; + } + + /** + * Convenience: derive private key from mnemonic and build PoP. + * + * @return array{pk: string, pop: string} + */ + public static function fromMnemonic(string $mnemonic): array + { + return self::buildProofOfPossession(self::deriveBlsPrivateKey($mnemonic)); + } +} diff --git a/tests/Unit/BLS/EIP2333Test.php b/tests/Unit/BLS/EIP2333Test.php new file mode 100644 index 0000000..0dd8ffc --- /dev/null +++ b/tests/Unit/BLS/EIP2333Test.php @@ -0,0 +1,19 @@ +toBe(EIP2333_EXPECTED_SK); +}); + +it('produces different private keys for different mnemonics', function () { + $a = EIP2333::deriveBlsPrivateKey(EIP2333_MNEMONIC); + $b = EIP2333::deriveBlsPrivateKey('zoo zoo zoo zoo zoo zoo zoo zoo zoo zoo zoo wrong'); + expect(bin2hex($a))->not->toBe(bin2hex($b)); +}); diff --git a/tests/Unit/BLS/ProofOfPossessionTest.php b/tests/Unit/BLS/ProofOfPossessionTest.php new file mode 100644 index 0000000..7bcefd3 --- /dev/null +++ b/tests/Unit/BLS/ProofOfPossessionTest.php @@ -0,0 +1,102 @@ +toBe(96) + ->and(strlen($result['pop']))->toBe(192); +}); + +it('is deterministic for the same secret key', function () { + $a = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_A_HEX)); + $b = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_A_HEX)); + expect($a['pk'])->toBe($b['pk']) + ->and($a['pop'])->toBe($b['pop']); +}); + +it('produces different pk and pop for different secret keys', function () { + $a = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_A_HEX)); + $b = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_B_HEX)); + expect($a['pk'])->not->toBe($b['pk']) + ->and($a['pop'])->not->toBe($b['pop']); +}); + +it('pk matches deriveBlsPublicKey for the same secret key', function () { + $result = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_A_HEX)); + $expected = ProofOfPossession::privateKeyToPublicKey(hex2bin(POP_SK_A_HEX)); + expect($result['pk'])->toBe($expected); +}); + +it('matches the pinned test vector for SK_A', function () { + $result = ProofOfPossession::buildProofOfPossession(hex2bin(POP_SK_A_HEX)); + expect($result['pk'])->toBe(EXPECTED_PK_A) + ->and($result['pop'])->toBe(EXPECTED_POP_A); +}); + +it('throws on a secret key of wrong length', function () { + expect(fn () => ProofOfPossession::buildProofOfPossession(str_repeat("\x00", 31)))->toThrow(InvalidArgumentException::class) + ->and(fn () => ProofOfPossession::buildProofOfPossession(str_repeat("\x00", 33)))->toThrow(InvalidArgumentException::class) + ->and(fn () => ProofOfPossession::buildProofOfPossession(''))->toThrow(InvalidArgumentException::class); +}); + +it('throws on the zero secret key', function () { + expect(fn () => ProofOfPossession::buildProofOfPossession(str_repeat("\x00", 32)))->toThrow(InvalidArgumentException::class); +}); + +// ------------------------------------------------------------------------- +// deriveBlsPublicKey +// ------------------------------------------------------------------------- + +it('returns a 96-character hex string (48-byte G1)', function () { + $pk = ProofOfPossession::deriveBlsPublicKey(POP_PASSPHRASE); + expect(strlen($pk))->toBe(96); +}); + +it('is deterministic for the same passphrase', function () { + $pk = ProofOfPossession::deriveBlsPublicKey(POP_PASSPHRASE); + expect($pk)->toBe(EXPECTED_MNEMONIC_PK); +}); + +it('matches the pinned pop for the same passphrase', function () { + $result = ProofOfPossession::fromMnemonic(POP_PASSPHRASE); + expect($result['pk'])->toBe(EXPECTED_MNEMONIC_PK) + ->and($result['pop'])->toBe(EXPECTED_MNEMONIC_POP); +}); + +// ------------------------------------------------------------------------- +// Table-driven derivation vectors +// Each entry: [mnemonic, private key (hex), public key (hex), proof of possession (hex)] +// ------------------------------------------------------------------------- + +$blsDataset = []; +foreach (json_decode(file_get_contents(__DIR__.'/../../fixtures/bls-keys.json'), true) as $lang => $vectors) { + foreach ($vectors as $i => $vector) { + $blsDataset["{$lang} #{$i}"] = array_values($vector); + } +} + +it('derives correct public key, private key, and pop for the given mnemonic', function (string $mnemonic, string $expectedSk, string $expectedPk, string $expectedPop) { + expect(bin2hex(EIP2333::deriveBlsPrivateKey($mnemonic)))->toBe($expectedSk); + + $result = ProofOfPossession::fromMnemonic($mnemonic); + expect($result['pk'])->toBe(substr($expectedPk, 2)) + ->and($result['pop'])->toBe(substr($expectedPop, 2)); +})->with($blsDataset); diff --git a/tests/fixtures/bls-keys.json b/tests/fixtures/bls-keys.json new file mode 100644 index 0000000..7c97867 --- /dev/null +++ b/tests/fixtures/bls-keys.json @@ -0,0 +1,322 @@ +{ + "czech": [ + { + "mnemonic": "najisto kazivost vpravo namluvit exkurze lord hladovka svoboda obejmout ukazatel pustina srpen metr ohrozit autobus pobyt omeleta bledule cizost petrolej nikl celkem jelen poezie", + "validatorPrivateKey": "6521a909bed1652044b99809b0a3c6999a9bd3a9c760e27e30fbda5931fa76a5", + "validatorPublicKey": "0x86e47e024116003fcf4a6b9150de36964d6590eb11b0f4a1607b89e11d99a4f8609e234eb8185ecf2c77edade1c95309", + "validatorPop": "0xae1f97166e6e444101184825116f03d1607d4387fcd3c0bc71c4a3d125858a8f236d948cab97c6bc1f9f8b6c487ed8f31439ec47e16321e090989bd20b9a4bab069a807935b2c141c221a04422a8ebe2fe84da839fc10dd665db170e24692069" + }, + { + "mnemonic": "louskat seshora hledat zahrada buvol vyrazit opravdu munice strom vyhledat barva vyrazit prorok lord manko hojnost zmizet dovozce lidojed bojovat nikdy hodiny spousta manko", + "validatorPrivateKey": "43aafbb031406eec46f79604a5615806c0880e0d8b2d6e722f03d7eba86db4e6", + "validatorPublicKey": "0x875032037e45a884e58629825c57d9e381e45ed0df3250b324aaf767fbc5a47a69a06a89af8998ed90a5c061e4cfbe20", + "validatorPop": "0xb4d356027006865734b10e05d4b943f3cde3628ca9763f719434a8d99e6f3ce5fae367c9806bfb7e9cdd5784f1b89afc160828fa4ff74ad0496453b7a83dfebf657ac016e601454146458c88fb7b4a5f123d18677f4200cdfa83eb63eee9100a" + }, + { + "mnemonic": "pastelka makak panna boubel pazourek zimnice louka prodej videohra chrlit referent smrk bulva varan smilstvo spis vztah potvora postava astma vystavit rampouch odpor duha", + "validatorPrivateKey": "3f941bba361aa5273e560cd4de20e747586e430efcb27fe14556f442808a477b", + "validatorPublicKey": "0x9684cc2ca48aca7f5827d1bdc33c1e6c8986c390309855221be1a74695986f9d7a9f8fa56e86027ab3e332b6f2a7a34e", + "validatorPop": "0x84b871933fe3a610000e581aa3d77c4d168ebc64691cf7ac702541b4eab54b5d0ac790c73e7675e52535274734a5e71b11f2bb16dcc8d366575450bedef56e32e1d4cf584f2795cdb2d4ea773a8931db739905ef91c5bb9db85a63848d3a23cf" + }, + { + "mnemonic": "dort okno zajatec tykev komando mlha lucifer astma malina puklina tendence starosta bacil baret mobil odjet propad zjemnit obava petrolej mezera baculka piha hadr", + "validatorPrivateKey": "3f09d1651e7a6d1d5f869db241fc94e578b1f3926977985ac96206225e047a3a", + "validatorPublicKey": "0xa774065223115fda52052087df0e792a17ba5ae3a1dddddafcd06c347f5905ac9dba5873e24df920c772d9ebe6a1548c", + "validatorPop": "0x8dda28ddf6c5589afc42c6cd3cf497e4f6da95343fafb1278154350338528cc624a3389bcc612bc7ecdc6a7fb2c6f4d511a3904170e4ca9fc371949fdbdbec3186dde06fc18644ba41c758a79f3aa4a55c544f550d56799d5f37434a71f21b4b" + }, + { + "mnemonic": "levitace truhlice otop ledvina buchta hala madlo jinoch doplnit baterka podzim dareba sluha cejn objasnit zastavit meditace mezera ulovit osten znalost exkurze plivat lucifer", + "validatorPrivateKey": "48bf069ca2917eeeee612e6fd50a1f6fb2c28af9167ee04cdd03c21240336d6d", + "validatorPublicKey": "0x858055545004fc6ef228bb4f23e2db530949d606f5e91620752a92d330dd59ef455bcb4214a64817adeb543aa2ea1287", + 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