sirius-press/plugins/sirius-press-core/includes/class-sp-secp256k1.php

<?php
/**
 * secp256k1 in pure PHP: recoverable message signatures, nothing else.
 *
 * Sirius Press replaces "prove you can read this mailbox" with "prove you hold
 * this key", so signature verification sits on the login path and cannot be
 * optional. Requiring a native secp256k1 extension would rule out most of the
 * shared hosts this fork is meant to run on, so the curve lives here.
 *
 * Scope is deliberately narrow — the two operations the fork actually needs:
 *
 *   sign_recoverable()  produce the 65-byte [flag|r|s] blob the BNS gateway
 *                       and the Sirius portal already speak.
 *   recover()           pull the compressed public key back out of one, so a
 *                       login signature can be turned into a CashAddress and
 *                       compared to the user's stored address.
 *
 * Point arithmetic is Jacobian, so a scalar multiply costs exactly one modular
 * inversion at the end instead of one per bit. That is what keeps the BCMath
 * fallback in the "noticeable pause" range rather than the "gateway timeout"
 * range.
 *
 * Signature format matches Argus/src/lib/wallet-web.js BuiltInWallet::signMessage
 * byte for byte: flag = 27 + 4 + recovery_id, then r, then s, all big-endian.
 * The +4 says "the public key was compressed"; the gateway recovers the id
 * back out with (flag - 27) & 3.
 *
 * @package SiriusPress
 */

defined( 'ABSPATH' ) || defined( 'SP_CLI' ) || exit;

require_once __DIR__ . '/class-sp-bn.php';

final class SP_Secp256k1 {

	const P  = 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f';
	const N  = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
	const GX = '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798';
	const GY = '483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8';

	/** Memoised curve constants, per request. */
	private static $c = null;

	private static function consts() {
		if ( null === self::$c ) {
			self::$c = array(
				'p'     => SP_BN::from_hex( self::P ),
				'n'     => SP_BN::from_hex( self::N ),
				'gx'    => SP_BN::from_hex( self::GX ),
				'gy'    => SP_BN::from_hex( self::GY ),
				'zero'  => SP_BN::from_int( 0 ),
				'one'   => SP_BN::from_int( 1 ),
				'two'   => SP_BN::from_int( 2 ),
				'three' => SP_BN::from_int( 3 ),
				'four'  => SP_BN::from_int( 4 ),
				'seven' => SP_BN::from_int( 7 ),
				'eight' => SP_BN::from_int( 8 ),
			);
			// n/2, the low-S boundary.
			self::$c['half_n'] = SP_BN::from_hex( '7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0' );
		}
		return self::$c;
	}

	// ------------------------------------------------------------- field ops

	private static function fadd( $a, $b ) {
		$c = self::consts();
		return SP_BN::mod( SP_BN::add( $a, $b ), $c['p'] );
	}

	private static function fsub( $a, $b ) {
		$c = self::consts();
		return SP_BN::mod( SP_BN::sub( $a, $b ), $c['p'] );
	}

	private static function fmul( $a, $b ) {
		$c = self::consts();
		return SP_BN::mod( SP_BN::mul( $a, $b ), $c['p'] );
	}

	// -------------------------------------------------- Jacobian point maths

	/** The point at infinity, in Jacobian coordinates (Z = 0). */
	private static function jinf() {
		$c = self::consts();
		return array( $c['one'], $c['one'], $c['zero'] );
	}

	private static function is_inf( $pt ) {
		return SP_BN::is_zero( $pt[2] );
	}

	/** Affine (x, y) into Jacobian with Z = 1. */
	private static function to_jacobian( $x, $y ) {
		$c = self::consts();
		return array( $x, $y, $c['one'] );
	}

	/** Jacobian back to affine: (X/Z^2, Y/Z^3). The one inversion. */
	private static function to_affine( $pt ) {
		$c = self::consts();
		if ( self::is_inf( $pt ) ) {
			return null;
		}
		$zi  = SP_BN::inv_mod( $pt[2], $c['p'] );
		$zi2 = self::fmul( $zi, $zi );
		$zi3 = self::fmul( $zi2, $zi );
		return array( self::fmul( $pt[0], $zi2 ), self::fmul( $pt[1], $zi3 ) );
	}

	/** Point doubling, a = 0 case (dbl-2009-l). */
	private static function jdouble( $pt ) {
		$c = self::consts();
		list( $x, $y, $z ) = $pt;
		if ( SP_BN::is_zero( $z ) || SP_BN::is_zero( $y ) ) {
			return self::jinf();
		}
		$a  = self::fmul( $x, $x );                                   // X^2
		$b  = self::fmul( $y, $y );                                   // Y^2
		$cc = self::fmul( $b, $b );                                   // Y^4
		$d  = self::fmul( $c['two'], self::fsub( self::fmul( self::fadd( $x, $b ), self::fadd( $x, $b ) ), self::fadd( $a, $cc ) ) );
		$e  = self::fmul( $c['three'], $a );
		$f  = self::fmul( $e, $e );
		$x3 = self::fsub( $f, self::fmul( $c['two'], $d ) );
		$y3 = self::fsub( self::fmul( $e, self::fsub( $d, $x3 ) ), self::fmul( $c['eight'], $cc ) );
		$z3 = self::fmul( self::fmul( $c['two'], $y ), $z );
		return array( $x3, $y3, $z3 );
	}

	/** Point addition, Jacobian + Jacobian (add-2007-bl). */
	private static function jadd( $p1, $p2 ) {
		$c = self::consts();
		if ( self::is_inf( $p1 ) ) {
			return $p2;
		}
		if ( self::is_inf( $p2 ) ) {
			return $p1;
		}
		list( $x1, $y1, $z1 ) = $p1;
		list( $x2, $y2, $z2 ) = $p2;

		$z1z1 = self::fmul( $z1, $z1 );
		$z2z2 = self::fmul( $z2, $z2 );
		$u1   = self::fmul( $x1, $z2z2 );
		$u2   = self::fmul( $x2, $z1z1 );
		$s1   = self::fmul( $y1, self::fmul( $z2, $z2z2 ) );
		$s2   = self::fmul( $y2, self::fmul( $z1, $z1z1 ) );

		if ( 0 === SP_BN::cmp( $u1, $u2 ) ) {
			return 0 === SP_BN::cmp( $s1, $s2 ) ? self::jdouble( $p1 ) : self::jinf();
		}

		$h  = self::fsub( $u2, $u1 );
		$i  = self::fmul( self::fmul( $c['two'], $h ), self::fmul( $c['two'], $h ) );
		$j  = self::fmul( $h, $i );
		$r  = self::fmul( $c['two'], self::fsub( $s2, $s1 ) );
		$v  = self::fmul( $u1, $i );
		$x3 = self::fsub( self::fsub( self::fmul( $r, $r ), $j ), self::fmul( $c['two'], $v ) );
		$y3 = self::fsub( self::fmul( $r, self::fsub( $v, $x3 ) ), self::fmul( $c['two'], self::fmul( $s1, $j ) ) );
		$z3 = self::fmul( self::fsub( self::fmul( self::fadd( $z1, $z2 ), self::fadd( $z1, $z2 ) ), self::fadd( $z1z1, $z2z2 ) ), $h );
		return array( $x3, $y3, $z3 );
	}

	/**
	 * Scalar multiply, left-to-right double-and-add.
	 *
	 * Not constant time. It does not need to be: every scalar multiplied here
	 * is either a public value (recovery) or a per-signature nonce on a host
	 * where the attacker able to time it can already read the private key off
	 * disk.
	 *
	 * @return array{0:mixed,1:mixed}|null Affine point, or null for infinity.
	 */
	private static function mul_point( $k, $px, $py ) {
		$c = self::consts();
		$k = SP_BN::mod( $k, $c['n'] );
		if ( SP_BN::is_zero( $k ) ) {
			return null;
		}
		$base = self::to_jacobian( $px, $py );
		$acc  = self::jinf();
		$bits = SP_BN::bits( $k );
		$len  = strlen( $bits );
		for ( $i = 0; $i < $len; $i++ ) {
			$acc = self::jdouble( $acc );
			if ( '1' === $bits[ $i ] ) {
				$acc = self::jadd( $acc, $base );
			}
		}
		return self::to_affine( $acc );
	}

	// ------------------------------------------------------------ public API

	/**
	 * Compressed public key for a private key.
	 *
	 * @param string $priv_bin 32 raw bytes.
	 * @return string 33 raw bytes, or '' if the key is out of range.
	 */
	public static function public_key( $priv_bin ) {
		$c = self::consts();
		$d = SP_BN::from_bin( $priv_bin );
		if ( SP_BN::is_zero( $d ) || SP_BN::cmp( $d, $c['n'] ) >= 0 ) {
			return '';
		}
		$pt = self::mul_point( $d, $c['gx'], $c['gy'] );
		return self::compress( $pt );
	}

	/** @param array|null $pt Affine point. */
	private static function compress( $pt ) {
		if ( null === $pt ) {
			return '';
		}
		return chr( SP_BN::is_odd( $pt[1] ) ? 0x03 : 0x02 ) . SP_BN::to_bin( $pt[0], 32 );
	}

	/**
	 * Sign a 32-byte digest, producing the 65-byte recoverable blob.
	 *
	 * Low-S normalised, so the same message and key always yield the same
	 * bytes and nothing downstream has to worry about malleability.
	 *
	 * @param string $digest   32 raw bytes (already hashed).
	 * @param string $priv_bin 32 raw bytes.
	 * @return string 65 raw bytes.
	 * @throws Exception When the key is out of range or the host has no bignum extension.
	 */
	public static function sign_recoverable( $digest, $priv_bin ) {
		if ( ! SP_BN::available() ) {
			throw new Exception( 'Sirius Press needs either the GMP or the BCMath PHP extension to sign.' );
		}
		if ( 32 !== strlen( $digest ) || 32 !== strlen( $priv_bin ) ) {
			throw new Exception( 'sign_recoverable expects a 32-byte digest and a 32-byte private key.' );
		}
		$c = self::consts();
		$d = SP_BN::from_bin( $priv_bin );
		if ( SP_BN::is_zero( $d ) || SP_BN::cmp( $d, $c['n'] ) >= 0 ) {
			throw new Exception( 'private key out of range' );
		}
		$z = SP_BN::mod( SP_BN::from_bin( $digest ), $c['n'] );

		foreach ( self::rfc6979_nonces( $digest, $priv_bin ) as $k ) {
			$pt = self::mul_point( $k, $c['gx'], $c['gy'] );
			if ( null === $pt ) {
				continue;
			}
			$r = SP_BN::mod( $pt[0], $c['n'] );
			if ( SP_BN::is_zero( $r ) ) {
				continue;
			}
			$s = SP_BN::mod(
				SP_BN::mul( SP_BN::inv_mod( $k, $c['n'] ), SP_BN::add( $z, SP_BN::mul( $r, $d ) ) ),
				$c['n']
			);
			if ( SP_BN::is_zero( $s ) ) {
				continue;
			}
			$recid = ( SP_BN::is_odd( $pt[1] ) ? 1 : 0 ) | ( SP_BN::cmp( $pt[0], $c['n'] ) >= 0 ? 2 : 0 );
			if ( SP_BN::cmp( $s, $c['half_n'] ) > 0 ) {
				$s      = SP_BN::sub( $c['n'], $s );
				$recid ^= 1;
			}
			return chr( 27 + 4 + $recid ) . SP_BN::to_bin( $r, 32 ) . SP_BN::to_bin( $s, 32 );
		}
		throw new Exception( 'could not find a valid signature nonce' );
	}

	/**
	 * Recover the compressed public key that produced a 65-byte signature.
	 *
	 * @param string $sig    65 raw bytes, [flag|r|s].
	 * @param string $digest 32 raw bytes.
	 * @return string 33 raw bytes, or '' when the signature is malformed or
	 *                does not correspond to any point on the curve.
	 */
	public static function recover( $sig, $digest ) {
		if ( ! SP_BN::available() || 65 !== strlen( $sig ) || 32 !== strlen( $digest ) ) {
			return '';
		}
		$c     = self::consts();
		$flag  = ord( $sig[0] );
		$recid = ( $flag - 27 ) & 3;
		$r     = SP_BN::from_bin( substr( $sig, 1, 32 ) );
		$s     = SP_BN::from_bin( substr( $sig, 33, 32 ) );
		if ( SP_BN::is_zero( $r ) || SP_BN::is_zero( $s )
			|| SP_BN::cmp( $r, $c['n'] ) >= 0 || SP_BN::cmp( $s, $c['n'] ) >= 0 ) {
			return '';
		}

		// x = r + (recid >> 1) * n, which is only on the curve for the
		// overflow cases the signer flagged.
		$x = $r;
		if ( $recid >= 2 ) {
			$x = SP_BN::add( $r, $c['n'] );
			if ( SP_BN::cmp( $x, $c['p'] ) >= 0 ) {
				return '';
			}
		}

		// y^2 = x^3 + 7; p ≡ 3 (mod 4) so the square root is a single powmod.
		$alpha = self::fadd( self::fmul( self::fmul( $x, $x ), $x ), $c['seven'] );
		$exp   = self::sqrt_exponent();
		$beta  = SP_BN::pow_mod( $alpha, $exp, $c['p'] );
		// Reject non-residues: if beta^2 != alpha there is no such point.
		if ( 0 !== SP_BN::cmp( self::fmul( $beta, $beta ), $alpha ) ) {
			return '';
		}
		$want_odd = ( $recid & 1 ) === 1;
		$y        = ( SP_BN::is_odd( $beta ) === $want_odd ) ? $beta : SP_BN::sub( $c['p'], $beta );

		// Q = r^-1 (sR - zG)
		$z    = SP_BN::mod( SP_BN::from_bin( $digest ), $c['n'] );
		$rinv = SP_BN::inv_mod( $r, $c['n'] );

		$sr = self::mul_point( $s, $x, $y );
		$zg = self::mul_point( SP_BN::mod( SP_BN::sub( $c['n'], $z ), $c['n'] ), $c['gx'], $c['gy'] );
		if ( null === $sr ) {
			return '';
		}
		$sum = null === $zg
			? self::to_jacobian( $sr[0], $sr[1] )
			: self::jadd( self::to_jacobian( $sr[0], $sr[1] ), self::to_jacobian( $zg[0], $zg[1] ) );
		$sum = self::to_affine( $sum );
		if ( null === $sum ) {
			return '';
		}
		$q = self::mul_point( $rinv, $sum[0], $sum[1] );
		return self::compress( $q );
	}

	/** (p + 1) / 4, precomputed as hex — the square-root exponent. */
	private static function sqrt_exponent() {
		return SP_BN::from_hex( '3fffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffff0c' );
	}

	// ---------------------------------------------------------------- nonces

	/**
	 * RFC 6979 deterministic nonces, yielded one at a time.
	 *
	 * Determinism matters here beyond tidiness: a PHP process on a shared host
	 * is exactly the place where a weak random source silently leaks the key
	 * across two signatures. Nothing in this path touches the system RNG.
	 *
	 * @return Generator
	 */
	private static function rfc6979_nonces( $digest, $priv_bin ) {
		$c  = self::consts();
		$h1 = $digest;
		// bits2octets(h1): reduce the digest mod n, re-pad to 32 bytes.
		$h1_oct = SP_BN::to_bin( SP_BN::mod( SP_BN::from_bin( $h1 ), $c['n'] ), 32 );

		$v = str_repeat( "\x01", 32 );
		$k = str_repeat( "\x00", 32 );

		$k = hash_hmac( 'sha256', $v . "\x00" . $priv_bin . $h1_oct, $k, true );
		$v = hash_hmac( 'sha256', $v, $k, true );
		$k = hash_hmac( 'sha256', $v . "\x01" . $priv_bin . $h1_oct, $k, true );
		$v = hash_hmac( 'sha256', $v, $k, true );

		for ( $attempt = 0; $attempt < 64; $attempt++ ) {
			$v   = hash_hmac( 'sha256', $v, $k, true );
			$cand = SP_BN::from_bin( $v );
			if ( ! SP_BN::is_zero( $cand ) && SP_BN::cmp( $cand, $c['n'] ) < 0 ) {
				yield $cand;
			}
			$k = hash_hmac( 'sha256', $v . "\x00", $k, true );
			$v = hash_hmac( 'sha256', $v, $k, true );
		}
	}
}