4a0b48588c
Aere Network public source. Everything here can be checked against the live chain (chain id 2800, https://rpc.aere.network). Scope note, stated up front rather than buried: consensus on chain 2800 is classical secp256k1 ECDSA QBFT. The post-quantum work in this repository is at the signature, precompile, account and transport layers. Nothing here makes the consensus post-quantum, and no document in it should be read as claiming so.
480 lines
22 KiB
Solidity
480 lines
22 KiB
Solidity
// SPDX-License-Identifier: MIT
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pragma solidity 0.8.23;
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/**
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* @title AereFalcon512Verifier, spec-complete NIST Falcon-512 signature verifier, on-chain
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* @notice A REAL, standalone Falcon-512 (FIPS 206 / NIST PQC round-3) signature
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* verifier that runs entirely on chain 2800. Given a public key, a
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* message, and a signature, it performs the full Falcon verification:
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*
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* 1. HashToPoint: SHAKE256(nonce || message) is streamed and
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* rejection-sampled into a challenge polynomial c in Z_q[x]/(x^512+1)
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* (q = 12289), exactly per the reference hash_to_point_vartime.
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* 2. Public-key decode: the 897-byte NIST public key (0x09 header + 512
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* coefficients packed at 14 bits each) is decoded to h.
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* 3. Signature decode: the compressed Gaussian encoding of s2 is decoded
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* (Falcon comp_decode: sign bit, 7 low bits, unary high bits).
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* 4. Recompute -s1 = s2*h - c in the ring (negacyclic convolution mod q),
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* then center coefficients into (-q/2, q/2].
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* 5. Norm check: accept iff ||(s1, s2)||^2 <= floor(beta^2) = 34034726,
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* the Falcon-512 acceptance bound.
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*
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* This is the actual lattice/hash cryptography, executed on-chain, not a
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* proof-of-a-proof. It is validated bit-for-bit against the OFFICIAL NIST
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* Falcon-512 Known-Answer-Test vectors (falcon512-KAT.rsp, SHA-256
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* dd75c946...b5cd, reproduced byte-for-byte from the round-3 reference):
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* real (pk, message, signature) triples verify true; tampered signatures
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* verify false.
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*
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* The chain's block gas limit is effectively unlimited, so the full
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* verification runs as an ordinary transaction; there is no trusted
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* prover and no off-chain step. Anyone can call verify() and get the same
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* accept/reject the reference C implementation produces.
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*/
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contract AereFalcon512VerifierHTP {
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// ----- Falcon-512 parameters -----
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uint256 public constant Q = 12289; // modulus
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uint256 public constant N = 512; // ring degree
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uint256 public constant L2BOUND = 34034726; // floor(beta^2), Falcon-512 acceptance bound
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uint256 internal constant HQ = 6144; // floor(q/2), centering threshold
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// Negacyclic NTT constants for Z_q[x]/(x^512+1), q = 12289:
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// PSI = primitive 1024th (2n-th) root of unity; W = PSI^2 (512th root)
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uint256 internal constant PSI = 49;
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uint256 internal constant PSI_INV = 1254;
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uint256 internal constant W = 2401; // PSI^2 mod q
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uint256 internal constant W_INV = 11813;
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uint256 internal constant N_INV = 12265; // 512^-1 mod q
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uint8 public constant PK_HEADER = 0x09; // 0x00 + logn, logn = 9
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uint8 public constant SIG_HEADER = 0x29; // 0x20 + logn, logn = 9 (NIST esig header)
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uint256 public constant NONCE_LEN = 40;
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// ----- recorded on-chain verification results (for state-changing calls) -----
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uint256 public verifyCount;
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bool public lastResult;
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event Verified(address indexed caller, bool result, uint256 index);
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// ==========================================================================
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// Keccak-f[1600] / SHAKE256
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// ==========================================================================
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/// @dev In-place Keccak-f[1600] permutation on a 25-lane state (one lane per
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/// 32-byte memory word, low 64 bits used). Written in assembly for gas:
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/// the naive array version cost ~1.26M gas per permutation. Validated
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/// against the FIPS 202 SHAKE256 KAT and the Falcon HashToPoint oracle.
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function _keccakf(uint64[25] memory st) internal view {
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assembly {
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function rol(x, n) -> r {
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r := and(0xffffffffffffffff, or(shl(n, x), shr(sub(64, n), x)))
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}
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let s := st
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let b := mload(0x40) // scratch (25 lanes), left above the free pointer
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let rc := add(b, 0x320) // 24 round constants after the scratch lanes
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// round constants
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mstore(add(rc, 0x000), 0x0000000000000001) mstore(add(rc, 0x020), 0x0000000000008082)
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mstore(add(rc, 0x040), 0x800000000000808a) mstore(add(rc, 0x060), 0x8000000080008000)
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mstore(add(rc, 0x080), 0x000000000000808b) mstore(add(rc, 0x0a0), 0x0000000080000001)
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mstore(add(rc, 0x0c0), 0x8000000080008081) mstore(add(rc, 0x0e0), 0x8000000000008009)
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mstore(add(rc, 0x100), 0x000000000000008a) mstore(add(rc, 0x120), 0x0000000000000088)
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mstore(add(rc, 0x140), 0x0000000080008009) mstore(add(rc, 0x160), 0x000000008000000a)
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mstore(add(rc, 0x180), 0x000000008000808b) mstore(add(rc, 0x1a0), 0x800000000000008b)
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mstore(add(rc, 0x1c0), 0x8000000000008089) mstore(add(rc, 0x1e0), 0x8000000000008003)
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mstore(add(rc, 0x200), 0x8000000000008002) mstore(add(rc, 0x220), 0x8000000000000080)
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mstore(add(rc, 0x240), 0x000000000000800a) mstore(add(rc, 0x260), 0x800000008000000a)
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mstore(add(rc, 0x280), 0x8000000080008081) mstore(add(rc, 0x2a0), 0x8000000000008080)
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mstore(add(rc, 0x2c0), 0x0000000080000001) mstore(add(rc, 0x2e0), 0x8000000080008008)
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for { let rnd := 0 } lt(rnd, 24) { rnd := add(rnd, 1) } {
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// ---- theta: column parities C[x] -> b[0..4] ----
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for { let x := 0 } lt(x, 5) { x := add(x, 1) } {
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let o := mul(x, 0x20)
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mstore(add(b, o),
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xor(xor(xor(xor(
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mload(add(s, o)),
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mload(add(s, add(o, 0xa0)))),
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mload(add(s, add(o, 0x140)))),
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mload(add(s, add(o, 0x1e0)))),
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mload(add(s, add(o, 0x280)))))
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}
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// D[x] = C[(x+4)%5] ^ rol(C[(x+1)%5],1) -> b[5..9]
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for { let x := 0 } lt(x, 5) { x := add(x, 1) } {
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let cm := mload(add(b, mul(mod(add(x, 4), 5), 0x20)))
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let cp := mload(add(b, mul(mod(add(x, 1), 5), 0x20)))
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mstore(add(b, add(0xa0, mul(x, 0x20))), xor(cm, rol(cp, 1)))
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}
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// apply D to state: lane (x + 5y) ^= D[x]
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for { let x := 0 } lt(x, 5) { x := add(x, 1) } {
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let d := mload(add(b, add(0xa0, mul(x, 0x20))))
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let o := mul(x, 0x20)
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mstore(add(s, o), xor(mload(add(s, o)), d))
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mstore(add(s, add(o, 0xa0)), xor(mload(add(s, add(o, 0xa0))), d))
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mstore(add(s, add(o, 0x140)), xor(mload(add(s, add(o, 0x140))), d))
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mstore(add(s, add(o, 0x1e0)), xor(mload(add(s, add(o, 0x1e0))), d))
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mstore(add(s, add(o, 0x280)), xor(mload(add(s, add(o, 0x280))), d))
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}
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// ---- rho + pi: b[piDest[i]] = rol(st[i], rho[i]) ----
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mstore(add(b, 0x000), rol(mload(add(s, 0x000)), 0))
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mstore(add(b, 0x140), rol(mload(add(s, 0x020)), 1))
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mstore(add(b, 0x280), rol(mload(add(s, 0x040)), 62))
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mstore(add(b, 0x0a0), rol(mload(add(s, 0x060)), 28))
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mstore(add(b, 0x1e0), rol(mload(add(s, 0x080)), 27))
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mstore(add(b, 0x200), rol(mload(add(s, 0x0a0)), 36))
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mstore(add(b, 0x020), rol(mload(add(s, 0x0c0)), 44))
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mstore(add(b, 0x160), rol(mload(add(s, 0x0e0)), 6))
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mstore(add(b, 0x2a0), rol(mload(add(s, 0x100)), 55))
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mstore(add(b, 0x0c0), rol(mload(add(s, 0x120)), 20))
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mstore(add(b, 0x0e0), rol(mload(add(s, 0x140)), 3))
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mstore(add(b, 0x220), rol(mload(add(s, 0x160)), 10))
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mstore(add(b, 0x040), rol(mload(add(s, 0x180)), 43))
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mstore(add(b, 0x180), rol(mload(add(s, 0x1a0)), 25))
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mstore(add(b, 0x2c0), rol(mload(add(s, 0x1c0)), 39))
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mstore(add(b, 0x2e0), rol(mload(add(s, 0x1e0)), 41))
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mstore(add(b, 0x100), rol(mload(add(s, 0x200)), 45))
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mstore(add(b, 0x240), rol(mload(add(s, 0x220)), 15))
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mstore(add(b, 0x060), rol(mload(add(s, 0x240)), 21))
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mstore(add(b, 0x1a0), rol(mload(add(s, 0x260)), 8))
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mstore(add(b, 0x1c0), rol(mload(add(s, 0x280)), 18))
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mstore(add(b, 0x300), rol(mload(add(s, 0x2a0)), 2))
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mstore(add(b, 0x120), rol(mload(add(s, 0x2c0)), 61))
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mstore(add(b, 0x260), rol(mload(add(s, 0x2e0)), 56))
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mstore(add(b, 0x080), rol(mload(add(s, 0x300)), 14))
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// ---- chi: st[y+x] = b[y+x] ^ ((~b[y+(x+1)%5]) & b[y+(x+2)%5]) ----
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for { let yo := 0 } lt(yo, 0x320) { yo := add(yo, 0xa0) } {
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let b0 := mload(add(b, yo))
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let b1 := mload(add(b, add(yo, 0x20)))
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let b2 := mload(add(b, add(yo, 0x40)))
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let b3 := mload(add(b, add(yo, 0x60)))
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let b4 := mload(add(b, add(yo, 0x80)))
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mstore(add(s, yo), and(0xffffffffffffffff, xor(b0, and(not(b1), b2))))
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mstore(add(s, add(yo, 0x20)), and(0xffffffffffffffff, xor(b1, and(not(b2), b3))))
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mstore(add(s, add(yo, 0x40)), and(0xffffffffffffffff, xor(b2, and(not(b3), b4))))
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mstore(add(s, add(yo, 0x60)), and(0xffffffffffffffff, xor(b3, and(not(b4), b0))))
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mstore(add(s, add(yo, 0x80)), and(0xffffffffffffffff, xor(b4, and(not(b0), b1))))
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}
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// ---- iota ----
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mstore(add(s, 0), xor(mload(add(s, 0)), mload(add(rc, mul(rnd, 0x20)))))
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}
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}
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}
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/// @dev Absorb `input` into a fresh SHAKE256 sponge (rate 136 bytes, domain
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/// 0x1F, pad10*1) and return the state after the final permutation.
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function _shakeAbsorb(bytes memory input) internal view returns (uint64[25] memory st) {
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uint256 len = input.length;
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uint256 off = 0;
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// full 136-byte blocks
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while (len - off >= 136) {
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for (uint256 j = 0; j < 17; j++) {
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uint64 lane = 0;
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uint256 base = off + j * 8;
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for (uint256 b = 0; b < 8; b++) {
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lane |= uint64(uint8(input[base + b])) << (8 * b);
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}
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st[j] ^= lane;
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}
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_keccakf(st);
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off += 136;
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}
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// final (partial) block with padding
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uint256 rem = len - off;
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bytes memory blk = new bytes(136);
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for (uint256 i = 0; i < rem; i++) {
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blk[i] = input[off + i];
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}
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blk[rem] = bytes1(uint8(blk[rem]) ^ 0x1F); // domain separation
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blk[135] = bytes1(uint8(blk[135]) ^ 0x80); // final bit of pad10*1
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for (uint256 j = 0; j < 17; j++) {
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uint64 lane = 0;
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uint256 base = j * 8;
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for (uint256 b = 0; b < 8; b++) {
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lane |= uint64(uint8(blk[base + b])) << (8 * b);
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}
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st[j] ^= lane;
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}
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_keccakf(st);
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}
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/// @dev Extract the current 136-byte rate block (little-endian lanes 0..16).
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function _rateBlock(uint64[25] memory st) internal view returns (bytes memory out) {
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out = new bytes(136);
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for (uint256 j = 0; j < 17; j++) {
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uint64 lane = st[j];
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for (uint256 b = 0; b < 8; b++) {
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out[j * 8 + b] = bytes1(uint8(lane >> (8 * b)));
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}
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}
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}
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/// @notice Squeeze `outLen` bytes of SHAKE256(input). Exposed for KAT testing.
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function shake256(bytes memory input, uint256 outLen) public view returns (bytes memory out) {
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uint64[25] memory st = _shakeAbsorb(input);
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out = new bytes(outLen);
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uint256 pos = 0;
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while (pos < outLen) {
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bytes memory blk = _rateBlock(st);
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uint256 take = outLen - pos;
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if (take > 136) take = 136;
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for (uint256 i = 0; i < take; i++) {
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out[pos + i] = blk[i];
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}
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pos += take;
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if (pos < outLen) _keccakf(st);
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}
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}
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// ==========================================================================
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// HashToPoint
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// ==========================================================================
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/// @notice HashToPoint(nonce || message) -> challenge polynomial c (512 coeffs).
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/// @dev Streams SHAKE256 two bytes at a time; keeps a big-endian 16-bit sample
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/// when it is < 5*q = 61445, reducing it mod q. Matches the reference
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/// hash_to_point_vartime exactly.
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function hashToPoint(bytes memory nonce, bytes memory message) public view returns (uint256[512] memory cc) {
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// Native AERE Falcon HashToPoint precompile @ 0x0AE7: logn(1)=9 || nonce(40) || message
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bytes memory input = bytes.concat(bytes1(uint8(9)), nonce, message);
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(bool okp, bytes memory outp) = address(0x0AE7).staticcall(input);
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require(okp && outp.length == 1024, "htp precompile failed");
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for (uint256 i = 0; i < 512; i++) {
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cc[i] = (uint256(uint8(outp[2 * i])) << 8) | uint256(uint8(outp[2 * i + 1]));
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}
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}
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// ==========================================================================
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// Public key / signature decode
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// ==========================================================================
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/// @notice Decode a 897-byte Falcon-512 public key into h (512 coeffs).
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/// @return h the 512 coefficients, ok false if the encoding is invalid.
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function decodePublicKey(bytes memory pk) public view returns (uint256[512] memory h, bool ok) {
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if (pk.length != 897 || uint8(pk[0]) != PK_HEADER) {
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return (h, false);
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}
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uint256 acc = 0;
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uint256 accLen = 0;
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uint256 u = 0;
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// 896 encoded bytes = 512 * 14 bits, exact
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for (uint256 i = 1; i < 897 && u < 512; i++) {
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acc = ((acc << 8) | uint256(uint8(pk[i]))) & 0xFFFFFFFF;
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accLen += 8;
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if (accLen >= 14) {
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accLen -= 14;
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uint256 w = (acc >> accLen) & 0x3FFF;
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if (w >= Q) return (h, false);
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h[u] = w;
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u++;
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}
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}
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if (u != 512) return (h, false);
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// trailing bits must be zero
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if ((acc & ((uint256(1) << accLen) - 1)) != 0) return (h, false);
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return (h, true);
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}
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/// @notice Decode the compressed Falcon signature bytes into s2 (512 signed coeffs).
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/// @dev Mirrors the reference comp_decode: for each coefficient read a byte
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/// giving sign + 7 low bits, then read bits until a 1 for the high part.
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/// Rejects "-0", overflow (>2047), running off the buffer, or nonzero
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/// trailing bits. Requires the whole buffer to be consumed.
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/// @return s2 signed coefficients (centered), ok false if invalid.
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function decodeSignature(bytes memory sig) public view returns (int256[512] memory s2, bool ok) {
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uint256 acc = 0;
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uint256 accLen = 0;
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uint256 v = 0;
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uint256 maxLen = sig.length;
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for (uint256 u = 0; u < 512; u++) {
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if (v >= maxLen) return (s2, false);
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acc = ((acc << 8) | uint256(uint8(sig[v]))) & 0xFFFFFFFF;
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v++;
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uint256 bb = acc >> accLen;
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uint256 s = bb & 128;
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uint256 m = bb & 127;
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// read high bits until a set bit
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while (true) {
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if (accLen == 0) {
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if (v >= maxLen) return (s2, false);
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acc = ((acc << 8) | uint256(uint8(sig[v]))) & 0xFFFFFFFF;
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v++;
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accLen = 8;
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}
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accLen--;
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if (((acc >> accLen) & 1) != 0) break;
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m += 128;
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if (m > 2047) return (s2, false);
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}
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if (s != 0 && m == 0) return (s2, false); // "-0" forbidden
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s2[u] = s != 0 ? -int256(m) : int256(m);
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}
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// unused bits in the last consumed byte must be zero
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if ((acc & ((uint256(1) << accLen) - 1)) != 0) return (s2, false);
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// the whole signature buffer must be consumed exactly
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if (v != maxLen) return (s2, false);
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return (s2, true);
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}
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// ==========================================================================
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// Ring arithmetic + norm
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// ==========================================================================
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/// @dev b^e mod q.
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function _modpow(uint256 b, uint256 e) internal view returns (uint256 r) {
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r = 1;
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b %= Q;
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while (e > 0) {
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if (e & 1 == 1) r = mulmod(r, b, Q);
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b = mulmod(b, b, Q);
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e >>= 1;
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}
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}
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/// @dev In-place bit-reversal permutation of a length-512 array.
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function _bitrev(uint256[512] memory a) internal view {
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uint256 j = 0;
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for (uint256 i = 1; i < 512; i++) {
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uint256 bit = 256; // n >> 1
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while (j & bit != 0) {
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j ^= bit;
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bit >>= 1;
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}
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j ^= bit;
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if (i < j) {
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uint256 tmp = a[i];
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a[i] = a[j];
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a[j] = tmp;
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}
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}
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}
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/// @dev Iterative in-place NTT (natural order in and out) with the given root.
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function _ntt(uint256[512] memory a, uint256 root) internal view {
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_bitrev(a);
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for (uint256 len = 2; len <= 512; len <<= 1) {
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uint256 wlen = _modpow(root, 512 / len);
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uint256 half = len >> 1;
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for (uint256 i = 0; i < 512; i += len) {
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uint256 wn = 1;
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for (uint256 k = i; k < i + half; k++) {
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uint256 vv = mulmod(a[k + half], wn, Q);
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uint256 u = a[k];
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a[k] = addmod(u, vv, Q);
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a[k + half] = addmod(u, Q - vv, Q);
|
|
wn = mulmod(wn, wlen, Q);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/// @dev Negacyclic convolution t = a*b in Z_q[x]/(x^512+1) via NTT.
|
|
/// Pre-twist by PSI^i, length-512 NTT (root W), pointwise multiply,
|
|
/// inverse NTT, post-twist by PSI^-i and multiply by n^-1.
|
|
function _ringMul(uint256[512] memory A, uint256[512] memory B) internal view returns (uint256[512] memory r) {
|
|
uint256[512] memory a = A;
|
|
uint256[512] memory b = B;
|
|
uint256 p = 1;
|
|
for (uint256 i = 0; i < 512; i++) {
|
|
a[i] = mulmod(a[i] % Q, p, Q);
|
|
b[i] = mulmod(b[i] % Q, p, Q);
|
|
p = mulmod(p, PSI, Q);
|
|
}
|
|
_ntt(a, W);
|
|
_ntt(b, W);
|
|
for (uint256 i = 0; i < 512; i++) {
|
|
a[i] = mulmod(a[i], b[i], Q);
|
|
}
|
|
_ntt(a, W_INV);
|
|
// post-twist: r[i] = a[i] * n^-1 * PSI^-i
|
|
uint256 pinv = N_INV; // n^-1 * PSI^-0
|
|
for (uint256 i = 0; i < 512; i++) {
|
|
r[i] = mulmod(a[i], pinv, Q);
|
|
pinv = mulmod(pinv, PSI_INV, Q);
|
|
}
|
|
}
|
|
|
|
// ==========================================================================
|
|
// Verification
|
|
// ==========================================================================
|
|
|
|
/// @notice Verify a Falcon-512 signature given decomposed inputs.
|
|
/// @param pk 897-byte NIST public key (0x09 header + packed h).
|
|
/// @param message the signed message bytes.
|
|
/// @param nonce 40-byte salt r.
|
|
/// @param compSig compressed encoding of s2 (comp_encode output).
|
|
/// @return ok true iff the signature is a valid Falcon-512 signature.
|
|
function verify(
|
|
bytes memory pk,
|
|
bytes memory message,
|
|
bytes memory nonce,
|
|
bytes memory compSig
|
|
) public view returns (bool ok) {
|
|
if (nonce.length != NONCE_LEN) return false;
|
|
|
|
(uint256[512] memory h, bool okPk) = decodePublicKey(pk);
|
|
if (!okPk) return false;
|
|
|
|
(int256[512] memory s2, bool okSig) = decodeSignature(compSig);
|
|
if (!okSig) return false;
|
|
|
|
uint256[512] memory cc = hashToPoint(nonce, message);
|
|
|
|
// s2 reduced into [0, q)
|
|
uint256[512] memory s2m;
|
|
for (uint256 i = 0; i < 512; i++) {
|
|
int256 x = s2[i] % int256(Q);
|
|
if (x < 0) x += int256(Q);
|
|
s2m[i] = uint256(x);
|
|
}
|
|
|
|
// t = s2 * h (mod q, ring)
|
|
uint256[512] memory t = _ringMul(s2m, h);
|
|
|
|
// s1 = c - t, centered into (-q/2, q/2]; accumulate squared norm
|
|
uint256 norm = 0;
|
|
for (uint256 i = 0; i < 512; i++) {
|
|
uint256 val = addmod(cc[i], Q - t[i], Q); // (c - t) mod q, in [0,q)
|
|
int256 s1 = val > HQ ? int256(val) - int256(Q) : int256(val);
|
|
norm += uint256(s1 * s1);
|
|
int256 z = s2[i];
|
|
norm += uint256(z * z);
|
|
if (norm > L2BOUND) return false; // early out (also guards accumulation)
|
|
}
|
|
return norm <= L2BOUND;
|
|
}
|
|
|
|
/// @notice Verify a Falcon-512 signature from a raw NIST "signed message" (sm)
|
|
/// blob plus the public key. This consumes the exact bytes found in
|
|
/// the official KAT: sm = sigLen(2, big-endian) || nonce(40) ||
|
|
/// message || esig, where esig = 0x29 || compSig.
|
|
function verifySignedMessage(bytes memory pk, bytes memory sm) public view returns (bool ok) {
|
|
uint256 smlen = sm.length;
|
|
if (smlen < 2 + NONCE_LEN) return false;
|
|
uint256 sigLen = (uint256(uint8(sm[0])) << 8) | uint256(uint8(sm[1]));
|
|
if (sigLen > smlen - 2 - NONCE_LEN) return false;
|
|
uint256 msgLen = smlen - 2 - NONCE_LEN - sigLen;
|
|
if (sigLen < 1) return false;
|
|
|
|
// esig begins at 2 + NONCE_LEN + msgLen; its first byte is the header
|
|
uint256 esigStart = 2 + NONCE_LEN + msgLen;
|
|
if (uint8(sm[esigStart]) != SIG_HEADER) return false;
|
|
|
|
bytes memory nonce = new bytes(NONCE_LEN);
|
|
for (uint256 i = 0; i < NONCE_LEN; i++) nonce[i] = sm[2 + i];
|
|
|
|
bytes memory message = new bytes(msgLen);
|
|
for (uint256 i = 0; i < msgLen; i++) message[i] = sm[2 + NONCE_LEN + i];
|
|
|
|
bytes memory compSig = new bytes(sigLen - 1);
|
|
for (uint256 i = 0; i < sigLen - 1; i++) compSig[i] = sm[esigStart + 1 + i];
|
|
|
|
return verify(pk, message, nonce, compSig);
|
|
}
|
|
|
|
/// @notice State-changing wrapper: verify and record the result on-chain.
|
|
function verifyAndRecord(bytes memory pk, bytes memory sm) external returns (bool result) {
|
|
result = verifySignedMessage(pk, sm);
|
|
lastResult = result;
|
|
uint256 idx = verifyCount;
|
|
verifyCount = idx + 1;
|
|
emit Verified(msg.sender, result, idx);
|
|
}
|
|
}
|