crypto/poi

poi — Proof-of-Inference verifier primitive

Freivalds-over-F_p matrix-product verification, plus a Merkle transcript and wire codec for on-chain openings. This is the canonical Go verifier that luxfi/precompile/aivmbridge/computeproof.go consumes and that hanzo-engine/src/poi.rs mirrors on the prover side.

See LP-5300 (Thinking Chains / Proof-of-Thought) for the receipt model this serves, and LP-5301 (AIVMBridge) for the precompile that calls this code in-EVM.

Overview

Proof-of-AI binds mint to genuine computation. An LLM forward pass is ~95% matrix multiplications C = A·B. Recomputing every C on-chain is prohibitive; Freivalds (1977) instead samples a random vector r and checks

A·(B·r) == C·r

in O(t·k + k·n + t·n) — an order cheaper than the O(t·k·n) recompute — and catches any fabricated C (a claimed output the prover never multiplied for) with probability >= 1 - 1/p per vector.

The verifier operates on the exact-integer accumulator of the engine's int8 matmul path (i8·i8 -> i32 promoted to int64). Working on the exact accumulator, not on floats, means the check is bit-exact with zero false-reject across CPU / GPU / backends — the determinism the whole scheme relies on.

Mathematical setup

• Field: F_p with prime modulus P = 2^61 - 1 (a Mersenne prime; see freivalds.go — const P uint64 = (1 << 61) - 1).
• Signed inputs are reduced into [0, p) by toField; a single Freivalds intermediate stays within 61 bits, so a 128-bit multiply never overflows.
• Soundness: 1/p ~ 2^-61 per challenge vector. k independent vectors give a soundness error of (1/p)^k. k = 2 yields ~2^-122, which is what the precompile ships with.
• Challenge derivation is Fiat–Shamir: DeriveChallenges(seed, n, k) folds keccak of seed || (j, i) into [0, p). In production the seed is keccak(beacon || root || index) (see OpeningSeed), so a prover cannot anticipate its challenges before committing the transcript root.

Public API

Freivalds core (freivalds.go):

symbol	signature	purpose
P	const uint64 = (1 << 61) - 1	Field modulus.
Mat	struct { Rows, Cols int; Data []int64 }	Row-major integer matrix.
NewMat	func(rows, cols int, data []int64) Mat	Constructor (panics on length mismatch).
Verify	func(a, b, c Mat, r []uint64) bool	One-vector Freivalds check.
VerifyMulti	func(a, b, c Mat, challenges [][]uint64) bool	k-vector check; false if any fails.
DeriveChallenges	func(seed []byte, n, k int) [][]uint64	Fiat–Shamir challenge derivation.

Transcript + Merkle (transcript.go):

symbol	signature	purpose
DomainMatmulLeaf	[]byte("hanzo/poi/matmul-leaf/v1")	Leaf domain tag.
ExactMatmul	func(a, b Mat) Mat	Whole-K int64 exact matmul (the proof-bearing GEMM).
MatmulLeaf	func(a, b, c Mat) [32]byte	`keccak(DOMAIN
MerkleRoot	func(leaves [][32]byte) [32]byte	Duplicate-last-on-odd keccak fold.
MerkleProof	func(leaves [][32]byte, index int) [][32]byte	Sibling path, bottom-up.
MerkleVerify	func(leaf, root [32]byte, index int, proof [][32]byte) bool	Inclusion check (matches AICoinMiner._verifyMerkle).
Opening	struct { Index int; A, B, C Mat; Proof [][32]byte }	What a prover reveals for one matmul.
ProofTranscript	struct w/ Matmul, CommitClaimed, Len, Root, Open	Append-only commitment to a forward pass's matmuls.
NewTranscript	func() *ProofTranscript	Constructor.
ChallengeIndex	func(beacon []byte, root [32]byte, length int) int	`keccak(beacon
OpeningSeed	func(beacon []byte, root [32]byte, index int) []byte	`keccak(beacon
VerifyOpening	func(root [32]byte, beacon []byte, op Opening, k int) bool	Merkle inclusion and k-vector Freivalds.

Wire codec + precompile payload (wire.go):

symbol	signature	purpose
MaxOpeningDim	const = 4096	Per-dimension bound (see below).
ErrShortOpening, ErrOpeningDims	error	Decode errors.
EncodeOpening	func(root [32]byte, beacon []byte, op Opening) []byte	Canonical wire frame.
DecodeOpening	func(b []byte) (root [32]byte, beacon []byte, op Opening, err error)	Bounds-checked parse.
CheckOpening	func(input []byte, k int) (included, freivaldsOK bool, err error)	Precompile payload: decode + verify.
CheckDecoded	func(root [32]byte, beacon []byte, op Opening, k int) (bool, bool, error)	Same, on an already-parsed opening.
FieldOps	func(op Opening, k int) uint64	k · (t·k + k·n + t·n) — drives precompile gas.

Wire codec

EncodeOpening produces (all integers big-endian):

root[32] | index u64 | beaconLen u32 | beacon | mat(A) | mat(B) | mat(C) | proofLen u32 | proof[32]*

mat(m) = rows u32 | cols u32 | data[i] as int64-BE   (rows*cols entries)

DecodeOpening reverses it, bounds-checking every length. The proof-length field is capped at 64 (a 2^64-leaf tree is absurd) to prevent OOM from a malicious frame; each matrix dimension is capped at MaxOpeningDim.

Bounds

MaxOpeningDim = 4096. A full LLM layer is challenged in slices no larger than this, so a malicious frame cannot allocate unboundedly inside the precompile. In practice a real-model opening is on the order of a few hundred per side, well under the cap; the constant exists to make the on-chain decoder's worst-case allocation finite and known.

Worked example

Prover commits two matmuls, opens the second, encodes it, hands the bytes to a verifier that decodes and checks:

package main

import (
	"encoding/hex"
	"fmt"

	"github.com/luxfi/crypto/poi"
)

func main() {
	// Prover side: build the exact-integer operands (the int8 accumulators in
	// production; here small int64 values for a runnable demo).
	A := poi.NewMat(2, 3, []int64{1, 2, 3, 4, 5, 6})
	B := poi.NewMat(3, 2, []int64{7, 8, 9, 10, 11, 12})

	// Commit two matmuls to the transcript.
	tr := poi.NewTranscript()
	_ = tr.Matmul(A, B) // index 0
	_ = tr.Matmul(A, B) // index 1
	root := tr.Root()

	// Challenger picks an opening (in production: keccak(beacon || root) mod N).
	beacon := []byte("beacon:demo")
	idx := poi.ChallengeIndex(beacon, root, tr.Len())
	op := tr.Open(idx)

	// Prover ships bytes.
	wire := poi.EncodeOpening(root, beacon, op)

	// Verifier side: decode + check with k=2 challenge vectors.
	rRoot, rBeacon, rOp, err := poi.DecodeOpening(wire)
	if err != nil {
		panic(err)
	}
	included, freivaldsOK, err := poi.CheckDecoded(rRoot, rBeacon, rOp, 2)
	if err != nil {
		panic(err)
	}
	fmt.Printf("root=%s included=%v freivaldsOK=%v\n", hex.EncodeToString(rRoot[:8]), included, freivaldsOK)
	// Expected: included=true freivaldsOK=true
}

Fraud path: mutate rOp.C.Data[0] before CheckDecoded and the second return flips to false with probability >= 1 - (1/p)^2 ~ 1 - 2^-122. The on-chain gate reads that as included && !freivaldsOK and slashes.

References

• LP-5300 — Thinking Chains / Cognitive Consensus / Proof-of-Thought. §Security is what this package operationalizes: the audit-ability promise is only real because a third party can decode an opening and rerun CheckDecoded against the on-chain root.
• LP-5301 — AIVMBridge. The computeproof precompile consumes exactly the wire format above.
• luxfi/precompile/aivmbridge/computeproof.go — line 17, import "github.com/luxfi/crypto/poi". That file is the sole in-tree caller of CheckOpening; keep the two in lockstep when changing the wire.
• hanzo-engine/src/poi.rs — the Rust prover-side mirror. Byte-for-byte identical serialization and keccak fold; an opening produced there verifies here (and on-chain) without re-hashing.