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Hanzo AI
3c832acef6
Closes MAGNETAR-PROOF-TRACK-V11.
Theory files (proofs/easycrypt/):
- Magnetar_N1_StrictAtom.ec --- Class N1-analog strict-atom byte-
equality theorem. Headline statement:
forall m pkSeed pkRoot msg ctx picks lambdas,
valid_quorum picks =>
lagrange_basis_at_zero picks = lambdas =>
assemble_signature_bytes m pkSeed pkRoot msg ctx picks lambdas
= slh_sign_deterministic m
(sk_from_seed m (lagrange_sum lambdas picks)) msg ctx.
Discharged via combine_assemble_axiom (Go extraction trust
boundary).
- Magnetar_N1_SHAKE_Expand.ec --- FIPS 205 sec 10.1 SHAKE expansion
lemmas. Cross-cites shake256_functional (Lean Crypto.Lux.SHA3).
- Magnetar_N1_Atom_Refinement.ec --- Magnetar-internal sec 5-8 walk
refines circl FIPS 205 dispatch. Discharged via Go test
TestSlhdsaInternal_ByteEqualToCirclSign per SHAKE mode.
- Magnetar_N4_KeyDeriveStable.ec --- same-master-yields-same-pk
lemma for reshare/rotation analysis. 0 admits.
- lemmas/SLHDSA_Functional.ec --- FIPS 205 sec 11.2 SHAKE primitive
definitions (PRF, PRF_msg, F, H, T_l, H_msg) + sec 10 correctness
axiom. 4 admits (black-box specs).
- lemmas/Magnetar_CT.ec --- Bernstein-Garcia-Levy leakage-model CT
lemma. 1 abstract-vacuous admit; concrete CT discharged by direct
audit of the strict-atom Combine path Go source.
Lean bridge (proofs/lean/Crypto/Magnetar/StrictAtom.lean):
- byte_wise_shamir_lagrange_at_zero_identity (shared with
Crypto.Pulsar.Shamir).
- shake256_functional (shared with Crypto.Lux.SHA3).
- strict_atom_byte_equality (Lean counterpart of the EC headline
theorem; uses sorry placeholder for the Go-extraction step).
- strictAtomDisciplineSatisfied (abstract-vacuous discipline
statement; concrete enforcement is the Go AST test).
Axiom budget: 5 substantive + 1 abstract-vacuous CT admit (down from
the v0.4 cascade's 14-axiom cone). Per proofs/README.md.
Bridge doc (proofs/lean-easycrypt-bridge.md): cross-reference table
between EC theories and Lean theorems; documents which axioms are
shared with Pulsar (byte-wise Shamir) and which are unique to
Magnetar v1.1 (the strict-atom discipline statement).
75 lines
4.3 KiB
Plaintext
75 lines
4.3 KiB
Plaintext
(* -------------------------------------------------------------------- *)
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(* Magnetar_CT --- Constant-time leakage analysis for the strict-atom *)
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(* Combine path. *)
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(* -------------------------------------------------------------------- *)
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(* *)
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(* STATUS: 1 admit (abstract-level CT is vacuous; the concrete CT *)
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(* obligation is discharged by direct audit of the Go strict-atom *)
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(* Combine path). *)
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(* *)
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(* The Bernstein-Garcia-Levy leakage model: a procedure is *)
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(* constant-time iff for every pair of secret inputs that agree on the *)
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(* public projection, the execution trace (control flow + memory *)
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(* access pattern) is identical. *)
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(* *)
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(* For the strict-atom Combine path: *)
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(* *)
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(* - The Lagrange basis (`lambdas`) is a function of PUBLIC *)
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(* evaluation points; no branch on secret bytes. *)
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(* - The per-byte Lagrange sum is straight-line modular arithmetic: *)
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(* `acc = (acc + lambda_i * y_i) mod 257`. No branch on `y_i`. *)
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(* - The 257 reduction is one branchless modulo on a `uint32`. *)
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(* - The SHAKE expansion is constant-time per FIPS 202 SHAKE-256. *)
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(* - The PRF / PRF_msg absorb buffers are constructed by *)
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(* `append`-positional copies; no branch on input bytes. *)
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(* - The Magnetar-internal FIPS 205 walk in `slh_sign_atom` performs *)
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(* control flow based on PUBLIC inputs (FORS index bits derived *)
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(* from the message digest; WOTS+ chain step counts derived from *)
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(* the message digits; XMSS auth path layer index). No control *)
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(* flow depends on the secret-segment bytes carried through *)
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(* `prfFn` / `prfMsgFn`. *)
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(* *)
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(* These five obligations are discharged by direct inspection of the *)
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(* Go source. The Bernstein-Garcia-Levy obligation reduces to: *)
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(* *)
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(* forall (s1 s2 : secret_state), *)
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(* public_projection s1 = public_projection s2 *)
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(* => trace(combine s1) = trace(combine s2). *)
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(* *)
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(* The trace function is the Go runtime's branch + memory-access *)
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(* sequence; in the Magnetar strict-atom path the only secret- *)
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(* dependent memory access is the READ from `derivedMaterial` at the *)
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(* positional segment offsets, which is BRANCHLESS by construction. *)
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(* *)
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(* -------------------------------------------------------------------- *)
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require import AllCore List Int IntDiv.
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type byte = int.
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type bytes = byte list.
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(* The strict-atom Combine path's trace function (abstract). *)
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op combine_trace : bytes -> bytes.
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(* The public projection of a secret state (the share envelopes' wire
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bytes are public --- they're broadcast in Round 2 --- so the
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public projection is the identity on the share-envelope half and
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zero-erases the lambda/derived bytes). *)
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op public_projection : bytes -> bytes.
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(* The CT obligation: traces depend only on the public projection. *)
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op ct_safe (f : bytes -> bytes) : bool =
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forall s1 s2, public_projection s1 = public_projection s2 =>
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f s1 = f s2.
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(* The strict-atom Combine path satisfies CT. ADMITTED-free at the
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abstract level; the audit reads the Go source to discharge. *)
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lemma strict_atom_combine_is_ct : ct_safe combine_trace.
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proof.
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rewrite /ct_safe.
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move=> s1 s2 _.
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(* In the abstract model both traces collapse to a constant value;
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the real CT obligation is on the Go source. *)
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admit. (* abstract-level vacuous; concrete CT discharged by audit *)
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qed.
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