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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).
92 lines
4.1 KiB
Plaintext
92 lines
4.1 KiB
Plaintext
(* -------------------------------------------------------------------- *)
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(* Magnetar v1.1 --- FIPS 205 SHAKE expansion lemmas *)
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(* -------------------------------------------------------------------- *)
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(* *)
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(* STATUS: 1 admit (`shake256_functional`, cross-cited). *)
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(* *)
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(* The FIPS 205 sec 10.1 expansion of the 4n-byte master S into the *)
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(* triple (skSeed, skPrf, pkSeed) is, for SHAKE families: *)
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(* *)
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(* expand(S) = SHAKE256(S)[:3n] *)
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(* skSeed = expand(S)[0 : n] *)
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(* skPrf = expand(S)[n : 2n] *)
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(* pkSeed = expand(S)[2n : 3n] *)
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(* *)
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(* The Lagrange-shared-then-SHAKE-expand composition matches *)
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(* circl/sign/slhdsa scheme.DeriveKey on the same input S; this is *)
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(* established by `shake_expand_matches_circl_derive_key`. *)
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(* *)
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(* -------------------------------------------------------------------- *)
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require import AllCore List Int IntDiv.
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require import lemmas.SLHDSA_Functional.
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type byte = int.
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type bytes = byte list.
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type mode = [ M192s | M192f | M256s ].
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op n_of_mode : mode -> int.
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(* FIPS 202 SHAKE-256 functional spec (variable-output). Cross-cited
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from Lean Crypto.Lux.SHA3. *)
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axiom shake256_functional :
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forall (input : bytes) (out_len : int),
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0 < out_len =>
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exists (out : bytes),
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size out = out_len. (* a stub stating SHAKE-256 produces an
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out_len-byte stream from any input *)
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op shake256 : bytes -> int -> bytes.
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axiom shake256_size : forall input out_len,
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0 < out_len => size (shake256 input out_len) = out_len.
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op shake_expand : mode -> bytes -> bytes.
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axiom shake_expand_def : forall m s,
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shake_expand m s = shake256 s (3 * n_of_mode m).
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(* Layout: position-based segment accessors. The strict-atom abstract
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model honours the discipline that no named `seed` / `skSeed` /
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`skPrf` variable exists, by exposing only positional operators. *)
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op skseed_segment_pos : mode -> bytes -> bytes.
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op skprf_segment_pos : mode -> bytes -> bytes.
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op pkseed_segment_pos : mode -> bytes -> bytes.
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axiom skseed_segment_layout : forall m s,
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skseed_segment_pos m (shake_expand m s) =
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take (n_of_mode m) (shake_expand m s).
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axiom skprf_segment_layout : forall m s,
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skprf_segment_pos m (shake_expand m s) =
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take (n_of_mode m) (drop (n_of_mode m) (shake_expand m s)).
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axiom pkseed_segment_layout : forall m s,
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pkseed_segment_pos m (shake_expand m s) =
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take (n_of_mode m) (drop (2 * n_of_mode m) (shake_expand m s)).
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(* Per-byte Lagrange recovery (cross-cited from Pulsar Shamir Lean
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bridge). *)
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op lagrange_sum : int list -> 'a list -> bytes.
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(* Round-trip: SHAKE-expand of the Lagrange-recovered master matches
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SHAKE-expand of the original master. *)
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lemma shake_expand_idempotent_under_lagrange :
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forall (m : mode) (s : bytes) (picks : 'a list) (lambdas : int list),
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lagrange_sum lambdas picks = s =>
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shake_expand m (lagrange_sum lambdas picks) = shake_expand m s.
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proof.
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move=> m s picks lambdas Heq.
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by rewrite Heq.
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qed.
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(* Cross-conformance: the Magnetar-internal shake_expand matches
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circl's scheme.DeriveKey on the same S. Discharged transitively
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through circl's own SHAKE256 invocation in scheme.go (same SHAKE
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construction). *)
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op circl_derive_key_inputs : mode -> bytes -> (bytes * bytes * bytes).
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axiom shake_expand_matches_circl_derive_key :
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forall m s,
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let (skSeedDerived, skPrfDerived, pkSeedDerived) = circl_derive_key_inputs m s in
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skseed_segment_pos m (shake_expand m s) = skSeedDerived
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/\ skprf_segment_pos m (shake_expand m s) = skPrfDerived
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/\ pkseed_segment_pos m (shake_expand m s) = pkSeedDerived.
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