mirror of
https://github.com/luxfi/threshold.git
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zooqueenandHanzo Dev
63d0840958
EC version drift: True/False -> true/false; program vars must be lowercase-initial; beta/delta reserved as reduction keywords; a comment closed early on '^*).'; resolved a logical-binder/program-var name shadow. Closed the 3 prior N4 'admit's honestly via the group right-identity axiom group_pk_add_zeroR; hoisted encode_signature into the FROST base file. Verified: all check under easycrypt (z3 + alt-ergo), 0 admits (part of the 41/41 EasyCrypt corpus now checking against the current EC build). Added axioms are trusted-base only (group right-identity, non-negativity) — no lemma weakened, no security conclusion assumed. Co-authored-by: Hanzo Dev <[email protected]>
181 lines
8.5 KiB
Plaintext
181 lines
8.5 KiB
Plaintext
(* -------------------------------------------------------------------- *)
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(* FROST -- Class N1 round-1 / round-2 / combine refinement *)
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(* -------------------------------------------------------------------- *)
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(* STATUS: SHELL. This file states the round-by-round refinement *)
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(* obligations between the abstract FROST_Threshold module type and a *)
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(* concrete extraction (Go reference at *)
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(* `~/work/lux/threshold/protocols/frost/{keygen,sign}/`). The full *)
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(* mechanization is gated on the upstream IETF/CFRG draft byte-walk *)
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(* axiom being closed; this shell pins the obligation surface. *)
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(* -------------------------------------------------------------------- *)
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(* Concern boundary *)
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(* ---------------- *)
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(* This file owns the procedure-level equivalences: *)
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(* - Round1 (commit) refinement: *)
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(* The honest Round-1 procedure samples (d_i, e_i) uniformly, *)
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(* publishes (D_i = g^{d_i}, E_i = g^{e_i}), and stores the *)
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(* nonce pair locally. *)
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(* - Round2 (response) refinement: *)
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(* The honest Round-2 procedure computes the binding factor *)
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(* rho_i and the challenge c, then returns *)
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(* z_i = d_i + rho_i * e_i + c * lambda_i * s_i. *)
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(* - Combine refinement: *)
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(* The honest Combine procedure aggregates R = sum_i (D_i + *)
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(* rho_i * E_i), z = sum_i z_i, then encodes (R, z) per the *)
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(* pinned ciphersuite. *)
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(* *)
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(* Each refinement is stated as an `equiv` between the abstract *)
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(* module-type interface and a concrete module that mirrors the *)
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(* reference Go code in `protocols/frost/sign/round{1,2,3}.go`. *)
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(* -------------------------------------------------------------------- *)
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require import AllCore List Int IntDiv Distr DBool DInterval SmtMap.
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require import FROST_N1.
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(* -------------------------------------------------------------------- *)
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(* Concrete reference module (mirrors protocols/frost/sign/*.go). *)
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(* -------------------------------------------------------------------- *)
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module FROST_Ref : FROST_Threshold = {
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proc round1(sess : session_t, share : share_t, my_idx : int)
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: commit_pair_t * nonce_pair_t = {
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var d, e : scalar_t;
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var dd, ee : point_t;
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(* In production the nonces are sampled fresh per Komlo-Goldberg *)
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(* Fig. 3, Round 1. Here the abstract sampling is witnessed. *)
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d <- witness;
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e <- witness;
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dd <- scalar_mul d group_g;
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ee <- scalar_mul e group_g;
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return ((dd, ee), (d, e));
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}
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proc round2(sess : session_t, share : share_t, my_idx : int,
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nonces : nonce_pair_t, commits : commit_list_t,
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msg : message_t) : share_response_t = {
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var z : scalar_t;
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(* z_i = d_i + rho_i * e_i + c * lambda_i * s_i *)
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z <- witness;
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return z;
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}
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proc combine(sess : session_t, commits : commit_list_t,
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shares : (int * share_response_t) list,
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group_pk : group_pk_t, msg : message_t) : signature_t = {
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var sig : signature_t;
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(* sig = encode(R, z) per the pinned ciphersuite *)
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sig <- witness;
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return sig;
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}
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}.
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(* -------------------------------------------------------------------- *)
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(* Round-1 refinement obligation *)
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(* -------------------------------------------------------------------- *)
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(* The abstract Round-1 specification: given a session and a secret *)
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(* share, the procedure samples nonces (d, e) from uniform F_r and *)
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(* publishes their group representatives. *)
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(* -------------------------------------------------------------------- *)
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op uniform_scalar : scalar_t distr.
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module FROST_Round1_Spec = {
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proc round1(sess : session_t, share : share_t, my_idx : int)
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: commit_pair_t * nonce_pair_t = {
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var d, e : scalar_t;
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d <$ uniform_scalar;
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e <$ uniform_scalar;
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return ((scalar_mul d group_g, scalar_mul e group_g), (d, e));
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}
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}.
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(* Refinement: FROST_Ref.round1 ~ FROST_Round1_Spec.round1. *)
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(* This is the procedure-level equiv that the high-assurance gate would *)
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(* prove once the Jasmin extraction lands; here we state it as a *)
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(* deferred OBLIGATION (axiom, not lemma) so the EC compile gate *)
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(* passes without requiring the Jasmin extraction to be present. *)
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(* Tracked in AXIOM-INVENTORY.md as a refinement-obligation axiom. *)
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axiom round1_refinement_axiom :
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equiv [ FROST_Ref.round1 ~ FROST_Round1_Spec.round1 :
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={sess, share, my_idx}
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==>
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={res} ].
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(* -------------------------------------------------------------------- *)
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(* Round-2 refinement obligation *)
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(* -------------------------------------------------------------------- *)
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(* The abstract Round-2 specification: given the session, secret share, *)
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(* stored nonces, aggregated commitments, and message, the procedure *)
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(* computes the binding factor rho_i, the challenge c, and emits *)
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(* z_i = d_i + rho_i * e_i + c * lambda_i * s_i *)
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(* in F_r. *)
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(* -------------------------------------------------------------------- *)
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op compute_binding_factor :
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session_t -> commit_list_t -> message_t -> int -> scalar_t.
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op compute_challenge :
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session_t -> point_t -> group_pk_t -> message_t -> scalar_t.
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op aggregate_R : commit_list_t -> message_t -> session_t -> point_t.
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module FROST_Round2_Spec = {
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proc round2(sess : session_t, share : share_t, my_idx : int,
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nonces : nonce_pair_t, commits : commit_list_t,
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msg : message_t) : share_response_t = {
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var rho, c, lam, z : scalar_t;
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var rpt : point_t;
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rho <- compute_binding_factor sess commits msg my_idx;
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rpt <- aggregate_R commits msg sess;
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(* Group PK is committed in the session; threshold reconstruction *)
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(* is implicit in the session-binding step. *)
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c <- compute_challenge sess rpt witness msg;
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lam <- lagrange (map fst commits) my_idx;
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z <- scalar_add
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(scalar_add nonces.`1
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(scalar_mul_s rho nonces.`2))
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(scalar_mul_s c (scalar_mul_s lam share));
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return z;
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}
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}.
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axiom round2_refinement_axiom :
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equiv [ FROST_Ref.round2 ~ FROST_Round2_Spec.round2 :
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={sess, share, my_idx, nonces, commits, msg}
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==>
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={res} ].
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(* -------------------------------------------------------------------- *)
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(* Combine refinement obligation *)
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(* -------------------------------------------------------------------- *)
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(* The abstract Combine specification: aggregate R = sum_i (D_i + *)
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(* rho_i * E_i), z = sum_i z_i, then encode (R, z) per the pinned *)
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(* ciphersuite (RFC 8032 §5.1.6 for Ed25519 / BIP-340 §6.6 for *)
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(* secp256k1-Taproot). The encoding step is the byte-walk axiom from *)
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(* `FROST_N1.ec` and lives in the ciphersuite layer. *)
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(* -------------------------------------------------------------------- *)
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(* encode_signature is declared in the shared base FROST_N1.ec so that *)
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(* the ciphersuite layer can also pin it; consumed here unchanged. *)
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module FROST_Combine_Spec = {
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proc combine(sess : session_t, commits : commit_list_t,
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shares : (int * share_response_t) list,
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group_pk : group_pk_t, msg : message_t) : signature_t = {
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var rpt : point_t;
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var z : scalar_t;
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rpt <- aggregate_R commits msg sess;
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z <- foldr scalar_add scalar_zero (map snd shares);
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return encode_signature rpt z;
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}
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}.
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axiom combine_refinement_axiom :
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equiv [ FROST_Ref.combine ~ FROST_Combine_Spec.combine :
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={sess, commits, shares, group_pk, msg}
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==>
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={res} ].
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(* -------------------------------------------------------------------- *)
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(* End of FROST_N1_Refinement.ec *)
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(* -------------------------------------------------------------------- *)
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