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frost_enrollment: add the test suite and the regression vectors

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Fourth of six commits. Twelve tests replacing the Phase 2 smoke test, plus
a vector generator and the frozen vectors it produces.

The regression vectors are the one part of this worth being precise
about, because they are easy to over-claim. FROST enrollment has no BIP
and no published vectors, and the reference proof of concept draws its
randomness from secrets.randbits, which is not seedable -- so there is
nothing to cross-validate against. tools/test_vectors_frost_enrollment_generate.py
therefore re-implements the math independently in stdlib-only Python,
including the group arithmetic written from the secp256k1 parameters
rather than borrowed, and freezes the output. What that buys: the two tag
strings, the params hash serialization, the share-splitting derivation
and the identifier conventions are now pinned, and changing any of them
is a loud vector-breaking change. What it does not buy is evidence of
protocol correctness. The generator header comment and the generated
file both say so, as does frost_enrollment.md.

The vectors passed on the first run against the C code, which is worth
recording: two independent implementations agree byte for byte on the
params hash, every delta, every sigma, the derived public share and the
final share, across four cases (2-of-3 minimal, 2-of-3 oversized at
u = 3 > t = 2, a 3-of-5 repair with a deliberately UNSORTED helper set,
and a 4-of-6 enrollment), covering both threshold-key Y parities.

The algebraic invariants are what actually carry correctness:

- Reconstruction (PoC test_generate_frost_share): after a 2-of-3 group
  enrolls id 3, every pair {i, 3} reconstructs the original threshold
  secret, and so does the untouched pair {0, 1}.
- Signing (PoC test_sign): a real BIP340 signature from {2, 3} verifying
  against the unchanged threshold public key, with every partial
  signature individually verified, plus the n -> n+1 bookkeeping --
  secp256k1_frost_threshold_info_validate must accept the public share
  table extended with pubshare_derive's output at n+1.
- Repair: byte-for-byte equality with the lost share, and the repaired
  participant keeps its old public share.
- Oversized helper set: u = 3 and u = 2 over the same key material
  produce the same share and the same derived public share.
- Randomized: COUNT iterations over 2 <= t <= u <= n <= 7, half
  enrollment and half repair, with EVERY HELPER GIVEN THE IDENTIFIER SET
  IN ITS OWN SHUFFLED ORDER. The params hash must come out identical
  while the delta buffers stay aligned per helper -- which is the whole
  point of canonicalizing ids inside the hash and nowhere else. Each
  iteration then checks every t-subset containing the new participant.

The negative tests are organized around what each gate is actually for:

- Fault injection flips a bit in one sigma. secshare_gen fails and wipes
  its output; the same call with expected_pubshare = NULL SUCCEEDS and
  returns a wrong share. That second assertion is the point -- it is the
  evidence that the parameter is load-bearing rather than decorative.
  Tampered public shares are caught earlier, by
  secp256k1_frost_threshold_info_validate, so the test exercises the
  recommended flow and not just the module.
- Parameter mismatch, four angles: (a) one helper runs round 1.1 for a
  different target and every other helper's share_agg aborts naming it
  by identifier; (b) a caller that IGNORES that abort and finishes round
  1.2 anyway still cannot produce a usable share, because the
  public-share check catches the inconsistent sum -- defence in depth,
  not a test of the test's own control flow; (c) the helpers agree with
  each other on new_id = 3 while the target expects 4, which round 1.2
  cannot see and round 2's own recomputation does; (d) two groups with
  identical (t, n, ids, new_id) get different hashes, and a hash from one
  fails share_agg in the other.
- Own-slot semantics: filling the caller's own slot of
  received_params_hashes32 with garbage changes nothing, because it is
  never read -- but the same garbage in a slot that IS read still aborts.
  That pair is what makes "recomputation, not string comparison"
  testable rather than merely asserted.
- Invalid parameters, including both deliberate divergences: t = 1
  refused, enrollment refused at n = 128 while repair at n = 128 is
  accepted, n_ids > 128 returning 0 with the output zeroed in a
  production build.

Three bugs found while writing these, all in the tests, all worth
naming:

- pubshare_derive takes public shares ALIGNED WITH ids, and the test
  helper was handing it the participant-indexed table. Those coincide
  exactly when the helper set is 0..u-1, which every test until the
  repair case used, so the first non-contiguous helper set {0, 2} was
  what exposed it. There is now one helper that does the gather, with a
  comment saying which confusion it exists to prevent.
- The fault-injection test compared against r.new_secshare without ever
  running round 2, and the mismatch test compared against
  r.params_hashes[0] one line before round 1.1 filled it. Both were
  reads of uninitialized memory that happened to pass; valgrind found
  both.

The randomized test loops COUNT times so -i scales it, following the
iceberg module (tests_impl.h:1322) rather than prefractal's run-once
convention -- a fuzzing loop that ignores the iteration count is not
much of one.

Verification: all twelve tests pass at the default iteration count, at
-i=200 and at -i=2000; ./tests, ./noverify_tests and ./exhaustive_tests
exit 0 with all five FROST-stack modules enabled; the module runs clean
under valgrind (0 errors from 0 contexts); ctime_tests is clean under
valgrind; regenerating vectors.h reproduces it byte for byte.

One note for anyone running these locally: ctime_tests must not be run
against a CPPFLAGS='-DVERIFY' build. secp256k1_scalar_verify branches on
scalar values, which ctime_tests deliberately marks secret, so every
scalar operation in the library reports a finding -- 75997 of them, none
in this module. The CI matrix already pairs -DVERIFY with
CTIMETESTS: 'no' (.github/workflows/ci.yml:119, :596) for this reason.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
Kgothatso Ngako
2026-09-04 04:24:21 +02:00
parent 89b253b50e
commit 303a7caeae
4 changed files with 1121 additions and 20 deletions
Download Patch File Download Diff File Expand all files Collapse all files

359
tools/test_vectors_frost_enrollment_generate.py Executable file
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#!/usr/bin/env python3
"""Generates src/modules/frost_enrollment/vectors.h.
These are REGRESSION vectors, not cross-validation vectors. FROST enrollment
has no BIP and therefore no published test vectors, and the reference proof of
concept (https://github.com/siv2r/frost-enrollment) draws its randomness from
secrets.randbits, which is not seedable -- so there is nothing to check the C
implementation against. This script therefore re-implements the same math
independently, in plain Python, and freezes the result.
What that buys is real but bounded: it pins the two tag strings, the exact
parameters hash serialization, the share-splitting derivation and the
identifier conventions, so that any change to them is a loud, deliberate,
vector-breaking change rather than a silent one. It is NOT evidence that the
protocol is implemented correctly -- the algebraic invariants in
src/modules/frost_enrollment/tests_impl.h are what carry that.
The one thing this file does establish independently is the group arithmetic:
the elliptic curve operations below are written from the secp256k1 parameters
rather than borrowed from the library, so a vector mismatch in the derived
public share or the threshold key really is a disagreement between two
implementations.
Usage: %s > src/modules/frost_enrollment/vectors.h
"""
import hashlib
import sys
import textwrap
# secp256k1 domain parameters.
P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
ORDER = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
GX = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
GY = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
G = (GX, GY)
MAX_PARTICIPANTS = 128
# --- group arithmetic (points are (x, y) or None for infinity) ---
def point_add(a, b):
if a is None:
return b
if b is None:
return a
if a[0] == b[0] and (a[1] + b[1]) % P == 0:
return None
if a == b:
lam = 3 * a[0] * a[0] * pow(2 * a[1], P - 2, P) % P
else:
lam = (b[1] - a[1]) * pow(b[0] - a[0], P - 2, P) % P
x = (lam * lam - a[0] - b[0]) % P
return (x, (lam * (a[0] - x) - a[1]) % P)
def point_mul(point, scalar):
result = None
scalar %= ORDER
while scalar:
if scalar & 1:
result = point_add(result, point)
point = point_add(point, point)
scalar >>= 1
return result
def cbytes(point):
"""33-byte compressed serialization."""
assert point is not None
return bytes([2 + (point[1] & 1)]) + point[0].to_bytes(32, "big")
# --- hashing ---
def tagged_hash(tag, msg):
tag_hash = hashlib.sha256(tag.encode()).digest()
return hashlib.sha256(tag_hash + tag_hash + msg).digest()
def ser32(x):
return x.to_bytes(4, "big")
# --- the protocol, mirroring src/modules/frost_enrollment/enrollment_impl.h ---
def params_hash(thresh_pk, ids, new_id, n_participants, threshold):
msg = cbytes(thresh_pk)
msg += ser32(n_participants) + ser32(threshold) + ser32(new_id)
msg += ser32(len(ids))
for i in sorted(ids):
msg += ser32(i)
return tagged_hash("FROST enrollment/params_hash", msg)
def lagrange_at(ids, my_id, new_id):
"""The Lagrange basis polynomial of my_id over ids, at the target.
Identifier space: the x-coordinate of identifier id is id + 1, so an
x-coordinate difference is an identifier difference and the +1 cancels."""
num, deno = 1, 1
for other in ids:
if other == my_id:
continue
num = num * (new_id - other) % ORDER
deno = deno * (my_id - other) % ORDER
return num * pow(deno, ORDER - 2, ORDER) % ORDER
def derive_mask(rand32, ph32, my_id, recipient_id):
msg = rand32 + ph32 + ser32(my_id) + ser32(recipient_id)
# from_bytes_wrapping: reduce mod the group order rather than reject.
return int.from_bytes(tagged_hash("FROST enrollment/share_split", msg), "big") % ORDER
def shares_gen(secshare, thresh_pk, ids, my_id, new_id, n_participants, threshold, secrand32):
ph32 = params_hash(thresh_pk, ids, new_id, n_participants, threshold)
v = lagrange_at(ids, my_id, new_id) * secshare % ORDER
rand32 = bytes(
a ^ b
for a, b in zip(
tagged_hash("FROST enrollment/share_split", secrand32),
secshare.to_bytes(32, "big"),
)
)
out = [0] * len(ids)
my_pos = ids.index(my_id)
for j, recipient in enumerate(ids):
if j == my_pos:
continue
out[j] = derive_mask(rand32, ph32, my_id, recipient)
v = (v - out[j]) % ORDER
out[my_pos] = v
return out, ph32
def trusted_dealer_keygen(thresh_sk, n_participants, threshold):
"""The frost module's trusted dealer (src/modules/frost/keygen_impl.h)."""
coeffs = []
for i in range(1, threshold):
h = tagged_hash("BIP0445/trusted/keygen", thresh_sk.to_bytes(32, "big") + ser32(i))
c = int.from_bytes(h, "big")
assert 0 < c < ORDER
coeffs.append(c)
secshares = []
for i in range(n_participants):
x = i + 1
share = 0
for c in coeffs:
share = (share * x + c) % ORDER
share = (share * x + thresh_sk) % ORDER
assert share != 0
secshares.append(share)
return secshares, point_mul(G, thresh_sk), [point_mul(G, s) for s in secshares]
def run_case(thresh_sk, n_participants, threshold, ids, new_id, seeds):
secshares, thresh_pk, pubshares = trusted_dealer_keygen(thresh_sk, n_participants, threshold)
ph32 = params_hash(thresh_pk, ids, new_id, n_participants, threshold)
shares = []
for k, my_id in enumerate(ids):
out, ph = shares_gen(
secshares[my_id], thresh_pk, ids, my_id, new_id, n_participants, threshold, seeds[k]
)
assert ph == ph32
shares.append(out)
# Round 1.2: helper j sums entry j of every helper's output.
sigmas = [sum(shares[i][j] for i in range(len(ids))) % ORDER for j in range(len(ids))]
# Round 2, and the independent check that the result really is f(x_new).
new_secshare = sum(sigmas) % ORDER
expected = sum(lagrange_at(ids, i, new_id) * secshares[i] for i in ids) % ORDER
assert new_secshare == expected
new_pubshare = None
for i in ids:
new_pubshare = point_add(new_pubshare, point_mul(pubshares[i], lagrange_at(ids, i, new_id)))
assert new_pubshare == point_mul(G, new_secshare)
return {
"n_participants": n_participants,
"threshold": threshold,
"ids": ids,
"new_id": new_id,
"thresh_pk": thresh_pk,
"pubshares": [pubshares[i] for i in ids],
"secshares": [secshares[i] for i in ids],
"seeds": seeds,
"params_hash": ph32,
"shares": shares,
"sigmas": sigmas,
"new_secshare": new_secshare,
"new_pubshare": new_pubshare,
}
# --- C emission ---
def byte_array(b):
return "{ %s }" % ", ".join("0x%02X" % x for x in b)
def scalar_array(x):
return byte_array(x.to_bytes(32, "big"))
def indent(s, level=1):
return textwrap.indent(s, 4 * level * " ")
def emit_case(c):
n_ids = len(c["ids"])
lines = []
lines.append("%d, %d, %d, %d," % (c["n_participants"], c["threshold"], n_ids, c["new_id"]))
lines.append("{ %s }," % ", ".join(str(i) for i in c["ids"]))
lines.append("%s," % byte_array(cbytes(c["thresh_pk"])))
lines.append("{ %s }," % ", ".join(byte_array(cbytes(p)) for p in c["pubshares"]))
lines.append("{ %s }," % ", ".join(scalar_array(s) for s in c["secshares"]))
lines.append("{ %s }," % ", ".join(byte_array(s) for s in c["seeds"]))
lines.append("%s," % byte_array(c["params_hash"]))
lines.append(
"{ %s },"
% ", ".join(
"{ %s }" % ", ".join("0x%02X" % b for s in row for b in s.to_bytes(32, "big"))
for row in c["shares"]
)
)
lines.append(
"{ %s },"
% ", ".join("0x%02X" % b for s in c["sigmas"] for b in s.to_bytes(32, "big"))
)
lines.append("%s," % scalar_array(c["new_secshare"]))
lines.append("%s" % byte_array(cbytes(c["new_pubshare"])))
return "{\n" + indent("\n".join(lines)) + "\n},"
# Fixed inputs. Nothing here is random at run time: the whole point is that
# regenerating this file without an intentional change reproduces it byte for
# byte.
CASES = [
# A 2-of-3 group enrolling a fourth participant with the minimum helper
# set. The base case, and the one the module documentation walks through.
# This key has EVEN Y; the three below have odd Y. Nothing in enrollment
# depends on the parity of the threshold key -- unlike frost signing, it
# never takes an x-only view of it -- so this is coverage rather than a
# distinction the code makes.
dict(
thresh_sk=0x0202020202020202020202020202020202020202020202020202020202020202,
n_participants=3,
threshold=2,
ids=[0, 1],
new_id=3,
seeds=[bytes([0x10 + i] * 32) for i in range(2)],
),
# The same group with an oversized helper set: u = 3 > t = 2. The resulting
# share must be the one the u = 2 case produces, which the C test checks
# separately; here it is simply frozen.
dict(
thresh_sk=0x0202020202020202020202020202020202020202020202020202020202020202,
n_participants=3,
threshold=2,
ids=[0, 1, 2],
new_id=3,
seeds=[bytes([0x20 + i] * 32) for i in range(3)],
),
# Repair: a 3-of-5 group reproducing participant 2's lost share. The helper
# set is deliberately unsorted, to pin that the parameters hash
# canonicalizes identifiers while the share buffers follow the caller's
# order.
dict(
thresh_sk=0x02030405060708090A0B0C0D0E0F101112131415161718191A1B1C1D1E1F2021,
n_participants=5,
threshold=3,
ids=[4, 0, 3],
new_id=2,
seeds=[bytes([0x30 + i] * 32) for i in range(3)],
),
# A larger enrollment, 4-of-6 to 4-of-7, and the only case whose DERIVED
# public share has odd Y.
dict(
thresh_sk=0x1122334455667788990011223344556677889900112233445566778899001122,
n_participants=6,
threshold=4,
ids=[0, 2, 3, 5],
new_id=6,
seeds=[bytes([0x40 + i] * 32) for i in range(4)],
),
]
def main():
cases = [run_case(**c) for c in CASES]
max_ids = max(len(c["ids"]) for c in cases)
out = """/**
* Automatically generated by tools/test_vectors_frost_enrollment_generate.py.
*
* REGRESSION vectors, not cross-validation vectors. FROST enrollment has no
* BIP and no published test vectors, and the reference proof of concept
* (https://github.com/siv2r/frost-enrollment) draws its randomness from
* secrets.randbits, which is not seedable, so there is nothing to check
* against. The generator re-implements the math independently in Python and
* freezes the result.
*
* What these pin: the two tag strings ("FROST enrollment/params_hash" and
* "FROST enrollment/share_split"), the parameters hash serialization, the
* share-splitting derivation, and the identifier conventions. Changing any of
* them is a vector-breaking change. What they do NOT establish is protocol
* correctness -- the algebraic invariants in tests_impl.h carry that.
*
* Used by the tests in src/modules/frost_enrollment/tests_impl.h. */
#ifndef SECP256K1_MODULE_FROST_ENROLLMENT_VECTORS_H
#define SECP256K1_MODULE_FROST_ENROLLMENT_VECTORS_H
#define FROST_ENROLLMENT_VEC_MAX_IDS %d
struct frost_enrollment_vec_case {
/* Parameters. */
size_t n_participants;
uint32_t threshold;
size_t n_ids;
uint32_t new_id;
uint32_t ids[FROST_ENROLLMENT_VEC_MAX_IDS];
/* Group key material, aligned with ids. */
unsigned char thresh_pk33[33];
unsigned char pubshares33[FROST_ENROLLMENT_VEC_MAX_IDS][33];
unsigned char secshares32[FROST_ENROLLMENT_VEC_MAX_IDS][32];
/* Round 1.1 inputs and outputs. shares32[i] is helper ids[i]'s output
* buffer, aligned with ids. */
unsigned char session_secrand32[FROST_ENROLLMENT_VEC_MAX_IDS][32];
unsigned char params_hash32[32];
unsigned char shares32[FROST_ENROLLMENT_VEC_MAX_IDS][FROST_ENROLLMENT_VEC_MAX_IDS * 32];
/* Round 1.2 and round 2 outputs. */
unsigned char sigmas32[FROST_ENROLLMENT_VEC_MAX_IDS * 32];
unsigned char new_secshare32[32];
unsigned char new_pubshare33[33];
};
static const struct frost_enrollment_vec_case frost_enrollment_vec_cases[%d] = {
""" % (
max_ids,
len(cases),
)
for c in cases:
out += indent(emit_case(c)) + "\n"
out += "};\n\n#endif /* SECP256K1_MODULE_FROST_ENROLLMENT_VECTORS_H */\n"
sys.stdout.write(out)
if __name__ == "__main__":
main()