feat(crypto): opt-in constant-time path for secret-exponent modexps [DO NOT MERGE]

[piotr-roslaniec]

⛔ DO NOT MERGE

This PR is not ready to merge. It is opened for review and discussion only.
Merging carries an external coordination cost (a Go toolchain bump that ripples
into keep-core — see "Blocking considerations" below) that must be agreed first.

Summary

Closes the timing side-channel / constant-time gap (CVE-2023-26557 class) identified in the
threshold-ECDSA variant analysis. Ports the upstream BNB tss-lib constant-time framework
(common/constant_time.go, built on filippo.io/bigmod —
the same constant-time bignum library used inside Go's crypto/rsa/crypto/ecdsa) and wires it,
behind a default-off runtime toggle, into the secret-exponent modular exponentiations.

math/big is variable-time and leaks information about secret exponents through execution time;
this provides a constant-time alternative for the operations that touch long-lived secrets.

What is wired (all behind common.IsConstantTimeEnabled())

File	Operation	CT primitive	Secret
crypto/paillier/paillier.go Decrypt	c^λ, Γ^λ mod N²; ModInverse(Lg, N)	ExpCT; NewCTModIntWithPhi.ModInverseCT	LambdaN, PhiN
crypto/paillier/paillier.go Proof	xs[i]^M mod N	ExpCT	M = N⁻¹ mod φ
crypto/dlnproof/proof.go NewDLNProof	h1^a mod N; c·x mod pq	ExpCT; MulCT	DLN witness x
crypto/paillier/factor_proof.go FactorProof	s^p, s^q mod NTilde	ExpCT	primes p, q
crypto/paillier/mod_proof.go ModProof + QR helpers	y^invN, x^e, x^((p-1)/2)	ExpCT	φ, p, q

Every modulus fed to bigmod is odd; the two φ(N)-even modular inverses (M, invN) stay on
math/big exactly as upstream documents. Each else branch preserves the original code verbatim.

Default-off / opt-in

constantTimeEnabled defaults to 0. With it off (the default), behavior and performance are
identical to before. A consumer enables it once at startup:

common.EnableConstantTimeOps()

The gap only closes once the consumer opts in. keep-core integration note: call
EnableConstantTimeOps() at startup, and note the Go-version requirement below.

Verification

• Default (CT-off), no regression: go build ./..., go vet (changed pkgs), full
  common/crypto/tss suites, ecdsa/keygen, ecdsa/signing all pass.
• CT-on, functionally equivalent: framework suite; per-proof equivalence — byte-identical for
  the deterministic ops (Decrypt, Proof, QR helpers), verifies for the randomized proofs;
  full CT-on keygen E2E (all parties agree on the public key) and CT-on signing E2E
  (valid ECDSA signature). Every CT test asserts IsConstantTimeEnabled() so it cannot pass
  vacuously, and the QR helper test covers an explicit non-residue.

Blocking considerations (why "do not merge" yet)

1. Go toolchain bump 1.16 → 1.23 (required by filippo.io/bigmod). keep-core pins this fork
   and would need to build with Go ≥1.23. The bump also crosses Go 1.22 loop-variable
   semantics — broader than just the bigmod floor. This coordination must be agreed before merge.
2. New dependency: filippo.io/bigmod v0.1.0.
3. Scope honesty:
   • isQuadResidueModPrime CT-wrapping goes beyond upstream (no analog) and is partial —
     only the exponentiation is constant-time; NewCTModInt(p)'s reduction of the secret prime is
     not. Consistent with upstream's own MulCT mod pMulQ, but a future upstream re-sync shows a
     delta here. Conscious choice, flagged for reviewer agreement.
   • Mixed CT / non-CT party interop is sound by construction (CT outputs are byte-identical;
     Verify is always non-CT over public data) but is not directly tested.

Out of scope (separate follow-up)

The secp256k1 EC scalar-mult side channel (2019 btcec NAF → btcec/v2) — large dependency
migration, rated low-exploitability in the variant analysis, and not part of "the constant_time.go
issue."

[mswilkison]

Update on blocking consideration 1: the Go >=1.23 compiler requirement is already satisfied on keep-core's dev branch. Its current go.mod declares go 1.24.0 and toolchain go1.24.1, and its Docker builders already use Go 1.24.

keep-core PR #4312 goes further: it raises the module minimum to Go 1.25.7 and aligns the toolchain, CI, and Docker builders on Go 1.26.8. That PR is currently open and unmerged, but the minimum-version requirement here does not depend on it landing.

The remaining consumer work is integrating the updated tss-lib revision, explicitly enabling constant-time operations where intended, and validating that integration. The keep-core PR retains the historical tss-lib pin, so its passing CI does not exercise this PR's constant-time implementation. The loop-variable semantics change from tss-lib's own go.mod bump also remains a library/integration-validation consideration: Go selects those semantics per module.

The minimum keep-core compiler-version requirement in this PR's blocker list can be marked satisfied for dev; consumer adoption and integration validation are separate follow-up work.