perf(ecsm): replace num-bigint with crypto-bigint

[Oppen]

Summary

• Replaces num-bigint/num-traits with crypto-bigint (already a transitive dep via elliptic-curve) in the ecsm crate
• AffinePoint coordinates and the scalar k are now U256 (fixed-size, no heap allocation)
• Witness quotient computation uses U1024 intermediates — necessary because the shifted-quotient offset 3p² exceeds U512
• All tests rewritten without num-bigint; test-only reference_field.rs uses DynResidue for modular Fp arithmetic
• Follow-up to the note in abfb0cb: "port the field/curve primitives we need to drop the num-bigint reference path entirely"

Test plan

• cargo test -p ecsm — 15/15 pass
• make test — all non-CUDA tests pass (CUDA failures are pre-existing on this machine)
• /bench on CI to measure impact

[Oppen]

/bench

[github-actions]

Benchmark — ethrex 20 transfers (median of 3)

_{Table parallelism: auto (cores / 3)}

Metric	main	PR	Δ
Peak heap	79957 MB	80227 MB	+270 MB (+0.3%) ⚪
Prove time	50.577s	49.859s	-0.718s (-1.4%) ⚪

✅ No significant change.

✅ Low variance (time: 1.2%, heap: 1.5%)

_{Commit: cb14979 · Baseline: built from main · Runner: self-hosted bench}

[Oppen]

/bench

[diegokingston]

/bench-verify

[github-actions]

⏳ Benchmark started on the bench server. The verifier bench takes ~5 min; the recursion-guest cycle comparison then adds guest builds — a few minutes when cached, up to ~1h on a cold run. The bench server is occupied until it finishes.

[github-actions]

Verifier benchmark — cb149799f9 vs main (20 pairs)

=== Verify ABBA result ===

Metric	main	PR	Δ
Verify time (per-side)	3.771s	5.136s	+36.20% 🔴
Proof size	204.46 MiB	308.03 MiB	+50.65% 🔴

Per-side (PR can't deserialize the baseline's proof — proof-format change): A/B/B/A cancels machine drift but not proof-specific variance — read the Verify-time Δ as approximate.

  pairs: 20   mean A (PR): 5.136s   mean B (main): 3.771s
  [parametric] paired-t   mean +36.20%   sd 1.03%   se 0.23%
               95% CI: [+35.72%, +36.68%]   (t df=19 = 2.093)
  [robust]     median +36.20%   Wilcoxon W+=210 W-=0  p(exact)=1.9e-06  (z=+3.90)

  run-to-run jitter:    A CV 0.56%   B CV 0.43%        (lower = steadier)
  within-session drift: +0.23% over the run, 1st->2nd half +0.06%

🔴 REAL REGRESSION — PR verifies ~36.20% slower (paired-t and Wilcoxon agree).

_{Drift-free interleaved A/B/B/A measurement. - = PR faster. Trust the verdict when paired-t and Wilcoxon agree.}

---

Recursion guest cycles (main vs PR)

⚠️ Recursion cycle bench did not complete (does not affect the verifier verdict above). Last log lines:

==> Pruning old ref worktree /tmp/recursion_cycles_run/wt_39abfadd (keeping newest 10)
==> Refs
   A (PR)       cb149799f9fb8429deac5c458644c4e33778dfb3  -> cb149799f9
   B (baseline) origin/main  -> f4a5887e68
   preset=min  work=/tmp/recursion_cycles_run  sysroot=/home/app/.lambda-vm-sysroot
==> Building MEASURE_CLI (cli, release) from f4a5887e68 ...
==> [baseline] Adding worktree /tmp/recursion_cycles_run/wt_f4a5887e @ f4a5887e
Preparing worktree (detached HEAD f4a5887e)
==> [baseline] make compile-recursion-elfs @ f4a5887e (this can take 10-20 min the first time) ...
==> [baseline] guest ELF: recursion-min.elf
==> [baseline] dumping recursion input blob (cargo test test_dump_recursion_input) ...
==> [baseline] blob: 401024 bytes -> /tmp/recursion_cycles_run/blob_f4a5887e_min.bin
==> [baseline] measuring: /tmp/recursion_cycles_run/measure_cli execute recursion-min.elf --private-input <blob> --cycles
==> [baseline] cycles=51408494 keccak=3885  (execute wall-time 1s)
==> [PR] Adding worktree /tmp/recursion_cycles_run/wt_cb149799 @ cb149799
Preparing worktree (detached HEAD cb149799)
==> [PR] make compile-recursion-elfs @ cb149799 (this can take 10-20 min the first time) ...
ERROR: [PR] 'make compile-recursion-elfs' failed for cb149799f9fb8429deac5c458644c4e33778dfb3 (cb149799). Tail of /tmp/recursion_cycles_run/build_guest_cb149799.log:
make: *** No rule to make target 'compile-recursion-elfs'.  Stop.