#!/usr/bin/env python
"""Generate tests/fixtures/ecdlp_instances.json for rho_engine.

10 generic prime-order curves for each of 20, 24, 28, 32 bits and 10 j = 0 curves (a = 0, p ≡ 1 mod 3)
for each of 24 and 32 bits, each with a random secret d and Q = dG, computed with the pure-Python
reference `wp34.ec` (point counting by PARI/GP `ellcard`). All integers are decimal strings.

Usage (from the repository root):  PYTHONPATH=src .venv/bin/python experiments/synthetic_ecdlp/rho_engine/scripts/gen_fixtures.py [--seed 34] [--out tests/fixtures/ecdlp_instances.json]
"""
import argparse, json, random, pathlib, sys, time

ROOT = pathlib.Path(__file__).resolve().parents[4]
sys.path.insert(0, str(ROOT / "src"))
from wp34.ec import random_prime_order_curve, cube_roots_of_unity, endomorphism_lambda  # noqa: E402


def main():
    ap = argparse.ArgumentParser()
    ap.add_argument("--seed", type=int, default=34)
    ap.add_argument("--out", default=str(ROOT / "tests" / "fixtures" / "ecdlp_instances.json"))
    ap.add_argument("--per-size", type=int, default=10)
    args = ap.parse_args()
    rng = random.Random(args.seed)
    plan = [(20, False), (24, False), (28, False), (32, False), (24, True), (32, True)]
    out = []
    t0 = time.time()
    for bits, j0 in plan:
        for i in range(args.per_size):
            E = random_prime_order_curve(bits, rng, j0=j0)
            d = rng.randrange(1, E.n)
            Q = E.mul(d, E.G)
            assert E.is_on_curve(Q) and Q is not None
            rec = {
                "label": f"{bits}b{'-j0' if j0 else ''}-{i:02d}",
                "bits": bits, "j0": j0,
                "p": str(E.p), "a": str(E.a), "b": str(E.b), "n": str(E.n),
                "gx": str(E.G[0]), "gy": str(E.G[1]), "qx": str(Q[0]), "qy": str(Q[1]),
                "d": str(d),
            }
            if j0:
                assert E.n % 3 == 1, "prime order n of a j=0 curve with p ≡ 1 mod 3 must be ≡ 1 mod 3"
                betas = cube_roots_of_unity(E.p, rng)
                beta = betas[0]
                lam = endomorphism_lambda(E, beta)
                assert (beta * E.G[0] % E.p, E.G[1]) == E.mul(lam, E.G)
                rec["beta"] = str(beta)
                rec["lambda"] = str(lam)
            out.append(rec)
            print(f"{rec['label']}: p={E.p} n={E.n} d={d}", file=sys.stderr)
    doc = {"generator": "experiments/synthetic_ecdlp/rho_engine/scripts/gen_fixtures.py", "seed": args.seed,
           "reference": "src/wp34/ec.py (random_prime_order_curve via PARI/GP ellcard)",
           "elapsed_s": round(time.time() - t0, 1), "instances": out}
    pathlib.Path(args.out).write_text(json.dumps(doc, indent=1) + "\n")
    print(f"wrote {len(out)} instances to {args.out}", file=sys.stderr)


if __name__ == "__main__":
    main()