From Shor's Dead End to the p-Adic Frontier
v0.1 Phase 5
Compute p-adic modular exponentiation — $c = a^b \bmod p$ for a 256-bit prime (secp256k1 modulus) — using only branch-respecting quantum operations on a hierarchical tree structure.
This is the ultrametric analog of the elliptic curve point addition targeted by the ecdsa.fail challenge.
| Gate Type | Base Cost | Cross-Branch Penalty |
|---|---|---|
| Single-qubit (within branch) | 1 | ×1 |
| Two-qubit (same branch) | 2 | ×1 |
| Two-qubit (cross-branch, distance k) | 2 | ×(1 + 0.5k) |
| Multi-qubit (n branches) | n² | ×max(penalty) |
git clone [repo-url] cd uqc-benchmark/src python verifier.py --test python verifier.py --submission submission.json
7 tests pass 16 vectors
{
"benchmark": "uqc-v0.1",
"target": "p-adic modexp",
"params": {"a": ..., "b": ..., "p": "secp256k1"},
"circuit": {
"tree_depth": 64,
"gates": [{"type": "cnot", "targets": [0], "controls": [1]}]
}
}