Validation of Quantum Elliptic Curve Point Addition Circuits

TL;DR

This paper verifies and corrects quantum circuits for elliptic curve point addition, ensuring their reliability for cryptographic applications against quantum attacks.

Contribution

It identifies inconsistencies in existing quantum elliptic curve point addition circuits and provides fixes without increasing gate complexity.

Findings

Four inconsistencies found in state-of-the-art circuits

Provided circuit corrections maintaining minimal resource use

Ensured circuit correctness by restoring ancilla qubits

Abstract

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic protocol's resistance against future quantum computers, researchers figure out minimal resource-count circuits for performing these operations while still being correct. To assure the correctness of a circuit, it is integral to restore all ancilla qubits used to their original states. Failure to do so could result in decoherence of the computation's final result. Through rigorous classical simulation and unit testing, I surfaced four inconsistencies in the state-of-the-art quantum circuit for elliptic curve point addition where the circuit diagram states the qubits are returned in the original ($|0\rangle$) state, but the intermediate values are not uncomputed. I provide fixes to the circuit without increasing the leading-order gate cost.