End-to-end compilable implementation of quantum elliptic curve logarithm in Qrisp

TL;DR

This paper presents a fully compilable implementation of elliptic curve arithmetic for quantum computers using the Qrisp language, verified through simulation, advancing quantum cryptography software support.

Contribution

It introduces one of the first end-to-end, compilable quantum elliptic curve logarithm implementations in Qrisp, bridging a gap in quantum cryptography software tools.

Findings

Implementation verified with Qrisp's simulator

Demonstrates feasibility of compiling EC algorithms for quantum devices

Enhances software support for quantum elliptic curve cryptography

Abstract

Elliptic curve cryptography (ECC) is a widely established cryptographic technique, recognized for its effectiveness and reliability across a broad range of applications such as securing telecommunications or safeguarding cryptocurrency wallets. Although being more robust than RSA, ECC is, nevertheless, also threatened by attacks based on Shor's algorithm, which made it a popular field of study in quantum information science. A variety of techniques have been proposed to perform EC arithmetic in quantum devices; however, software support for compiling these algorithms into executables is extremely limited. Within this work, we leverage the Qrisp programming language to realize one of the first fully compilable implementations of EC arithmetic and verify its correctness using Qrisp's built-in sparse matrix simulator.