An Optimized Quantum Implementation of ISD on Scalable Quantum Resources

TL;DR

This paper presents the first detailed quantum circuit implementation of the ISD algorithm, demonstrating that it can be efficiently realized with manageable overhead and hybrid classical-quantum trade-offs for code-based cryptography security analysis.

Contribution

It provides the first quantum circuit design for full ISD, with complexity estimates and hybrid strategies to optimize quantum resource usage.

Findings

Prange's ISD can be implemented efficiently on quantum computers

Hybrid classical-quantum approaches enable resource tailoring

Overcoming previous optimality results on constrained quantum search

Abstract

The security of code based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, it is still unclear whether a real quantum circuit could yield actual improvements or suffer an enormous overhead due to its implementation. This leads to different considerations of these quantum attacks in the security analysis of code based proposals. In this work we clarify this doubt by giving the first quantum circuit design of the fully-fledged ISD procedure, an implementation in the quantum simulation library Qibo as well as precise estimates of its complexities. We show that against common belief, Prange's ISD algorithm can be implemented rather efficiently on a quantum computer, namely with only a logarithmic overhead in circuit depth compared to a classical implementation. As another major contribution, we leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs, that allow to tailor the necessary qubits to any available amount, while still providing quantum speedups. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search.