Engineering Practical Rank-Code-Based Cryptographic Schemes on Embedded Hardware. A Case Study on ROLLO

Hu, Jingwei; Wang, Wen; Gaj, Kris; Wang, Liping; Wang, Huaxiong

doi:10.1109/tc.2022.3225080

Cited by 1 publication

(1 citation statement)

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“…A component that solves linear systems modulo 2 is therefore required in various applications. Choosing an optimal approach typically depends on features including the dimension, number of equations, and sparsity; research on this problem is ongoing [35]. While it is unlikely that Mod2VQLS would have a significant enough advantage over block Wiedermann to motivate the expense of developing quantum computers for this purpose, it is much more likely that large-scale quantum computers will become commercially available for a range of applications, and that Mod2VQLS will have particular niches in this environment.…”

Section: Applications Of Mod2vqls and Related Techniquesmentioning

confidence: 99%

Mod2VQLS: A Variational Quantum Algorithm for Solving Systems of Linear Equations Modulo 2

Aboumrad,

Widdows

2024

Applied Sciences

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This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem.

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Section: Applications Of Mod2vqls and Related Techniquesmentioning

confidence: 99%