Extending Regev’s Quantum Algorithm to Elliptic Curves

2026
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Authors: Razvan Barbulescu; Mugurel Barcau; Vicenţiu Paşol
Published in: Progress in Cryptology – LATINCRYPT 2025
Publisher: Springer Nature Switzerland

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Abstract

The article delves into the extension of Regev's quantum algorithm to elliptic curves, addressing the discrete logarithm problem (DLP) in cryptography. It discusses the potential of this extension to outperform existing algorithms like Shor's algorithm, particularly in the context of elliptic curve cryptography (ECC). The text explores the theoretical foundations of Regev's algorithm and its application to elliptic curves, highlighting the importance of finding small points on these curves to enhance the algorithm's efficiency. It also examines the implications of this extension for future cryptographic systems, suggesting that Regev's algorithm could provide a significant speedup in solving the DLP on elliptic curves. The article concludes with a discussion on the practical implementation of the algorithm and its potential impact on the security of cryptographic systems.

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Title: Extending Regev’s Quantum Algorithm to Elliptic Curves
Authors: Razvan Barbulescu
Mugurel Barcau
Vicenţiu Paşol
Publisher: Springer Nature Switzerland
Book: Progress in Cryptology – LATINCRYPT 2025
Print ISBN: 978-3-032-06753-1

Electronic ISBN: 978-3-032-06754-8

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-06754-8_9

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