International Association for Cryptologic Research

International Association
for Cryptologic Research


(Verifiable) Delay Functions from Lucas Sequences

Charlotte Hoffmann , Institute of Science and Technology Austria
Pavel Hubáček , Czech Academy of Sciences and Charles University
Chethan Kamath , Tel Aviv University, Israel
Tomáš Krňák , Charles University
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Presentation: Slides
Conference: TCC 2023
Abstract: Lucas sequences are constant-recursive integer sequences with a long history of applications in cryptography, both in the design of cryptographic schemes and cryptanalysis. In this work, we study the sequential hardness of computing Lucas sequences over an RSA modulus. First, we show that modular Lucas sequences are at least as sequentially hard as the classical delay function given by iterated modular squaring proposed by Rivest, Shamir, and Wagner (MIT Tech. Rep. 1996) in the context of time-lock puzzles. Moreover, there is no obvious reduction in the other direction, which suggests that the assumption of sequential hardness of modular Lucas sequences is strictly weaker than that of iterated modular squaring. In other words, the sequential hardness of modular Lucas sequences might hold even in the case of an algorithmic improvement violating the sequential hardness of iterated modular squaring. Second, we demonstrate the feasibility of constructing practically-efficient verifiable delay functions based on the sequential hardness of modular Lucas sequences. Our construction builds on the work of Pietrzak (ITCS 2019) by leveraging the intrinsic connection between the problem of computing modular Lucas sequences and exponentiation in an appropriate extension field.
  title={(Verifiable) Delay Functions from Lucas Sequences},
  author={Charlotte Hoffmann and Pavel Hubáček and Chethan Kamath and Tomáš Krňák},