The One-Wayness of Jacobi Signatures

Henry Corrigan-Gibbs; David J. Wu

Paper 2023/1638

The One-Wayness of Jacobi Signatures

Henry Corrigan-Gibbs

, Massachusetts Institute of Technology

David J. Wu

, The University of Texas at Austin

Abstract

We show that under a mild number-theoretic conjecture, recovering an integer from its Jacobi signature modulo $N = p^2 q$, for primes $p$ and $q$, is as hard as factoring $N$. This relates, for the first time, the one-wayness of a pseudorandom generator that Damgård proposed in 1988, to a standard number-theoretic problem. In addition, we show breaking the Jacobi pseudorandom function is no harder than factoring.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: A minor revision of an IACR publication in CRYPTO 2024
Keywords: Jacobi symbol Legendre symbol quadratic residuosity
Contact author(s): henrycg @ csail mit edu
dwu4 @ cs utexas edu
History: 2024-09-25: last of 4 revisions; 2023-10-21: received; See all versions
Short URL: https://ia.cr/2023/1638
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1638,
      author = {Henry Corrigan-Gibbs and David J. Wu},
      title = {The One-Wayness of Jacobi Signatures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1638},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1638}
}