New Number-Theoretic Cryptographic Primitives

Eric Brier; Houda Ferradi; Marc Joye; David Naccache

Paper 2019/484

New Number-Theoretic Cryptographic Primitives

Eric Brier, Houda Ferradi, Marc Joye, and David Naccache

Abstract

This paper introduces new $p^{r} q$ -based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat--Shamir transform. In the basic signature scheme, the signer generates multiple RSA-like moduli $n_{i} = p_{i}^{2} q_{i}$ and keeps their factors secret. The signature is a bounded-size prime whose Jacobi symbols with respect to the 's match the message digest. The generalized signature schemes replace the Jacobi symbol with higher-power residue symbols. Given of their very unique design the proposed signature schemes seem to be overlooked missing species in the corpus of known signature algorithms.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. NutMiC 2019 | J. Math. Cryptol.
Keywords: th-power residue symbol th-order imprint moduli number theory one-way functions digital signatures cryptographic primitives.
Contact author(s): houda ferradi @ ens fr
marc joye @ gmail com
History: 2019-11-16: last of 12 revisions; 2019-05-13: received; See all versions
Short URL: https://ia.cr/2019/484
License: CC BY

BibTeX

@misc{cryptoeprint:2019/484,
      author = {Eric Brier and Houda Ferradi and Marc Joye and David Naccache},
      title = {New Number-Theoretic Cryptographic Primitives},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/484},
      year = {2019},
      url = {https://eprint.iacr.org/2019/484}
}