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 $n_i$'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
- $r$th-power residue symbol$r$th-order imprint$p^r q$ modulinumber theoryone-way functionsdigital signaturescryptographic 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}
}
