Paper 2019/484
New Number-Theoretic Cryptographic Primitives
Eric Brier and Houda Ferradi and 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. The case of 8th-power residue symbols is fully detailed along with an efficient implementation thereof. 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)
- Category
- Foundations
- Publication info
- Published elsewhere. NutMiC 2019
- 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
- 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