## Cryptology ePrint Archive: Report 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.

Given of their very unique design the proposed signature schemes seem to be overlooked missing species in the corpus of known signature algorithms.

Category / Keywords: foundations / $r$th-power residue symbol; $r$th-order imprint; $p^r q$ moduli; number theory; one-way functions; digital signatures; cryptographic primitives.

Original Publication (in the same form): NutMiC 2019

Date: received 12 May 2019, last revised 19 Jul 2019

Contact author: houda ferradi at ens fr

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/484

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