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# Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

CiteScore 2018: 1.41

SCImago Journal Rank (SJR) 2018: 0.342
Source Normalized Impact per Paper (SNIP) 2018: 1.076

Mathematical Citation Quotient (MCQ) 2018: 0.75

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1862-2984
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# New number-theoretic cryptographic primitives

Éric Brier
/ Marc Joye
/ David Naccache
Published Online: 2019-11-09 | DOI: https://doi.org/10.1515/jmc-2019-0035

## 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.

MSC 2010: 94A60; 11T71; 11A15; 11R18

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Accepted: 2019-09-15

Published Online: 2019-11-09

Citation Information: Journal of Mathematical Cryptology, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976,

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