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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 / Dawson, Ed / 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 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 7, Issue 4


Generating safe primes

Joachim von zur Gathen / Igor E. Shparlinski
Published Online: 2013-11-14 | DOI: https://doi.org/10.1515/jmc-2013-5011


Safe primes and safe RSA moduli are used in several cryptographic schemes. The most common notion is that of a prime p, where is also prime. The latter is then a Sophie Germain prime. Under appropriate heuristics, they exist in abundance and can be generated efficiently. But the modern methods of analytic number theory have – so far – not even allowed to prove that there are infinitely many of them. Thus for this notion of safe primes, there is no algorithm in the literature that is unconditionally proven to terminate, let alone to be efficient. This paper considers a different notion of safe primes and moduli. They can be generated in polynomial time, without any unproven assumptions, and are good enough for the cryptographic applications that we are aware of.

Keywords: Safe prime; Sophie Germain prime; Hofheinz–Kiltz–Shoup cryptosystem

About the article

Received: 2013-03-08

Accepted: 2013-08-05

Published Online: 2013-11-14

Published in Print: 2013-12-01

Citation Information: Journal of Mathematical Cryptology, Volume 7, Issue 4, Pages 333–365, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2013-5011.

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