Journal of Mathematical Cryptology
Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran
Editorial Board Member: 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
SCImago Journal Rank (SJR) 2015: 0.313
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Impact per Publication (IPP) 2015: 0.396
Mathematical Citation Quotient (MCQ) 2015: 0.24
Random subgroups and analysis of the length-based and quotient attacks
1McGill University, 805 Sherbrooke West, Montreal, H3A 2K6, Canada. Email: email@example.com
2Stevens Institute of Technology, Castle Point on Hudson, Hoboken NJ 07030-5991, USA. Email: firstname.lastname@example.org
Citation Information: Journal of Mathematical Cryptology. Volume 2, Issue 1, Pages 29–61, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: 10.1515/JMC.2008.003, May 2008
- Published Online:
In this paper we discuss generic properties of “random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they “sit” inside G in a very particular way. This gives a strong mathematical foundation for cryptanalysis of several group-based cryptosystems and indicates on how to chose “strong keys”. To illustrate our technique we analyze the Anshel-Anshel-Goldfeld (AAG) cryptosystem and give a mathematical explanation of recent success of some heuristic length-based attacks on it. Furthermore, we design and analyze a new type of attack, which we term the quotient attacks. Mathematical methods we develop here also indicate how one can try to choose “parameters” in AAG to foil the attacks.
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