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Cryptography 2018, 2(3), 16; https://doi.org/10.3390/cryptography2030016

Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn

1
MACIMTE, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
2
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 21 May 2018 / Revised: 13 July 2018 / Accepted: 16 July 2018 / Published: 19 July 2018
(This article belongs to the Special Issue Public Key Cryptography)
Full-Text   |   PDF [251 KB, uploaded 19 July 2018]

Abstract

In 2008, Doliskani et al. proposed an ElGamal-style encryption scheme using the symmetric group Sn as mathematical platform. In 2012, an improvement of the cryptosystem’s memory requirements was suggested by Othman. The proposal by Doliskani et al. in particular requires the discrete logarithm problem in Sn, using its natural representation, to be hard. Making use of the Chinese Remainder Theorem, we describe an efficient method to solve this discrete logarithm problem, yielding a polynomial time secret key recovery attack against Doliskani et al.’s proposal. View Full-Text
Keywords: cryptanalysis; symmetric group; public key encryption cryptanalysis; symmetric group; public key encryption
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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González Vasco, M.I.; Robinson, A.; Steinwandt, R. Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn. Cryptography 2018, 2, 16.

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