Abstract. Sensitive electronic data may be required to remain confidential for long periods of time. Yet encryption under a computationally secure cryptosystem cannot provide a guarantee of long term confidentiality, due to potential advances in computing power or cryptanalysis. Long term confidentiality is ensured by information theoretically secure ciphers, but at the expense of impractical key agreement and key management. We overview known methods to alleviate these problems, whilst retaining some form of information theoretic security relevant for long term confidentiality.
This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.
Stickel's key agreement scheme was successfully cryptanalysed by V. Shpilrain when GL.n; q/ is used as a platform. Shpilrain suggested the algebra of all (not necessarily invertible) n n matrices defined over some finite ring R would make a more secure platform. He also suggested a more general method of generating keys, involving polynomials of matrices over R. When R D F q , we show that these variants of Stickel's scheme are susceptible to a linear algebra attack. We discuss other natural candidates for R, and conclude that until a suitable ring is proposed, the variant schemes may be considered insecure.
We cryptanalyse a matrix-based key transport protocol due to Baumslag, Camps, Fine, Rosenberger and Xu from 2006. We also cryptanalyse two recently proposed matrix-based key agreement protocols, due to Habeeb, Kahrobaei and Shpilrain, and due to Romanczuk and Ustimenko.
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