119 research outputs found
Group theory in cryptography
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.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
A new key exchange protocol based on the decomposition problem
In this paper we present a new key establishment protocol based on the
decomposition problem in non-commutative groups which is: given two elements
of the platform group and two subgroups (not
necessarily distinct), find elements such that . Here we introduce two new ideas that improve the security of key
establishment protocols based on the decomposition problem. In particular, we
conceal (i.e., do not publish explicitly) one of the subgroups , thus
introducing an additional computationally hard problem for the adversary,
namely, finding the centralizer of a given finitely generated subgroup.Comment: 7 page
Heisenberg Groups as Platform for the AAG key-exchange protocol
Garber, Kahrobaei, and Lam studied polycyclic groups generated by number
field as platform for the AAG key-exchange protocol. In this paper, we discuss
the use of a different kind of polycyclic groups, Heisenberg groups, as a
platform group for AAG by submitting Heisenberg groups to one of AAG's major
attacks, the length-based attack.Comment: arXiv admin note: text overlap with arXiv:1305.054
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