Group theory in cryptography
Simon R. Blackburn⋆, Carlos Cid, Ciarán Mullan · Cambridge University Press eBooks · 2011
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. Introduction In the last few years, many papers have proposed cryptosystems based on group theoretic concepts. Notes from a recent advanced course on the subject by Myasnikov, Shpilrain and Ushakov have recently been published as a monograph [63], and a textbook (with a rather different focus) by González Vasco, Magliveras and Steinwandt [31] is promised in 2010. Group-based cryptosystems have not yet led to practical schemes to rival RSA and Diffie–Hellman, but the ideas are interesting and the different perspective leads to some worthwhile group theory. The cryptographic literature is vast and diverse, and it is difficult for a newcomer to the area to find the right sources to learn from. (For example, there are many introductory textbooks aimed at the mathematical audience that introduce RSA. How many of these textbooks hint that the basic RSA scheme is insecure if refinements such as message padding are not used? For a discussion of these issues, see Smart [78, Chapters 17,18 and 20], for example.) Our paper will provide some pointers to some sources that, in our opinion, provide a good preparation for reading the literature on group-based cryptography; the paper will also provide a high level overview of the subject.