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Affine braid groups: a better platform than braid groups for cryptology?

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In recent years, various cryptographic protocols using infinite non-commutative groups, notably braid groups, have been proposed. Both experimental and theoretical evidence collected so far, however, makes it appear likely that braid groups are not a good choice for the platform. In this paper, we thus consider to use affine braid groups, a natural generalization of braid groups, as a platform. Like braid groups, affine braid groups have a very nice geometrical interpretation and have several properties that make them acceptable for cryptographic purposes. On the other hand, there are also essential differences between their structures; for example, unlike braid groups, affine braid groups have no Garside structure, which makes the conjugacy problem in these groups more difficult. We examine the feature that makes affine braid groups useful to cryptography and then conclude that this class of groups could provide a promising alternative platform for group-based cryptography.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ping Zhu

  2. State key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ping Zhu & Qiaoyan Wen

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  1. Ping Zhu
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  2. Qiaoyan Wen
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Correspondence to Ping Zhu.

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Zhu, P., Wen, Q. Affine braid groups: a better platform than braid groups for cryptology?. AAECC 22, 375–391 (2011). https://doi.org/10.1007/s00200-011-0157-1

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