Cryptographic Group and Semigroup Actions

2023/01/04 by Oliver W. Gnilke, Gnilke, Oliver W., Jens Zumbrägel +1 · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #Cryptography and Data Security #Advanced Authentication Protocols Security

paper · pdf · doi:10.48550/arxiv.2301.01657

Abstract

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based cryptography. We introduce generic algorithms for the semigroup action problem and discuss lower and upper bounds. Also, we investigate Pohlig-Hellman type attacks in a general sense. In particular, we consider reductions provided by non-invertible elements in a semigroup, and we deal with subgroups in the case of group actions.

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• Semigroup action based on skew polynomial evaluation with applications to Cryptography

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