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arXiv · 2301.01657

Cryptographic Group and Semigroup Actions

Oliver W. Gnilke·Jens Zumbrägel
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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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Oliver W. Gnilke, Jens Zumbrägel. 2023-01-04. Cryptographic Group and Semigroup Actions. https://arxiv.org/abs/2301.01657

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