Homomorphic Public-Key Cryptosystems over Groups and Rings

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Title: Homomorphic Public-Key Cryptosystems over Groups and Rings

Abstract: This research proposes a new homomorphic public-key cryptosystem for non-identity finite groups and rings, based on the difficulty of the membership problem for groups of integer matrices. The study introduces a homomorphic cryptosystem for the first time over finite commutative rings. The main result is a homomorphic public-key cryptosystem over arbitrary non-identity finite groups, based on the difficulty of the membership problem for groups of integer matrices. This work suggests that the infinity of the group is not a barrier for performing encryption and decryption algorithms, and introduces a new approach to secret computations in cryptography.

Link to Article: https://arxiv.org/abs/0309010v1 Authors: arXiv ID: 0309010v1

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