Stream Cipher Based on Quasigroup String Transformations in Z Z∗p

Title: Stream Cipher Based on Quasigroup String Transformations in Z Z∗p

Abstract: This research proposes a stream cipher that utilizes the algebraic structure of the multiplicative group Z Z∗p (where p is a big prime number used in the ElGamal algorithm). The cipher employs quasigroup order p−1 transformations and quasigroup string transformations. The cryptographic strength of the proposed stream cipher is based on the difficulty of breaking it, which is at least as hard as solving systems of multivariate polynomial equations modulo big prime number p, a problem that is NP-hard and has no known fast randomized or deterministic algorithms. The speed of this stream cipher is comparable to the fastest symmetric-key stream ciphers, making it a promising solution for public-key encryption.

Main Research Question: Can a stream cipher based on quasigroup string transformations in Z Z∗p provide a secure and efficient method for public-key encryption?

Methodology: The study combines the theory of finite fields and quasigroups, using Latin squares and quasigroup string transformations. It designs a stream cipher that operates in Z Z∗p, using quasigroup order p−1 transformations to ensure cryptographic strength.

Results: The research demonstrates that the proposed stream cipher is as secure as solving systems of multivariate polynomial equations modulo big prime number p, a problem that is NP-hard. Furthermore, the cipher's speed is comparable to the fastest symmetric-key stream ciphers, making it an efficient choice for public-key encryption.

Implications: The stream cipher based on quasigroup string transformations in Z Z∗p offers a promising solution for public-key encryption, combining the security of quasigroup transformations with the efficiency of stream ciphers. It provides an alternative to existing public-key algorithms, particularly those that are slower due to their use of modular exponentiation.

Link to Article: https://arxiv.org/abs/0403043v2 Authors: arXiv ID: 0403043v2