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

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

Abstract: This research proposes a new stream cipher that uses the algebraic structure of the multiplicative group Z Z∗ⁿ (where ⁿ is a big prime number used in the ElGamal algorithm). The cipher's security relies on the difficulty of solving systems of multivariate polynomial equations modulo big prime number ⁿ, which is an NP-hard problem. The cipher's speed is comparable to the fastest symmetric-key stream ciphers, making it an attractive option for public-key cryptography.

Main Research Question: Can we design a fast public-key stream cipher with a strong cryptographic foundation?

Methodology: The study uses the theory of quasigroups and quasigroup string transformations to create a stream cipher. It defines a quasigroup of order ⁿ and performs quasigroup string transformations to encrypt and decrypt messages. The cipher's security is based on the difficulty of breaking the quasigroup structure, which is linked to the NP-hard problem of solving multivariate polynomial equations modulo big prime number ⁿ.

Results: The research presents a new stream cipher that combines the advantages of quasigroup theory and public-key cryptography. The cipher's speed is comparable to the fastest symmetric-key stream ciphers, making it an attractive option for public-key cryptography.

Implications: The new stream cipher offers a fast and secure public-key cryptographic solution. It also demonstrates the potential of quasigroup theory in cryptography, providing a new approach to designing secure ciphers.

Link to Article: https://arxiv.org/abs/0403043v1 Authors: arXiv ID: 0403043v1