Paper 2023/1664

On the Complexity and Admissible Parameters of the Crossbred Algorithm in $\mathbb{F}_{q\geq2}$

Abstract

[IMPORTANT NOTE] This work was mostly done whilst I as a Master's student at Royal Holloway. Unfortunately, I do not believe it is of sufficient quality or rigor, and maybe even worse, is very sloppy and at times, confusing. Hence, I am leaving this note to point readers in the direction of other publications that also concern themselves with the complexity of the Crossbred algorithm. These works have done a much better job, and I do not believe that I have the profile at the moment to continue working on this particular topic. [1] J. Baena, D. Cabarcas, S. K. Tiwari, J. Verbel, and L. Villota, ‘Admissible parameters for the Crossbred algorithm and semi-regular sequences over finite fields’, Designs, Codes and Cryptography, Mar. 2025. [2] D. Vidal, C. Delaplace, and S. Ionica, ‘An analysis of the Crossbred Algorithm for the MQ Problem’, IACR Communications in Cryptology, vol. 1, no. 3, 2024.