Nonlinear congruential generator over a GF(2^8) and its applications in improving AES key expansion algorithm

Yuxuan Li

doi:10.1117/12.2683161

26 June 2023 Nonlinear congruential generator over a GF(2⁸) and its applications in improving AES key expansion algorithm

Yuxuan Li

Author Affiliations +

Proceedings Volume 12714, International Conference on Computer Network Security and Software Engineering (CNSSE 2023); 127140F (2023) https://doi.org/10.1117/12.2683161
Event: Third International Conference on Computer Network Security and Software Engineering (CNSSE 2023), 2023, Sanya, China

Abstract

The block cipher stands out among the reliable methods for data security. Key expansion is a crucial step in the block encryption algorithm and is thus important to develop secure round keys that are statistically independent and sensitive. Using Nonlinear Congruential Generators (NCGs), we propose a key expansion algorithm that helps to design more secure block encryption algorithms or hash functions. Despite the advancement in digital technologies, NCGs remain the effective method of Pseudorandom Number Generation (PRNG). However, conventional linear congruence generators have difficulties in applying the key expansion algorithm. In contrast to the conventional linear congruence generator, the round constant extension algorithm requires a random sequence of 01, which produces random integers within a certain range. To improve the Advanced Encryption Standard (AES) key expansion algorithm, we propose an NCG over a Galois field GF ( 2⁸ ). Our analysis includes analyzing a key expansion of 128 bits in length and a key of other lengths performed similarly. The experimental results show that the proposed algorithm is feasible and resistant to side-channel attacks. Our findings can be used to improve existing block cipher algorithms and make them more secure.

Citation Download Citation

Yuxuan Li "Nonlinear congruential generator over a GF(2⁸) and its applications in improving AES key expansion algorithm", Proc. SPIE 12714, International Conference on Computer Network Security and Software Engineering (CNSSE 2023), 127140F (26 June 2023); https://doi.org/10.1117/12.2683161

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