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Journal of Electrical and Computer Engineering
Volume 2017 (2017), Article ID 9828967, 9 pages
https://doi.org/10.1155/2017/9828967
Research Article

Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis

1Department of Computer Science and Technology, Henan Institute of Technology, Xinxiang 453003, China
2School of Computer Science and Technology, Anhui University, Hefei 230039, China

Correspondence should be addressed to Jie Cui; nc.ude.ctsu.liam@eijiuc

Received 22 October 2016; Accepted 22 January 2017; Published 23 February 2017

Academic Editor: Jucheng Yang

Copyright © 2017 Kaixin Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The zero-dimensional Gröbner basis construction is a crucial step in Gröbner basis cryptanalysis on AES-256. In this paper, after performing an in-depth study on the linear transformation and the system of multivariate polynomial equations of AES-256, the zero-dimensional Gröbner basis construction method is proposed by choosing suitable term order and variable order. After giving a detailed construction process of the zero-dimensional Gröbner basis, the necessary theoretical proof is presented. Based on this, an algebraic cryptanalysis scheme of AES-256 using Gröbner basis is proposed. Analysis shows that the complexity of our scheme is lower than that of the exhaustive attack.