Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis

The zero-dimensional Gr&#-10;bner basis construction is a crucial step in Gr&#-10;bner 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 Gr&#-10;bner basis construction method is proposed by choosing suitable term order and variable order. After giving a detailed construction process of the zero-dimensional Gr&#-10;bner basis, the necessary theoretical proof is presented. Based on this, an algebraic cryptanalysis scheme of AES-256 using Gr&#-10;bner basis is proposed. Analysis shows that the complexity of our scheme is lower than that of the exhaustive attack.

[1]  Vincent Rijmen,et al.  The Design of Rijndael: AES - The Advanced Encryption Standard , 2002 .

[2]  Weijun Liu,et al.  W-Gröbner basis and monomial ideals under polynomial composition , 2011 .

[3]  Jean-Charles Faugère,et al.  On the complexity of the F5 Gröbner basis algorithm , 2013, J. Symb. Comput..

[4]  SalvyBruno,et al.  On the complexity of the F 5 Gröbner basis algorithm , 2015 .

[5]  Sean Murphy,et al.  Remarks on security of AES and XSL technique , 2002 .

[6]  Yang Wei.  Algebraic Attack on Rijndael-192 Based on Grobner Basis , 2013 .

[7]  Johannes A. Buchmann,et al.  A Zero-Dimensional Gröbner Basis for AES-128 , 2006, FSE.

[8]  Gaëtan Leurent,et al.  An Analysis of the XSL Algorithm , 2005, ASIACRYPT.

[9]  Vincent Rijmen,et al.  Linear hulls with correlation zero and linear cryptanalysis of block ciphers , 2014, Des. Codes Cryptogr..

[10]  Ed Dawson,et al.  Algebraic Analysis of Small Scale LEX-BES , 2010, CRYPTO 2010.

[11]  Vladimir P. Gerdt,et al.  Noetherian quotients of the algebra of partial difference polynomials and Grobner bases of symmetric ideals , 2013, 1304.7967.

[12]  Abhijit Das,et al.  An Improvement of Linearization-Based Algebraic Attacks , 2011, InfoSecHiComNet.

[13]  Sean Murphy.  Comments on the Security of the AES and the XSL Technique , 2002 .

[14]  Antoine Joux,et al.  Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases , 2003, CRYPTO.

[15]  Johannes A. Buchmann,et al.  Block Ciphers Sensitive to Gröbner Basis Attacks , 2006, CT-RSA.

[16]  Amir Hashemi,et al.  Sharper Complexity Bounds for Zero-Dimensional GRöBner Bases and Polynomial System Solving , 2011, Int. J. Algebra Comput..

[17]  Yu Sasaki,et al.  Known-Key Attacks on Rijndael with Large Blocks and Strengthening ShiftRow Parameter , 2010, IWSEC.