W-Gröbner basis and monomial ideals under polynomial composition

Li, Dongmei; Liu, Jinwang; Liu, Weijun

doi:10.1007/s11766-011-2695-5

Cited by 4 publications

(3 citation statements)

References 11 publications

(10 reference statements)

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“…is advantageous to have this property for Gröbner basis computations. By using Corollary 6.56 of [16], we can determine whether an ideal is zero-dimensional. Below we state a reduced version of this corollary.…”

Section: Gröbner Basis Theorymentioning

confidence: 99%

“…It is needed to improve (15) and (16) to meet the requirements of Gröbner basis. From (15), it is easy to get 24 polynomial equations of round (1 ≤ ≤ 13) as shown in…”

Section: (Mnmentioning

confidence: 99%

“…Similarly, from (16), the 32 polynomial equations of the final round can be obtained as shown in For degree lexicographical order, the head term of polynomial in (23) and (24) is 254 , , 0 ≤ ≤ 13, 0 ≤ ≤ 31. It is easy to see that the head term has no nontrivial common factor; that is, the greatest common factor is 1.…”

Section: (Mnmentioning

confidence: 99%

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Algebraic Cryptanalysis Scheme of AES-256 Using Gröbner Basis

Zhao¹,

Cui

Xie

2017

Journal of Electrical and Computer Engineering

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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.

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Section: Gröbner Basis Theorymentioning

confidence: 99%

“…It is needed to improve (15) and (16) to meet the requirements of Gröbner basis. From (15), it is easy to get 24 polynomial equations of round (1 ≤ ≤ 13) as shown in…”

Section: (Mnmentioning

confidence: 99%