Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory

Buchberger, Bruno

doi:10.1007/978-94-009-5225-6_6

Cited by 797 publications

(609 citation statements)

References 12 publications

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“…In [14], 6 rounds of DES are attacked with only a single known plaintext/ciphertext pair using a SAT solver. Erickson et al [15] used the SAT solver and Gröbner basis [16] attacks against SMS4 on equation system over GF (2) and GF(2 8 ). In [17], a practical Gröbner basis [16] attack using Magma was applied against the ciphers Flurry and Curry, recovering the full cipher key by requiring only a minimal number of plaintext/ciphertext pairs.…”

Section: Modern Algebraic Tools and Their Applications To Cryptographymentioning

confidence: 99%

A Comparison between Two Off-the-Shelf Algebraic Tools for Extraction of Cryptographic Keys from Corrupted Memory Images

Kamal

Zahno²,

Youssef³

2013

Security Engineering and Intelligence Informatics

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Abstract.Cold boot attack is a class of side channel attacks which exploits the data remanence property of random access memory (RAM) to retrieve its contents which remain readable shortly after its power has been removed. Specialized algorithms have been previously proposed to recover cryptographic keys of several ciphers from decayed memory images. However, these techniques were cipher-dependent and certainly uneasy to develop and fine tune. On the other hand, for symmetric ciphers, the relations that have to be satisfied between the subround key bits in the key schedule always correspond to a set of nonlinear Boolean equations. In this paper, we investigate the use of an off-the-shelf SAT solver (CryptoMiniSat), and an open source Gröbner basis tool (PolyBoRi) to solve the resulting system of equations. We also provide the pros and cons of both approaches and present some simulation results for the extraction of AES and Serpent keys from decayed memory images using these tools.

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Section: Modern Algebraic Tools and Their Applications To Cryptographymentioning

confidence: 99%

A Comparison between Two Off-the-Shelf Algebraic Tools for Extraction of Cryptographic Keys from Corrupted Memory Images

Kamal

Zahno²,

Youssef³

2013

Security Engineering and Intelligence Informatics

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“…For example, a bicubic patch has an implicit equation of degree 18 with 1330 terms!!! In general, the implicitization algorithms are based on resultants, a classical technique [71], Gröbner bases techniques [8] and on the Wu-Ritt method [89]. Resultants provide a set of techniques [39] for eliminating variables from systems of nonlinear equations.…”

Section: Implicitizationmentioning

confidence: 99%

Computational Methods for Geometric Processing. Applications to Industry

Iglesias

Gálvez

Puig-Pey

2001

Computational Science — ICCS 2001

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“…More generally: Definition 1. 8 An ideal J of a commutative ring R is prime if and only if: V ri, r 2 £ R, ri r 2 £ / T\ € I or r 2 € / Proposition 1.7…”

Section: Prime Ideals and Nil Radicalsmentioning

confidence: 99%

“…The first one, called Criterion 2 by Buchberger, [8], avoids certain reductions by forecasting that certain very particular S-polynomials can be reduced to 0. The second one is a recent refinement by Gebauer and Moller, [16], of Criterion 1 by Buchberger.…”

Section: Improvements In the Algorithmmentioning

confidence: 99%