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On the security of UOV

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by Jean-charles Faugère , Ludovic Perret
Citations:2 - 0 self
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BibTeX

@MISC{Faugère_onthe,
    author = {Jean-charles Faugère and Ludovic Perret},
    title = {On the security of UOV},
    year = {}
}

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Abstract

Abstract. In this short note, we investigate the security of the Unbalanced Oil and Vinegar Scheme [16]. To do so, we use a hybrid approach for solving the algebraic systems naturally arising when mounting a signatureforgery attack. The basic idea is to compute Gröbner bases of several modified systems rather than a Gröbner basis of the initial system. It turns out that our approach is efficient in practice. We have obtained a complexity bounded from above by 2 40.3 (or 9 hours of computation) to forge a signature on a set of parameters proposed by the designers of UOV. 1

Citations

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42 Computer algebra, symbolic and algebraic computation, Computing Supplementum - Buchberger, Collins, et al. - 1982
35 Étude des systèmes algébriques surdéterminés. Applications aux codes correcteurs et à la cryptographie - Bardet - 2004
29 Unbalanced oil and vinegar signature schemes - Hotzvim, Patarin, et al. - 1999
28 Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems - Bardet, Faugère, et al. - 2005
15 A study of the security of unbalanced oil and vinegar signature schemes - Braeken, Wolf, et al. - 2004
15 Cryptanalysis of SFLASH with Slightly Modified Parameters - Dubois, Fouque, et al. - 2007
11 On asymptotic security estimates in XL and gröbner bases-related algebraic cryptanalysis - Yang, Chen, et al. - 2004
5 Multivariate quadratic polynomials in public key cryptography - Wolf - 2005
2 SFLASH, a Fast Symmetric Signature Scheme for low-cost Smartcards – Primitive Specification and Supporting documentation. Available at www.minrank.org/sflash-b-v2.pdf - Courtois, Goubin, et al.
1 Salvy On the complexity of Grˇsbner basis computation of semi-regular overdetermined algebraic equations - Bardet, Faugère, et al. - 2004
1 Salvy On the complexity of Grbner basis computation of semi-regular overdetermined algebraic equations - Bardet, Faugère, et al. - 2004
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