On the security of UOV

On the security of UOV

Cached

Download Links

by Jean-charles Faugère , Ludovic Perret

Citations:

BibTeX

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

Bookmark

OpenURL

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

2507	A method for obtaining digital signatures and public-key cryptosystems - Rivest, Shamir, et al.
2292	New directions in cryptography - Diffie, Hellmen - 1976
756	Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer - Shor - 1997
323	Gr"obner Bases: An algorithmic method in polynomial ideal theory - Buchberger - 1985
197	A new efficient algorithm for computing Gröbner bases without reduction to zero (F5 - Faugère - 2002
136	T.: Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering - Faugère, Gianni, et al. - 1993
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