Differential Cryptanalysis for Multivariate Schemes

Fouque, Pierre-Alain; Granboulan, Louis; Stern, Jacques

doi:10.1007/11426639_20

Cited by 76 publications

(66 citation statements)

References 15 publications

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“…Q(f ) plays a role in masking the original public key E and randomizing it. r is appended to the polynomial sets in order to cope with the differential attack [9,6]. Note that t random variables x p+1 , .…”

Section: Mpkcs In Generalmentioning

confidence: 99%

“…In 2005 Fouque, Granboulan, and Stern [9] adapted the differential cryptanalysis to MPKCs in order to break MI and its variant, called PMI [3]. In the differential attack, the attacker tries…”

Section: Differential Attackmentioning

confidence: 99%

“…From this point of views of efficiency, NLPHPV method can be a good alternative to the internal perturbation method. We also discuss on security benefit of the NLPHPV method against major known attacks, i.e., the Gröbner basis attack, the rank attack [37], and the differential attack [9]. Based on also our security considerations, we suggest concrete parameter sizes for the NLPHPV method.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Piece In Hand Perturbation Vector Method for Enhancing Security of Multivariate Public Key Cryptosystems

Fujita

Tadaki

Tsujii

2008

Post-Quantum Cryptography

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Abstract. The piece in hand (PH) is a general scheme which is applicable to any reasonable type of multivariate public key cryptosystems for the purpose of enhancing their security. In this paper, we propose a new class PH method called NLPHPV (NonLinear Piece in Hand Perturbation Vector) method. Although our NLPHPV uses similar perturbation vectors as is used for the previously known internal perturbation method, this new method can avoid redundant repetitions in decryption process. With properly chosen parameter sizes, NLPHPV achieves an observable gain in security from the original multivariate public key cryptosystem. We demonstrate these by both theoretical analyses and computer simulations against major known attacks and provides the concrete sizes of security parameters, with which we even expect the grater security against potential quantum attacks.

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Section: Mpkcs In Generalmentioning

confidence: 99%

Section: Differential Attackmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Piece In Hand Perturbation Vector Method for Enhancing Security of Multivariate Public Key Cryptosystems

Fujita

Tadaki

Tsujii

2008

Post-Quantum Cryptography

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“…The differential of the public key of a multivariate scheme has been introduced in a systematic cryptanalytic method by Fouque et al in [9]. Later, this method has been developed and extended in [6,7,5,4] to attack various systems.…”

Section: Differential and Properties For Monomialsmentioning

confidence: 99%

Key Recovery on Hidden Monomial Multivariate Schemes

Fouque¹,

Macario-Rat

Stern³

Advances in Cryptology – EUROCRYPT 2008

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Abstract. The problem we study in this paper is the key recovery problem on the C * schemes and generalizations where the quadratic monomial of C * (the product of two linear monomials) is replaced by a product of three or more linear monomials. This problem has been further generalized to any multivariate polynomial hidden by two invertible linear maps and named the Isomorphism of Polynomials (IP ) problem by Patarin et al. Some cryptosystems have been built on this appearing hard problem such as a traitor tracing scheme proposed by Billet and Gilbert. Here we show that if the hidden multivariate monomial is a quadratic monomial, as in SFLASH, or a cubic (or higher) monomial as in the traitor tracing scheme, then it is possible to recover an equivalent secret key in polynomial time O(n d ) where n is the number of variables and d is the degree of the public polynomials.

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“…A simpler internal variation had been previously proposed based on the Matsumoto-Imai cryptosystem [2] and had already been asserted to provide immunity against algebraic attacks [3]. Unfortunately, the Matsumoto-Imai cryptosystem has a very specific structure and the internal perturbation could actually be removed using the recently introduced differential technique [8]. In this work, we consider the enhanced internal perturbation variation as applied to HFE and defined in [4].…”

Section: Introductionmentioning

confidence: 99%

Cryptanalysis of HFE with Internal Perturbation

Dubois

Granboulan

Stern

Public Key Cryptography – PKC 2007

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Abstract. Multivariate Cryptography has been an active line of research for almost twenty years. While most multivariate cryptosystems have been under attack, variations of the basic schemes came up as potential repairs. In this paper, we study the Internal Perturbation variation of HFE recently proposed by Ding and Schmidt. Although several results indicate that HFE is vulnerable against algebraic attacks for moderate size parameters, Ding and Schmidt claim that the cryptosystem with internal perturbation should be immune against them. However in this paper, we apply the recently discovered method of differential analysis to the Internal Perturbation of HFE and we find a subtle property which allows to disclose the kernel of the perturbation. Once this has been achieved, the public key can be inverted by attacking the underlying HFE provided the parameters were taken low enough to make the perturbed scheme of competitive performance.

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Differential Cryptanalysis for Multivariate Schemes

Cited by 76 publications

References 15 publications

Nonlinear Piece In Hand Perturbation Vector Method for Enhancing Security of Multivariate Public Key Cryptosystems

Nonlinear Piece In Hand Perturbation Vector Method for Enhancing Security of Multivariate Public Key Cryptosystems

Key Recovery on Hidden Monomial Multivariate Schemes

Cryptanalysis of HFE with Internal Perturbation

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