Fast cryptanalysis of the Matsumoto-Imai public key scheme
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Analysis of a public key approach based on polynomial substitution
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Efficient signature schemes based on birational permutations
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Finite fields
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
QUARTZ, 128-Bit Long Digital Signatures
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
The Security of Hidden Field Equations (HFE)
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
FLASH, a Fast Multivariate Signature Algorithm
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptoanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Asymmetric Cryptography with a Hidden Monomial
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Oil & Vinegar Signature Scheme
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
C*-+ and HM: Variations Around Two Schemes of T. Matsumoto and H. Imai
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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In public key schemes based on multivariate cryptography, the public key is a finite set of m (generally quadratic) polynomial equations and the private key is a trapdoor allowing the owner of the private key to invert the public key. In existing schemes, a signature or an answer to an authentication is valid if all the m equations of the public key are satisfied. In this paper, we study the idea of probabilistic multivariate cryptography, i.e., a signature or an authentication value is valid when at least α equations of the m equations of the public key are satisfied, where α is a fixed parameter of the scheme. We show that many new public key signature and authentication schemes can be built using this concept. We apply this concept on some known multivariate schemes and we show how it can improve the security of the schemes.