Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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
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
Analytic models for token-ring networks
Analytic models for token-ring networks
The functional decomposition of polynomials
The functional decomposition of polynomials
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Cryptanalysis of Imai and Matsumoto Scheme B Asymmetric Cryptosystem
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Cryptanalysis of Rational Multivariate Public Key Cryptosystems
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
A subliminal channel in secret block ciphers
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Public-Key identification schemes based on multivariate cubic polynomials
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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The function decomposition problem can be stated as: Given the algebraic expression of the composition of two mappings, how can we identify the two factors? This problem is believed to be in general intractable [1]. Based on this belief, J. Patarin and L. Goubin designed a new family of candidates for public key cryptography, the so called "2R-schemes" [10, 11]. The public key of a "2R"-scheme is a composition of two quadratic mappings, which is given by n polynomials in n variables over a finite field K with q elements. In this paper, we contend that a composition of two quadratic mappings can be decomposed in most cases as long as q 4. Our method is based on heuristic arguments rather than rigorous proofs. However, through computer experiments, we have observed its effectiveness when applied to the example scheme "D**"given in [10].