Efficient signature schemes based on polynomial equations
Proceedings of CRYPTO 84 on Advances in cryptology
An efficient solution of the congruence x2+ky2=m (modn)
IEEE Transactions on Information Theory
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
Attacks on the birational permutation signature schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Asymmetric cryptography with S-Boxes
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
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Structural Cryptanalysis of SASAS
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of Imai and Matsumoto Scheme B Asymmetric Cryptosystem
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography
Journal of Symbolic Computation
Cryptanalysis of Boolean permutation-based key escrow scheme
Computers and Electrical Engineering
Backdoor attacks on black-box ciphers exploiting low-entropy plaintexts
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
A cryptanalysis of the double-round quadratic cryptosystem
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Key recovery on hidden monomial multivariate schemes
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
A subliminal channel in secret block ciphers
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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In a series of papers Patarin proposes new efficient public key systems. A very interesting proposal, called 2-Round Public Key System with S Boxes, or 2R, is based on the difficulty of decomposing the structure of several rounds of unknown linear transformations and S boxes. This difficulty is due to the difficulty of decomposing compositions of multivariate binary functions. In this paper we present a novel attack which breaks the 64-bit block variant with complexity about 230 steps, and the more secure 128-bit blocks variant with complexity about 260 steps. It is interesting to note that this cryptanalysis uses only the ciphertexts of selected plaintexts, and does not analyze the details of the supplied encryption code.