Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
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
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of ``2 R'' Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Fast exhaustive search for polynomial systems in F2
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Probabilistic multivariate cryptography
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
On the affine transformations of HFE-Cryptosystems and systems with branches
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Equivalent keys in HFE, c*, and variations
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
Large superfluous keys in multivariate quadratic asymmetric systems
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Cryptanalysis of HFEv and internal perturbation of HFE
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
A study of the security of unbalanced oil and vinegar signature schemes
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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In [1]T. Matsumoto and H. Imai have presented a very efficient, "candidate" algorithm, called C*, for asymmetric cryptography. This algorithm was broken in [2]. Then in [3], I have suggested two algorithms, HFE and IP, to repair C*. However the secret key computations of HFE and IP are not as efficient as in the original algorithm C*. IS it possible to repair C* with the same kind of very easy secret key computations? This question is the subject of this paper. Unfortunately, we will see that for all the "easy" transformations of C* the answer is no. However one of the new ideas of this paper will enable us to suggest a candidate algorithm for assymetric signatures of length only 64 bits. An extended version of this paper can be obtained from the author.