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Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
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SIAM Journal on Computing
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Computers and Intractability: A Guide to the Theory of NP-Completeness
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
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CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
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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
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
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PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Small public keys and fast verification for multivariate quadratic public key systems
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Similar keys of multivariate quadratic public key cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
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CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
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In this article, we show that public key schemes based on multivariate quadratic equations allow many equivalent, and hence superfluous private keys. We achieve this result by investigating several transformations to identify these keys and show their application to Hidden Field Equations (HFE), C*, and Unbalanced Oil and Vinegar schemes (UOV). In all cases, we are able to reduce the size of the private – and hence the public – key space by at least one order of magnitude. We see applications of our technique both in cryptanalysis of these schemes and in memory efficient implementations.