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Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
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CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
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Designs, Codes and Cryptography
A method for obtaining digital signatures and public-key cryptosystems
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AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
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CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
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ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the security of stepwise triangular systems
Designs, Codes and Cryptography
Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups
MATH'08 Proceedings of the American Conference on Applied Mathematics
Algebraic Attack on the MQQ Public Key Cryptosystem
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
l-invertible cycles for multivariate quadratic (MQ) public key cryptography
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
New differential-algebraic attacks and reparametrization of rainbow
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
Cryptanalysis of multivariate and odd-characteristic HFE variants
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Building secure tame-like multivariate public-key cryptosystems: the new TTS
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
A fast cryptanalysis of the isomorphism of polynomials with one secret problem
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Polynomial equivalence problems: algorithmic and theoretical aspects
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Implementing minimized multivariate PKC on low-resource embedded systems
SPC'06 Proceedings of the Third international conference on Security in Pervasive Computing
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We present MQQ-SIG, a signature scheme based on "Multivariate Quadratic Quasigroups". The MQQ-SIG signature scheme has a public key consisting of $\frac{n}{2}$ quadratic polynomials in n variables where n=160, 192, 224 or 256. Under the assumption that solving systems of $\frac{n}{2}$ MQQ's equations in n variables is as hard as solving systems of random quadratic equations, we prove that in the random oracle model our signature scheme is CMA (Chosen-Message Attack) resistant. From efficiency point of view, the signing and verification processes of MQQ-SIG are three orders of magnitude faster than RSA or ECDSA. Compared with other MQ signing schemes, MQQ-SIG has both advantages and disadvantages. Advantages are that it has more than three times smaller private keys (from 401 to 593 bytes), and the signing process is an order of magnitude faster than other MQ schemes. That makes it very suitable for implementation in smart cards and other embedded systems. However, MQQ-SIG has a big public key (from 125 to 512 Kb) and it is not suitable for systems where the size of the public key has to be small.