Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
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
Cryptanalysis of the Oil & Vinegar Signature Scheme
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
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INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Cryptanalysis of the TTM Cryptosystem
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Solving Underdefined Systems of Multivariate Quadratic Equations
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
On the Security of HFE, HFEv- and Quartz
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
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
Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
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
Cryptanalysis of variants of UOV
ISC'06 Proceedings of the 9th international conference on Information Security
Building secure tame-like multivariate public-key cryptosystems: the new TTS
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
A "medium-field" multivariate public-key encryption scheme
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Proposal of a signature scheme based on STS trapdoor
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
On provable security of UOV and HFE signature schemes against chosen-message attack
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Solving underdetermined systems of multivariate quadratic equations revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Efficient implementations of MQPKS on constrained devices
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
A variant of rainbow with shorter secret key and faster signature generation
Proceedings of the first ACM workshop on Asia public-key cryptography
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
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The Unbalanced Oil and Vinegar scheme (UOV) is a signature scheme based on multivariate quadratic equations. It uses m equations and n variables. A total of v of these are called “vinegar variables”. In this paper, we study its security from several points of view. First, we are able to demonstrate that the constant part of the affine transformation does not contribute to the security of UOV and should therefore be omitted. Second, we show that the case n ≥ 2m is particularly vulnerable to Gröbner basis attacks. This is a new result for UOV over fields of odd characteristic. In addition, we investigate a modification proposed by the authors of UOV, namely to chose coefficients from a small subfield. This leads to a smaller public key. But due to the smaller key-space, this modification is insecure and should therefore be avoided. Finally, we demonstrate a new attack which works well for the case of small v. It extends the affine approximation attack from Youssef and Gong against the Imai-Matsumoto Scheme B for odd characteristic and applies it against UOV. This way, we point out serious vulnerabilities in UOV which have to be taken into account when constructing signature schemes based on UOV.