Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
FLASH, a Fast Multivariate Signature Algorithm
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th 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
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
High order linearization equation (HOLE) attack on multivariate public key cryptosystems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Practical cryptanalysis of SFLASH
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
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
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The public key of the Oil-Vinegar scheme consists of a set of m quadratic equations in m+n variables over a finite field Fq. Kipnis and Shamir broke the balanced Oil-Vinegar scheme where d = n-m = 0 by finding equivalent keys of the cryptosytem. Later their method was extended by Kipnis et al to attack the unbalanced case where 0 d m and d is small with a complexity of O(qd-1m4). This method uses the matrices associated with the quadratic polynomials in the public key, which needs to be symmetric and invertible. In this paper, we give an optimized search method for Kipnis el al's attack. Moreover, for the case that the finite field is of characteristic 2, we find the situation becomes very subtle, which, however, was totally neglected in the original work of Kipnis et al. We show that the Kipnis-Shamir method does not work if the field characteristic is 2 and d is a small odd number, and we fix the situation by proposing an alternative method and give an equivalent key recovery attack of complexity O(qd+1m4). We also prove an important experimental observation by Ding et al for the Kipnis-Shamir attack on balanced Oil-Vinegar schemes in characteristic 2.