An efficient solution of the congruence x2+ky2=m (modn)
IEEE Transactions on Information Theory
Algorithmic algebra
On the generation of multivariate polynomials which are hard to factor
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient signature schemes based on birational permutations
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Attacks on the birational permutation signature schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Can O.S.S. be repaired?: proposal for a new practical signature scheme
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
An efficient signature scheme based on quadratic equations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On the security of stepwise triangular systems
Designs, Codes and Cryptography
Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
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At Crypto 93, Shamir proposed a family of signature schemes using algebraic bases. Coppersmith, Stern and Vaudenay presented an attack on one variant of the cryptosystem. Their attack does not recover the secret key. For one of the variants proposed by Shamir we show how to recover the secret key. Our attack is based on algebraic methods which are also applicable to many other instances of polynomial equations in the presence of some trapdoor condition.