An efficient solution of the congruence x2+ky2=m (modn)
IEEE Transactions on Information Theory
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
An efficient signature scheme based on quadratic equations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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This note continues a sequence of attempts to define efficient digital signature schemes based on low-degree polynomials, or to break such schemes. We consider a scheme proposed by Satoh and Araki (1997), which generalizes the Ong-Schnorr-Shamir scheme to the noncommutative ring of quaternions. We give two different ways to break the scheme.