How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
A Signature Scheme Based on the Intractability of Computing Roots
Designs, Codes and Cryptography
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
On diffie-hellman key agreement with short exponents
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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A variant of Schnorr's signature scheme called RDSA has been proposed by I. Biehl, J. Buchmann, S. Hamdy and A. Meyer in order to be used in finite abelian groups of unknown order such as the class group of imaginary quadratic orders. We describe in this paper a total break of RDSA under a plain known-message attack for the parameters that were originally proposed. It recovers the secret signature key from the knowledge of less than 10 signatures of known messages, with a very low computational complexity. We also compare a repaired version of RDSA with GPS scheme, another Schnorr variant with similar properties and we show that GPS should be preferred for most of the applications.