An interactive identification scheme based on discrete logarithms and factoring
Journal of Cryptology - Eurocrypt '90
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
On the security of the Schnorr scheme using preprocessing
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Batch exponentiation: a fast DLP-based signature generation strategy
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Security and Performance of Server-Aided RSA Computation Protocols
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
How to securely outsource cryptographic computations
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
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Schnorr's preprocessing algorithms [6, 7] are designed to speed up the 'random' exponentiation often performed by the prover/signer in identification and signature schemes.In this paper, an attack on these preprocessing algorithms is presented. For the proposed parameters, the attack requires about 231 steps, and 700 identifications or signatures to retrieve the secret key. Here the underlying scheme may be Schnorr, Brickell-McCurley, ElGamal or DSS.