A course in computational algebraic number theory
A course in computational algebraic number theory
Efficient Implementation of Cryptosystems Based on Non-maximal Imaginary Quadratic Orders
SAC '99 Proceedings of the 6th Annual International Workshop on Selected Areas in Cryptography
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Reducing Logarithms in Totally Non-maximal Imaginary Quadratic Orders to Logarithms in Finite Fields
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
An Efficient NICE-Schnorr-Type Signature Scheme
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Designs, Codes and Cryptography
On the Security of Cryptosystems with Quadratic Decryption: The Nicest Cryptanalysis
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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In [7] there was proposed a Schnorr-type signature scheme based on non-maximal imaginary quadratic orders, which signature generation is - for the same conjectured level of security - about twice as fast as in the original scheme [15].In this work we will significantly improve upon this result, by speeding up the generation of NICE-Schnorr-type signatures by another factor of two. While in [7] one used the surjective homomorphism F*p驴F*p 驴 Ker(驴Cl-1) to generate signatures by two modular exponentiations, we will show that there is an efficiently computable isomorphism F*p 驴 Ker(驴Cl-1) in this case, which makes the signature generation about four times as fast as in the original Schnorr scheme [15].