Topics in Cryptology — CT-RSA 2001

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 IFp⊗IFp → Ker(φ−1 Cl ) to generate signatures by two modular exponentiations, we will show that there is an efficiently computable isomorphism IFp ∼ = Ker(φ−1 Cl ) in this case, which makes the signature generation about four times as fast as in the original Schnorr scheme [15].

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