Efficient Blind Signatures without Random Oracles

The only known blind signature scheme that is secure in the standard model~\cite{juels97security} is based on general results about multi-party computation, and thus it is extremly inefficient. The main result of this paper is the first provably secure blind signature scheme which is also efficient. We develop our construction as follows. In the first step, which is a significant result on its own, we devise and prove the security of a new variant for the Cramer-Shoup-Fischlin signature scheme. We are able to show that for generating signatures, instead of using randomly chosen \textit{prime} exponents one can securely use randomly chosen \textit{odd integer} exponents which significantly simplifies the signature generating process. We obtain our blind signing function as a secure and efficient two-party computation that cleverly exploits its algebraic properties and those of the Paillier encryption scheme. The security of the resulting signing protocol relies on the Strong RSA assumption and the hardness of decisional composite residuosity; we stress that it does not rely on the existence of random oracles.