International Association
for Cryptologic Research

We present a general way to get a provably collision-resistant hash function from any (suitable) $\Sigma$-protocol. This enables us to both get new designs and to unify and improve previous work. In the first category, we obtain, via a modified version of the Fiat-Shamir protocol, the fastest known hash function that is provably collision-resistant based on the \textit{standard} factoring assumption. In the second category, we provide a modified version VSH^* of VSH which is faster when hashing short messages. (Most Internet packets are short.) We also show that $\Sigma$-hash functions are chameleon, thereby obtaining several new and efficient chameleon hash functions with applications to on-line/off-line signing, chameleon signatures and designated-verifier signatures.