Hash Functions from Sigma Protocols and Improvements to VSH

We present a general way to get a provably collision-resistanthash function from any (suitable) Σ-protocol. This enables usto both get new designs and to unify and improve previous work. Inthe first category, we obtain, via a modified version of theFiat-Shamir protocol, the fastest known hash function that isprovably collision-resistant based on the standard factoring assumption. In the second category, we provide a modifiedversion VSH* of VSH which is faster when hashingshort messages. (Most Internet packets are short.) We also showthat Σ-hash functions are chameleon, thereby obtainingseveral new and efficient chameleon hash functions withapplications to on-line/off-line signing, chameleon signatures anddesignated-verifier signatures.

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