Attacking and repairing batch verification schemes

Abstract

Batch verification can provide large computational savings when several signatures, or other constructs, are verified together. Several batch verification algorithms have been published in recent years, in particular for both DSA-type and RSA signatures. We describe new attacks on several of these published schemes. A general weakness is explained which applies to almost all known batch verifiers for discrete logarithm based signature schemes. It is shown how this weakness can be eliminated given extra properties about the underlying group structure. A new general batch verifier for exponentiation in any cyclic group is also described as well as a batch verifier for modified RSA signatures.