Machine-generated algorithms, proofs and software for the batch verification of digital signature schemes

As devices everywhere increasingly communicate with each other, many security applications will require low-bandwidth signatures that can be processed quickly. Pairing-based signatures can be very short, but are often costly to verify. Fortunately, they also tend to have efficient batch verification algorithms. Finding these batching algorithms by hand, however, can be tedious and error prone. We address this by presenting AutoBatch, an automated tool for generating batch verification code in either Python or C++ from a high level representation of a signature scheme. AutoBatch outputs both software and, for transparency, a LaTeX file describing the batching algorithm and arguing that it preserves the unforgeability of the original scheme. We tested AutoBatch on over a dozen pairing-based schemes to demonstrate that a computer could find competitive batching solutions in a reasonable amount of time. Indeed, it proved highly competitive. In particular, it found an algorithm that is significantly faster than a batching algorithm from Eurocrypt 2010. Another novel contribution is that it handles cross-scheme batching, where it searches for a common algebraic structure between two distinct schemes and attempts to batch them together. We describe other features and performance details herein. AutoBatch is a useful tool for cryptographic designers and implementors, and to our knowledge, it is the first attempt to outsource to machines the design, proof writing and implementation of signature batch verification schemes.