On the Practicality of Short Signature Batch Verification

As pervasive communication becomes a reality, where everything from vehicles to heart monitors constantly communicate with their environments, system designers are facing a cryptographic puzzle on how to authenticate messages. These scenarios require that : (1) cryptographic overhead remain short, and yet (2) many messages from many different signers be verified very quickly. Pairingbased signatures have property (1) but not (2), whereas schemes like RSA have property (2) but not (1). As a solution to this dilemma, in Eurocrypt 2007, Camenisch, Hohenberger and Pedersen showed how to batch verify two pairing-based signatures so that the total number of pairing operations was independent of the number of signatures to verify. CHP left open the task of batching privacy-friendly authentication, which is desirable in many pervasive communication scenarios. In this work, we revisit this issue from a more practical standpoint and present the following results: 1. We describe a framework, consisting of general techniques, to help scheme and system designers understand how to securely and efficiently batch the verification of pairing equations. 2. We present a detailed study of when and how our framework can be applied to existing regular, identity-based, group, ring, and aggregate signature schemes. To our knowledge, these batch verifiers for group and ring signatures are the first proposals for batching privacy-friendly authentication, answering an open problem of Camenisch et al. 3. While prior work gave mostly asymptotic efficiency comparisons, we show that our framework is practical by implementing our techniques and giving detailed performance measurements. Additionally, we discuss how to deal with invalid signatures in a batch and our empirical results show that when ≤ 10% of signatures are invalid, batching remains more efficient that individual verification. Indeed, our results show that batch verification for short signatures is an effective, efficient approach.