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

Abstract

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. In particular, it found an algorithm that is 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.In this work, we expand upon our paper on AutoBatch appearing in ACM CCS 2012 [2] in a number of ways. We add a new loop-unrolling technique and show that it helps cut the batch verification cost of one scheme by roughly half. We describe our pruning and search algorithms in greater detail, including pseudocode and diagrams. All experiments were also re-run using the RELIC pairing library. We compare those results to our earlier results using the MIRACL library, and discuss why RELIC outperforms MIRACL in all but two cases. Automated proofs of several new batching algorithms are also included.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.

Refined Shacham–Waters ring signature scheme in Seo–Cheon framework

“…In several pairing‐based signature schemes, the verifier needs to perform the validity check that involves more than one pairing computation . One common technique is to consolidate the verification equation . In our case, we have many pairing equations associated to NIWI proof.…”

Automated Analysis and Synthesis of Block-Cipher Modes of Operation

“…Several works have recently considered automated generation and/or analysis of cryptographic algorithms. Akinyele et al [AGHP12,AGH13] developed tools for automatically generating batch-verification algorithms for digital-signature schemes [AGHP12], for converting schemes using symmetric bilinear groups into ones using asymmetric bilinear groups [AGH13], and for compiling signature schemes to schemes achieving stronger security properties [AGH13]. In all these cases, their tools do not directly analyze or verify security of new constructions; instead, they take as input schemes that are assumed to be secure, and then attempt to apply a fixed set of transformations that have been proven to preserve (or amplify) security.…”

New efficient batch verification for an identity‐based signature scheme

“…In order to resolve the problem, ‘batch verification’, which allows to verify many signatures at a time, has attracted much attention. Batch verification can be used for diverse applications , for example, authenticated database, auction/bidding system, electronic commerce treating many coins, and voting protocols to verify a huge number of votes and vehicular communications. Also, the primary examples in cryptographic protocols include multiparty key agreement (KA) and multiparty computation.…”

“…Batch verification for an IBS scheme has been suggested to authenticate multiple signatures at a time while still gaining the advantage of the simplified key management procedure. In particular, it is applicable when resource requirements are restricted, because an IBS scheme uses short public keys or identities.…”

“…To date, efficient IBS schemes have been constructed from various cryptographic techniques. In addition, an automated tool was recently presented to generate a batch verifier for a given IBS scheme according to a predefined procedure . But, even if a batch verifier resulting from the tool gives optimized computation for an IBS scheme, it does not imply that the batch verifier has better efficiency, compared to other batch verifiers.…”