Codes Identifying Bad Signatures in Batches

Abstract

The work is concerned with identification of bad signatures in a sequence which is validated using batching. Identification codes (id-codes) are defined and their general properties are investigated. A taxonomy of id-codes is given. The generic construction for a wide range of id-codes is given and its instantiation using mutually orthogonal Latin squares is described. Hierarchical identification is studied for two cases when the identification procedure uses a family of id-codes and when there is a single underlying id-code. Remarks about future research conclude the work.

Group Testing and Batch Verification

“…The first two are by Pastuszak et al [30,29]. They consider a generic Batch function for a signature scheme and study the divide-andconquer method of finding bad signatures in [29].…”

“…The second paper [30] approaches the problem using identification codes (id-codes), a code which encodes an ISF algorithm, by specifying subsets of B to test with Batch in such a way that all bad signatures may be identified. This approach is an instance of well-known non-adaptive group testing algorithms based on cover-free, separable and disjunct matrices, discussed in §2.3.1.…”

“…This approach is an instance of well-known non-adaptive group testing algorithms based on cover-free, separable and disjunct matrices, discussed in §2.3.1. A limitation of [30,29] is that either the number of bad signatures in a batch, or a bound on the number of bad signatures is required a priori. This is common to most group testing algorithms as well.…”

Faster Batch Forgery Identification

“…Pastuszak, Pieprzyk, and Seberry in [26] considered the possibility of nonadaptively choosing subbatches to verify. All available evidence suggests that this non-adaptivity restriction compromises performance even when the number of forgeries is somehow known in advance, and it certainly does not improve performance.…”

Batch Pairing Delegation

“…Otherwise, the verifier knows there is at least one bad signature. Further work on this topic studies efficient means to identify bad signatures [34,35]. Similarly, our idea of delegating pairing computation in batch tries to improve overall efficiency by delegating in batch rather than one by one independently.…”