Identification of bad signatures in batches

Abstract

The paper addresses the problem of bad signature identification in batch verification of digital signatures. The number of generic tests necessary to identify all bad signatures in a batch instance, is used to measure the efficiency of verifiers. The divide-and-conquer verifier DCVα(x,n) is defined. The verifier identifies all bad signatures in a batch instance x of the length n by repeatedly splitting the input into α sub-instances. Its properties are investigated. In particular, probability distributions for the number of generic tests necessary to identify one, two and three bad signatures, are derived. The average numbers of GT tests necessary to identify bad signatures ranging from 1 to 16 are obtained from computer simulation. Further, a Hamming verifier (HV) is defined which allows to identify a single bad signature in a batch of the length n = 2k −1 using k + 2 tests. HV is generalised into the two-layer Hamming verifier (2HV). Given a batch instance of the length 2k − 2, the 2HV verifier identifies a single bad signature using k + 2 tests and two bad signatures in expense of 3k + 3 tests. The work is concluded by comments about a general model for verification codes identifying t bad signatures and the design of verifiers using combinatorial structures.