Code-based Sequential Aggregate Signature Scheme

Abstract

This paper proposes the first code-based quantum immune sequential aggregate signature (SAS) scheme and proves the security of the proposed scheme in the random oracle model. Aggregate signature (AS) schemes and sequential aggregate signature schemes allow a group of potential signers to sign different messages respectively, and all the signatures of those users on those messages can be aggregated into a single signature such that the size of the aggregate signature is much smaller than the total size of all individual signatures. Because of the aggregation of many signatures into a single short signature, AS and SAS schemes can reduce bandwidth and save storage; moreover, when a SAS is verified, not only the valid but also the order in which each signer signed can be verified. AS and SAS schemes can be applied to traffic control, banking transaction and military applications. Most of the existing AS and SAS schemes are based either on pairing or Rivest-Shamir-Adleman (RSA), and hence, can be broken by Shor's quantum algorithm for Integer Factoring Problem (IFP) and Discrete Logarithm Problem (DLP). There are no quantum algorithms to solve syndrome decoding problems. Hence, code-based cryptography is seen as one of the promising candidates for post-quantum cryptography. This paper shows how to construct quantum immune sequential aggregate signatures based on coding theory. Specifically, we construct our scheme with the first code based signature scheme proposed by Courtois, Finiasz and Sendrier (CFS). Compared to the CFS signature scheme without aggregation, the proposed sequential aggregate signature scheme can save about 90% storage when the number of signers is asymptotically large.

Insecurity of Chait et al.’s RSA-Based Aggregate Signature Scheme

“…So, it can be applied for various scenarios, e.g., sensor networks [1], vehicular ad-hoc network [2], smart city applications [3], and blockchain [4], [5]. Due to its wideranging applications, since it was firstly introduced by Boneh et al [6], there have been proposed numerous aggregate signature schemes and their variants under diverse settings, e.g., discrete-log (DL) [1]- [5], [7]- [14], lattices [15], [16], codes [17], and RSA [18]- [21].…”