Paper 2021/922

Provably Secure Short Signature Scheme from Isogeny between Elliptic Curves

Kunal Dey and Sumit Kumar Debnath

Abstract

Digital signature is one of the most important public key cryptographic primitive for message authentication. In a digital signature scheme, receiver of a message-signature pair gets assurance about the fact that the message belongs to the sender and neither receiver nor any third party can manipulate the message. In the current state of art, most of the existing digital signatures' security relies on classical cryptographic assumption based hard problems, such as discrete log, integer factorization, etc. However, rapid development of quantum computing creates a security threat to these classical digital signature schemes. It indicates the recruitment of an alternative solution which can prevent quantum attacks. We focus on this concern by implementing a post-quantum secure isogeny based digital signature scheme without making use of SIDH and CSIDH. Our scheme achieves uf-cma security under a hard problem in isogeny. The proposed signature scheme incurs 256 byte public key size and 128 byte signature size to achieve 128-bit security level (NIST-1 level of security). In particular, the size of signature of our design is smaller than all other IBC based signature schemes at the 128-bit security level.