Heisenberg Group-Based Digital Signatures for Secure Communications

Abstract

This paper proposes a new digital signature algorithm that employs the Heisenberg group over a prime field and exploits its structure to provide strong cryptographic properties. The developed scheme involves the Heisenberg group within a commutator-based authentication system contributing to key exchange while providing secure means of authentication as well as data integrity. The proposed method for digital signature generation and verification is described by a comprehensive algorithm, which proof of correctness is provided by a confirmation theorem. The security analysis establishes the strength of the scheme against different cryptanalytic attacks and proves the effectiveness of non-repudiation and message integrity in the digital environment. The efficiency of the presented security scheme is also evaluated in practice, using the finite field $\mathbb {Z}_{11}$ , where it is measured against other standards such as ECDSA and RSA. While it has a bigger signature size, the scheme is still efficient when it comes to signing and verifying messages which highlights its suitability for protecting communications under post-quantum cryptography. It supports the on-going progress of cryptography, giving added security to new technologies when faced with the threat of complex attacks.

Keywords

• Heisenberg group
• digital signature
• hashing
• cryptographic verification
• group-based cryptography
• message authentication