Heisenberg Group-Based Digital Signatures for Secure Communications
Najla Althuniyan, Ahmed Alamer, Awais Yousaf, Muhammad Waseem, Sarah Aljohani · IEEE Access · 2025
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 Z11, 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.