A chaotic digital signature algorithm based on a dynamic substitution box

Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In this research, we propose the DSADHπ algorithm, which introduces a confusion step directly into the signature itself, rather than only applying it to the message, using a dynamic substitution box. It is generated with the number pi and changes with each signing. In addition, to enhance security, this work uses a 2048-bit prime, double the length frequently used. This proposal induces chaotic behavior in the signature, making it highly sensitive to any changes in the signer's private key or message content, thereby enhancing authentication and integrity verification. Moreover, the proposed algorithm computes a single multiplicative modular inverse during verification and none during signing, unlike other approaches that require inverse computation in both stages. Since the required inverse is for the Diffie-Hellman session key, it always exists and can be precomputed per communication rather than per message. Consequently, DSADHπ is on average 45 times faster than DSA. Additionally, we introduce a method to assess signature security by constructing images from signature bytes generated by slight changes to the signer's private key and message. Then, their chaotic behavior is evaluated with cryptographic metrics.