A chaotic digital signature algorithm based on a dynamic substitution box.

Area of Science:

• Cryptography
• Computer Science
• Information Security

Background:

• Digital signatures are crucial for internet security, verifying message authenticity and integrity.
• Minimizing computationally intensive operations like modular inverses is key without sacrificing security.
• Existing methods often require complex computations during both signing and verification.

Purpose of the Study:

• To propose a novel digital signature algorithm, DSADHπ, that enhances security and computational efficiency.
• To introduce a dynamic confusion step within the signature itself.
• To reduce the computational overhead associated with digital signature generation and verification.

Main Methods:

• Developed the DSADHπ algorithm incorporating a dynamic substitution box generated with pi for confusion.
• Utilized a 2048-bit prime for enhanced security, doubling the commonly used length.
• Implemented a method to assess security by visualizing signature byte changes and evaluating chaotic behavior with cryptographic metrics.

Main Results:

• DSADHπ induces chaotic behavior, increasing sensitivity to private key or message alterations for robust verification.
• The algorithm requires only one modular inverse computation during verification and none during signing.
• DSADHπ demonstrates an average speed increase of 45 times compared to the Digital Signature Algorithm (DSA).

Conclusions:

• The DSADHπ algorithm offers a significant improvement in speed and security for digital signatures.
• Its unique approach to confusion and reduced computational requirements make it a viable alternative to existing methods.
• The proposed security assessment method provides a novel way to evaluate the robustness of cryptographic signatures.