A signature algorithm based on chaotic maps and factoring problems

Abstract

There has been a great deal of interest in researching the behavior of chaotic systems over the past decade. They are distinguished by their sensitivity to initial conditions, continuous broad-band power spectrum, and similarity to random behavior. Chaos has possible applications in the encryption, compression, and modulation blocks of a digital communication system. The possibility of self-synchronization of chaotic oscillations has spawned a deluge of research on the cryptographic applications of chaos. FAC (Factoring) and CM (Chaotic maps) are used in this research to develop a new signature system (CM). Our system has a higher security level than any other based on a single hard number-theoretic problem since it is extremely unlikely that FAC and CM can be solved effectively at the same time. We further demonstrate that the scheme’s performance involves only minimal operations in signing and validating logarithms, and that it is impervious to attack.

Subject Classification:

• 11-XX Number theory – 11T71 Algebraic coding theory
• Cryptography

Keywords:

• Digital signature
• Factorization
• Chaotic maps
• Cryptography
• Crypto analysis