Design of a new self-shrinking 2-adic cryptographic system with application to image encryption

This paper proposes a novel cryptographic system based on a combination of Al Jabri self-shrinking rule and 2-adic Fibonacci representation of feedback-with-carry shift register (FCSR). It provides better security for critical telecommunication nodes and wireless sensors by using 256-bit key and 255-bit initialization vector. A crypto resistance security analysis illustrates that the nonlinear exit from the proposed scheme is stable against known cryptographic attacks. A NIST statistical test applied to the new cryptographic approach shows perfect random-like behavior of output bit sequences. We applied the proposed algorithm to encrypt color images (24 bits/pixels) and estimated results by histogram analysis, correlation coefficients of adjacent pixels, key sensitive test, and information entropy analysis. The encrypted images were also tested by the statistical differential attack, estimating the two criteria: number of pixels change rate and unified average changing intensity. The experimental results confirm that the proposed method is efficient and provides a high level of security. We find that the new self-shrinking 2-adic cryptographic system is suitable for applications such as secure transmission of confidential information in public networks and encryption of digital color images.