A refinement of the logistic map for cryptographic applications

This paper proposes a one-dimensional chaotic map that is a refinement of the well-known logistic map. The proposed map exhibits chaotic behavior over a much wider domain for its control parameter compared to the logistic map. Furthermore, it generates random-like sequences, which makes it suitable as a building block in cryptographic applications. As an illustration, we propose a block-based probabilistic image encryption scheme, which is shown to possess excellent security properties. Furthermore, this scheme is shown to be competitive with existing schemes.