Unkeyed hash function based on chaotic sponge construction and fixed-point arithmetic

Abstract

Chaotic maps have various properties that mirror the security requirements of cryptographic algorithms. As such, researchers have utilized them in the design of algorithms such as hash functions. Although there exist a wide range of chaos-based hash functions in literature, most of them are designed in an ad hoc manner rather than relying on well-established design paradigms. In addition, they are commonly implemented using floating-point operations which are inefficient as compared to their bitwise counterparts. The combination of convoluted designs and floating-point representation also leads to hash functions that are difficult to analyze; therefore, claims of security cannot be verified easily. These issues are some of the reasons why chaos-based hash functions have not seen widespread use in practice. This paper proposes a new unkeyed hash function based on a chaotic sponge construction and fixed-point arithmetic to overcome the aforementioned problems. The use of a sponge construction provides provable security justifications, whereas the use of fixed-point arithmetic allows chaotic map operations to be implemented using bitwise operations. The combination of these design elements leads to a design that is both efficient and facilitates future cryptanalysis for security verification. Security and performance evaluations indicate that the proposed hash function has near-ideal diffusion, confusion, collision resistance, and distribution properties in addition to a hashing speed that is at least on par with the current state of the art in chaos-based hash functions.