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A chaos-based keyed hash function based on fixed point representation

Abstract

Chaotic maps are used in the design of hash functions due to their characteristics that are analogous to cryptographic requirements. However, these maps are commonly implemented using floating point representation which has high computational complexity. They also suffer from interoperability problems and are not easy to analyse from the binary point of view. These drawbacks lead to a lack of acceptance of chaos-based cryptography for practical use. This paper overcomes these problems by introducing a chaos-based hash function implemented using fixed point representation which computes digital chaotic maps using integers. Its design is based on the Merkle–Damgård construction and the generalised Feistel structure for strong security justifications. Security evaluation indicates that the proposed hash function has near-perfect statistical properties which include diffusion, confusion, collision resistance and distribution. The proposed hash function also surpasses existing chaos-based hash functions in terms of performance, making it a viable hash function for practical implementation.

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Notes

  1. A full description of fixed point is available in [20].

  2. See [6] for the full calculation of the theoretically ideal values

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Acknowledgements

This work has been partially supported by Universiti Sains Malaysia under Grant No. 304/PKOMP/6315190 and also the National Natural Science Foundation of China under Grant No. 61702212.

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Correspondence to Je Sen Teh.

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Teh, J.S., Tan, K. & Alawida, M. A chaos-based keyed hash function based on fixed point representation. Cluster Comput 22, 649–660 (2019). https://doi.org/10.1007/s10586-018-2870-z

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Keywords

  • Chaotic iterations
  • Chaotic map
  • Hash function
  • Security evaluation
  • Fixed point arithmetic
  • Cryptography