Cryptographic hash functions are security primitives that compute check sums of messages in a strong manner and this way are of fundamental importance for ensuring integrity and authenticity in secure communications. However, recent developments in cryptanalysis indicate that conventional approaches to the design of cryptographic hash functions may have some shortcomings.Therefore it is the intention of this contribution to propose a novel way how to design cryptographic hash functions. Our approach is based on the idea that the hash value of a message is computed as a message-dependent permutation generated by very special chaotic permutation systems, so called Kolomogorov systems. Following this systems theoretic approach we obtain arguably strong hash functions with the additional useful property of excellent scalability.
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