Cryptographic Hash Functions from Expander Graphs

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Zarei, Afshin | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46200 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): khazaei, Shahram
Abstract:
A hash function maps efficiently every finite length string to a fixed one. The output represents the entire content of the input, similar to digital fingerprint of input text. In order to be able to use a hash function in cryptography, it should be hard to find two distinct inputs with the same output (collision), because finding a collision in hash functions leads to malicious attacks on many security systems.We say a hash function is provably collision resistant, if finding a collision can be reduced to the known hard problems. Family of MD hash functions are one of the most famous applied hash functions which are considerably used in industrial applications. However, they are not provably collision resistant. There exist some hash functions that are provably collision resistant, e.g. VSH and SWIFFT. In this study, we explain the structure of hash functions based on Pizer expander graphs. Then, the mathematical structure of the Pizer graph is used to investigate the collision resistance property of these hash functions
Keywords:
Cryptography ; Expander Graph ; Hash Function ; Pizer's Graph