Probabilistic Analysis of Cryptographic Hash Functions.

Date of Submission

December 2009

Date of Award

Winter 12-12-2010

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Applied Statistics Unit (ASU-Kolkata)


Sarkar, Palash (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

A multicollision for a hash function is a set of two or more distinct domain points all mapping to the same range point. Multicollision freeness has been suggested as an important security property of hash functions. Joux has shown that multicollisions are not harder to find than ordinary collisions for hash functions based on an iterated construction. For general hash functions, the best known attack is the generic birthday attack. For truly random functions, the complexity of finding r-collisions is Θ(m(r−1)/r) where m is the size of the range of the hash function. But such functions are seldom encountered in practice.For the case of r = 2, Bellare and Kohno analyze the success rate of the birthday attack on a specific hash function rather than analyzing one chosen at random. They define balance of a hash function h, denoted µ(h), which is a measure of the “amount of regularity” of h and study its impact on the birthday attack.In this thesis we extend the notion of balance to that of r-balance. We then analyze the performance of the birthday attack via the r-balance. We derive bounds on the probability of finding r-collisions using the birthday attack for a given hash function h. Using these bounds we show that the complexity of finding r collisions is roughly Θ(m( r−1/r )µr(h) ) where µr(h) is the r-balance of h. Our results indicate that higher the r-balance, higher will be the complexity of finding r-collisions. For r = 2, our analysis provides slightly better bounds than the ones given by Bellare and Kohno.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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