| Popis: |
Title: Binary Signed Digit Representations of Integers in Cryptanalysis of Hash Functions Author: Jiří Vábek Department: Department of Algebra Supervisor: doc. RNDr. Jiří Tůma, DrSc., Department of Algebra Abstract: The work summarizes two main papers, A New Type of 2-block Colli- sions in MD5 and On the Number of Binary Signed Digit Representations of a Given Weight, while containing also the wider introduction to the topic of crypt- analysis of MD5 and binary signed digit representations (BSDR's). In the first paper we have implemented and applied Stevens algorithm to the newly proposed initial message differences and constructed a new type of collisions in MD5. In the second paper we have introduced and proved a new improved bound for the number of optimal BSDR's and also a new recursive bound for the number of BSDR's of a given integer with a given overweight. In addition to the results in mentioned papers, the generalized result is stated with the new bound for the number of optimal D-representations of natural numbers with D = {0, 1, 3}. Keywords: hash function, MD5, binary signed digit representation (BSDR), non- adjacent form (NAF) 1 |
