Attacking the SL2 hashing scheme
Tillich and Zémor proposed a definition of a new hash function which uses SL2(2, 2n), the group of unimodular two-dimensional matrices with entries in GF(2n, to compute the hash values of binary strings. This hashing scheme has several attractive features; hash values can be computed quickly and small modifications to the input text can be detected. However, this scheme is weak. Using a group theoretic argument we are able to produce two distinct binary strings of small length which hash to the same value in SL2(2,2n) for the range specified by Tillich and Zémor.
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