Introductiondouble block hashhash functions based block cipherslars

e : {0, 1}κ × {0, 1}n → {0, 1}n, m = κ + n > n

Hash based on fixed permutations

128, 192 or 256

Yuval: collisions based on birthday paradox (79) (Merkle 79)

- hi

e : {0, 1}κ × {0, 1}n → {0, 1}n MD4, Rivest 1990

Matyas-Meyer-Oseas

Preneel-Miyaguchi

Hash based on fixed permutations

Hash based on fixed permutations 18 / 25 Hash based on fixed permutations Double block hash Hash based on fixed permutations

Based on work by Nandi, 2005

e : {0, 1}κ × {0, 1}n → {0, 1}n, κ > n, c nonzero constant

20 / 25

h2 i

Shrimpton-Stamm, 2007, construction with three bijections.

Collision in time ≈ 2n/2 but same for preimages..