This paper proposes a construction for collision resistant

$2n$-bit hash functions, based

on $n$-bit block ciphers with $2n$-bit keys. The construction is analysed

in the ideal cipher model; for $n=128$ an adversary would need roughly

$2^{122}$ units of time to find a collision.

The construction employs ``combinatorial'' hashing

as an underlying building block (like

Universal Hashing for cryptographic

message authentication by Wegman and Carter).

The construction runs at rate~1, thus improving on a similar

rate~1/2 approach by Hirose (FSE 2006).