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).
@InProceedings{lucks:DagSemProc.07021.3, author = {Lucks, Stefan}, title = {{A Collision-Resistant Rate-1 Double-Block-Length Hash Function}}, booktitle = {Symmetric Cryptography}, pages = {1--14}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {7021}, editor = {Eli Biham and Helena Handschuh and Stefan Lucks and Vincent Rijmen}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07021.3}, URN = {urn:nbn:de:0030-drops-10172}, doi = {10.4230/DagSemProc.07021.3}, annote = {Keywords: Hash function, provable security, double-block-length} }
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