The Collision Security of Tandem-DM in the Ideal Cipher Model

Jooyoung Lee, Martijn Stam, and John Steinberger
Faculty of Mathematics and Statistics, Sejong University, Seoul, Korea; Department of Computer Science, University of Bristol, United Kingdom; and Institute of Theoretical Computer Science, Tsinghua University, Beijing, China

Abstract. We prove that Tandem-DM, which is one of the two “classical” schemes for turning a blockcipher of 2n-bit key into a double block length hash function, has birthday-type collision resistance in the ideal cipher model. A collision resistance analysis for Tandem-DM achieving a similar birthday-type bound was already proposed by Fleischmann, Gorski and Lucks at FSE 2009 [3]. As we detail, however, the latter analysis is wrong, thus leaving the collision resistance of Tandem-DM as an open problem until now. Our analysis exhibits a novel feature in that we introduce a trick not used before in ideal cipher proofs.

Keywords: Hash functions, collision resistance, ideal cipher model.