ded abstract of this paper appears in Advances in Cryptology { Crypto 97 Proceedings, Lecture Notes in Computer Science Vol. 1294, B. Kaliski ed., Springer-Verlag, 1997. This is the full version. Collision-Resistant Hashing: Towards Making UOWHFs Practical Mihir Bellare Phillip Rogawayy July 17, 1997 Recent attackson the cryptographichash functions MD4 and MD5 make it clear that (strong) collision-resistanceis a hard-to-achievegoal. We looktowardsa weakernotion, the universal oneway hash functions (UOWHFs) of Naor and Yung, and investigate their practical potential. The goal is to build UOWHFs not based on number theoretic assumptions, but from the primitives