Amplifying Collision Resistance: A Complexity-Theoretic Treatment
- Cite this paper as:
- Canetti R., Rivest R., Sudan M., Trevisan L., Vadhan S., Wee H. (2007) Amplifying Collision Resistance: A Complexity-Theoretic Treatment. In: Menezes A. (eds) Advances in Cryptology - CRYPTO 2007. CRYPTO 2007. Lecture Notes in Computer Science, vol 4622. Springer, Berlin, Heidelberg
We initiate a complexity-theoretic treatment of hardness amplification for collision-resistant hash functions, namely the transformation of weakly collision-resistant hash functions into strongly collision-resistant ones in the standard model of computation. We measure the level of collision resistance by the maximum probability, over the choice of the key, for which an efficient adversary can find a collision. The goal is to obtain constructions with short output, short keys, small loss in adversarial complexity tolerated, and a good trade-off between compression ratio and computational complexity. We provide an analysis of several simple constructions, and show that many of the parameters achieved by our constructions are almost optimal in some sense.