Security Amplification for Interactive Cryptographic Primitives
- Cite this paper as:
- Dodis Y., Impagliazzo R., Jaiswal R., Kabanets V. (2009) Security Amplification for Interactive Cryptographic Primitives. In: Reingold O. (eds) Theory of Cryptography. TCC 2009. Lecture Notes in Computer Science, vol 5444. Springer, Berlin, Heidelberg
Security amplification is an important problem in Cryptography: starting with a “weakly secure” variant of some cryptographic primitive, the goal is to build a “strongly secure” variant of the same primitive. This question has been successfully studied for a variety of important cryptographic primitives, such as one-way functions, collision-resistant hash functions, encryption schemes and weakly verifiable puzzles. However, all these tasks were non-interactive. In this work we study security amplification of interactive cryptographic primitives, such as message authentication codes (MACs), digital signatures (SIGs) and pseudorandom functions (PRFs). In particular, we prove direct product theorems for MACs/SIGs and an XOR lemma for PRFs, therefore obtaining nearly optimal security amplification for these primitives.
Our main technical result is a new Chernoff-type theorem for what we call Dynamic Weakly Verifiable Puzzles, which is a generalization of ordinary Weakly Verifiable Puzzles which we introduce in this paper.