Introduction to Cryptography November 2 , 2006 Lecture 20 : Digital Signatures II

In the last lecture, we developed a digital signature scheme for message in {0, 1} n and proved it to be one-time secure. We also showed how to construct a family of Collision-Resistant Hash Functions (CRH) and claimed that they would be useful in constructing one-time secure digital signature schemes for messages in {0, 1} *. The following theorem makes this claim more formally. Theorem 1 If there exists a CRH from {0, 1} * −→ {0, 1} n and there exists a one-way function (OWF), then there exists a one-time secure digital signature scheme for {0, 1} *. Proof. We will only provide a sketch of the proof here.