Advanced Topics in Cryptography April 22 , 2004 Lecture 23 Lecturer : Jonathan Katz Scribe ( s ) : Nicholas Sze

Advanced Topics in Cryptography January 27 , 2004 Lecture 1 Lecturer : Jonathan Katz Scribe ( s ) : Jonathan Katz 1 Introduction to These Notes

We give two definitions of trapdoor permutations. The first is completely formal, and maps well onto the (conjectured) trapdoor permutations that are used in practice. The second is slightly less formal, but is simpler to use and somewhat easier to understand. Generally speaking, however, proofs of security using the second of the two definitions can be easily modified to work for the first def...

Lecture 16 Lecturer: Jonathan Katz Scribe(s): 1 Digital Signature Schemes

• Vrfy takes as input a public key, a message, and a (purported) signature; it outputs a single bit b with b = 1 indicating acceptance and b = 0 indicating rejection. (We assume for simplicity that Vrfy is deterministic.) We write this as b = Vrfypk(m,σ). For correctness, we require that for all (pk, sk) output by Gen(1k), for all messages m, and for all σ output by Signsk(m) we have Vrfypk(m,σ...

Lecturer : Jonathan Katz Scribe ( s ) : Nikolai Yakovenko Jeffrey

In a previous lecture, we showed a zero-knowledge (ZK) proof system for the language of graph isomorphism. Our goal here is to show a ZK proof system for any language inNP . To do so, it suffices to show a ZK proof system Π for any NP-complete language L (note that graph isomorphism is not believed to be NP-complete); given such a Π and any L ′ ∈ NP , we then obtain a ZK proof for L by (1) redu...

Advanced Topics in Cryptography April 29 , 2004 Lecture 25 Lecturer : Jonathan

In this lecture, we discuss concrete applications of zero-knowledge proof systems to the task of constructing (public-key 1) identification schemes. We begin with an informal definition of what these are. Definition 1 A (public-key) identification scheme consists of a prover P who has generated some public-/private-key pair (P K, SK), and wants to prove his identity to a verifier V who knows P ...

Advanced Topics in Cryptography March 4 , 2004 Lecture 12