# Cryptography: Theory and Practice

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COMS W4995 Introduction to Cryptography October 30, 2003 Lecture 18: Digital Signature Schemes Lecturer: Tal Malkin Scribes: Hua Shuo Cai Summary Definition of Digital Signature scheme. Brief description of Paradox. And construc- tion of Lamport’s One-Time Signature for one bit message. 1 Authenticity How do you know that relieved message is from who you think it is? And that it wasn’t tampered with? Adv can intercept the cipher and change the cipher. We have two authentication schemes : DigitalSignature - Public Key World. MessageAuthenticationCode - Private Key World. 2 Digital Signature Definition 1 A Digital Signature Scheme is a triple of algorithms { GEN, SIGN, V ER } such that: GEN (The key generate algorithm) - a randomized algorithm that on input 1 k outputs ( PK, SK ) . SIGN (The Signing algorithm)- a (Possibly randomized algorithm) that on in- put SK , m output a signature σ . 1

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σ SIGN SK ( m ) V ER (The Verification algorithm) - takes as input PK , m , σ outputs accept or reject.
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