tailieunhanh - Digital Signature Schemes

This thesis will attempt to describe in detail the concepts of digital signatures and the related background issues. We will begin with a general introduction to cryptography and digital signatures and follow with an overview of the requisite math involved in cryptographic applications. | Digital Signature Schemes Nick Carruthers Department of Math and Computer Science Middlebury College December 9 1997 Abstract This thesis will attempt to describe in detail the concepts of digital signatures and the related background issues. We will begin with a general introduction to cryptography and digital signatures and follow with an overview of the requisite math involved in cryptographic applications. We will then discuss in detail two digital signature schemes based on the discrete logarithm problem the ElGamal scheme and its derivative the United States Digital Signature Standard. Having done this we will explore the problems and insecurities involved in their use. 1 1 Digital Signatures - A Quick Concepts of Public-Key One-Way Symmetric vs. Applicability to Digital 2 Mathematical Complexity Primality . 11 Modular Arithmetic. 12 Fast Inverses Mod a Chinese Remainder Theorem . 14 Generators . 15 Quadratic Residues. 16 The Legendre The Discrete Logarithm Problem. 16 Galois 3 Digital Definition of a Signature Role of Hash ElGamal Digital Signature An The Digital Signature Standard DSS . 21 Modifications to the ElGamal Description of Speedups . 23 The Secure Hash Algorithm SHA . 24 Parameter Generation . 25 Derivative Schemes . 26 4 Security 2 Classification of Existential Forgery Using Universal Forgery Using Brute Force Shank s Pohlig-Hellman The Random Parameter Random Number Linear Congruential .