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Note for Cryptography And Network Security - CNS by pentareddy n

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An Introduction to Cryptography Mohamed Barakat, Christian Eder, Timo Hanke September 20, 2018

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Preface Second Edition Lecture notes of a class given during the summer term 2017 at the University of Kaiserslautern. The notes are based on lecture notes by Mohamed Barakat and Timo Hanke [BH12] (see also below). Other good sources and books are, for example, [Buc04, Sch95, MVO96]. Many thanks to Raul Epure for proofreading and suggestions to improve the lecture notes. First Edition These lecture notes are based on the course “Kryptographie” given by Timo Hanke at RWTH Aachen University in the summer semester of 2010. They were amended and extended by several topics, as well as translated into English, by Mohamed Barakat for his course “Cryptography” at TU Kaiserslautern in the winter semester of 2010/11. Besides the literature given in the bibliography section, our sources include lectures notes of courses held by Michael Cuntz, Florian Heß, Gerhard Hiß and Jürgen Müller. We would like to thank them all. Mohamed Barakat would also like to thank the audience of the course for their helpful remarks and questions. Special thanks to Henning Kopp for his numerous improvements suggestions. Also thanks to Jochen Kall who helped locating further errors and typos. Daniel Berger helped me with subtle formatting issues. Many thanks Daniel. i

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Contents Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i Contents ii 1 Introduction 1 2 Basic Concepts 2.1 Quick & Dirty Introduction to Complexity Theory . . . . . . . . . . . . . . . . . . . . . 2.2 Underlying Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Investigating Security Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 7 11 3 Modes of Ciphers 3.1 Block Ciphers . . . . . . . . . . . . . . 3.2 Modes of Block Ciphers . . . . . . . . 3.3 Stream Ciphers . . . . . . . . . . . . . 3.4 A Short Review of Historical Ciphers . . . . 13 13 14 23 25 4 Information Theory 4.1 A Short Introduction to Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Perfect Secrecy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 27 31 35 5 Pseudorandom Sequences 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Linear recurrence equations and pseudorandom bit generators 5.3 Finite fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Statistical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Cryptographically secure pseudorandom bit generators . . . . . . . . . 47 47 48 53 62 66 6 Modern Symmetric Block Ciphers 6.1 Feistel cipher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Data Encryption Standard (DES) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Advanced Encryption Standard (AES) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 70 71 74 7 Candidates of One-Way Functions 7.1 Complexity classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Squaring modulo n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 77 78 . . . . . . . . ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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