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This book covers public-key cryptography, describing in depth all major public-key cryptosystems in current use, including ElGamal, RSA, Elliptic Curve, and digital signature schemes. It explains the underlying mathematics needed to build these schemes, and examines the most common techniques used in attacking them. Illustrated with many examples, the book provides a solid foundation for professionals in government, cloud service providers, and large enterprises using public-key systems to secure their data. It is also useful for those taking the CISSP exam (Certified Information Systems Security Professional).
Professor Lynn Batten holds the Deakin Chair in Mathematics and is the Director of the Information Security Research Group at Deakin University. Her research interests include combinatorial geometry, computer network security and computational chemistry. As Associate Dean for Academic and Industrial Research at the University of Manitoba, her former institution, she established a number of agreements between the University and various industry and government sectors.
Table of Contents
0 Introduction 1
0.1 The Meaning of the Word Cryptography 2
0.2 Symmetric Key Cryptography 2
0.3 Public Key (Asymmetric) Cryptography 5
0.4 Key Establishment 8
0.5 Cryptography — more than just Hiding Secrets 9
0.6 Standards 10
0.7 Attacks 11
1 Congruence Equations 13
1.1 Congruence Arithmetic 13
1.1.1 Computer Examples 17
1.1.2 Problems 18
1.2 The Euclidean Algorithm — Finding Inverses 19
1.2.1 Computer Examples 26
1.2.2 Problems 27
1.3 Discrete Logarithms and Diffie-Hellman Key Exchange 27