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Algebra for applications: cryptography, secret sharing, error-correcting, fingerprinting, compression
CONTENTS:
1.Integers
1.1.Natural Numbers
1.2.The Euclidean Algorithm
1.3.Fermat's Little Theorem and Its Generalisations
1.4.The Ring of Integers Modulo n. The Field Zp
1.5.Representation of Numbers
2.Cryptology
2.1.Classical Secret-Key Cryptology
2.2.Modern Public-Key Cryptology
2.3.Computational Complexity
2.4.The RSA Public-Key Cryptosystem
2.5.Applications of Cryptology
3.Groups
3.1.Permutations
3.2.General Groups
3.3.The Abelian Group of an Elliptic Curve
3.4.Applications to Cryptography
4.Fields
4.1.Introduction to Fields
4.2.The Multiplicative Group of a Finite Field Is Cyclic
4.3.The Elgamal Cryptosystem Revisited
5.Polynomials
5.1.The Ring of Polynomials
5.2.Finite Fields
6.Secret Sharing
6.1.Introduction to Secret Sharing
6.2.A General Theory of Secret Sharing Schemes
7.Error-Correcting Codes
7.1.Binary Error-Correcting Codes
7.2.Non-binary Error-Correcting Codes
7.3.Fingerprinting Codes
8.Compression
8.1.Prefix Codes
8.2.Fitingof's Compression Code
8.3.Information and Uncertainty
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