Ch04

Cryptography and Network Security Third Edition by William Stallings Lecture slides by Lawrie Brown

Chapter 4 – Finite Fields ,[object Object],[object Object]

Introduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Group ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Cyclic Group ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ring ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Field ,[object Object],[object Object],[object Object],[object Object]

Modular Arithmetic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Modulo 7 Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Divisors ,[object Object],[object Object],[object Object],[object Object],[object Object]

Modular Arithmetic Operations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Modular Arithmetic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Greatest Common Divisor (GCD) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Euclid's GCD Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example GCD(1970,1066) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Galois Fields ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Galois Fields GF(p) ,[object Object],[object Object],[object Object],[object Object]

Finding Inverses ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Polynomial Arithmetic ,[object Object],[object Object],[object Object],[object Object],[object Object]

Ordinary Polynomial Arithmetic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Polynomial Arithmetic with Modulo Coefficients ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Modular Polynomial Arithmetic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Polynomial GCD ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Computational Considerations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ch04

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