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savin g numbers groups cryptography 2018

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Textbook in PDF format Euclidean Algorithm Euclidean Algorithm Fundamental Theorem of Arithmetic Uniqueness of Factorization Efficiency of the Euclidean Algorithm Groups and Arithmetic Groups Congruences Modular arithmetic Theorem of Lagrange Chinese Remainder Theorem Rings and Fields Fields and Wilson’s Theorem Field Characteristic and Frobenius Quadratic Numbers Primes Infinitude of primes Primes in progression Perfect Numbers and Mersenne Primes The Lucas Lehmer test Roots Roots Property of the Euler Function Primitive roots Discrete logarithm Cyclotomic Polynomials Quadratic Reciprocity Squares modulo p Fields of order p^2 When is 2 a square modulo p? Quadratic Reciprocity Applications of Quadratic Reciprocity Fermat primes Quadratic Fields and the Circle Group Lucas Lehmer test revisited Sums of two squares Sums of two squares Gaussian integers Method of descent revisited Pell’s Equations Shape numbers and Induction Square-Triangular Numbers and Pell Equation Dirichlet’s approximation Pell Equation: classifying solutions Continued Fractions Cryptography Diffie-Hellman key exchange RSA Code ElGamal Code Primality testing Miller Rabin test p −1 method p +1 method Quadratic sieve Elliptic curves Cubic curves Degenerate curves Curves modulo p The curve y^2 = x^3 + bx Factoring and testing using elliptic curves Lenstra’s factoring method Degenerate curves modulo p Elliptic curve test for Mersenne primes

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Savin G. Numbers, Groups and Cryptography 2018.pdf 1.9 MB

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savin g numbers groups cryptography 2018