Course Ma2c03, Hilary Term 2014 Section 9: Introduction to Number Theory and Cryptography
نویسنده
چکیده
9 Introduction to Number Theory 168 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 168 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 168 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 169 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 173 9.6 The Infinitude of Primes . . . . . . . . . . . . . . . . . . . . . 174 9.7 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 9.8 Computing Powers in Modular Arithmetic . . . . . . . . . . . 176 9.9 The Chinese Remainder Theorem . . . . . . . . . . . . . . . . 178 9.10 A Theorem of Fermat . . . . . . . . . . . . . . . . . . . . . . . 180 9.11 The Mathematics underlying the RSA cryptographic system . 181
منابع مشابه
Course Ma2c03, Hilary Term 2014 Section 7: Periodic Series and Functions
7 Periodic Series and Functions 128 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 128 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 130 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 131 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 133 7.5 The Exponential of a Complex Number . . . . . . . . . . . . . 133 7.6...
متن کاملCourse Ma2c03, Hilary Term 2014 Section 8: Vectors and Quaternions
8 Vectors and Quaternions 145 8.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8.2 Displacement Vectors . . . . . . . . . . . . . . . . . . . . . . . 145 8.3 The Parallelogram Law of Vector Addition . . . . . . . . . . . 146 8.4 The Length of Vectors . . . . . . . . . . . . . . . . . . . . . . 147 8.5 Scalar Multiples of Vectors . . . . . . . . . . . . . . . . . . ....
متن کاملCourse MA 2 C 02 , Hilary Term 2013
9 Introduction to Number Theory 63 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 63 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 63 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 64 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 67 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 68 9....
متن کاملCourse MA2C03, Michaelmas Term 2014 Section 2: Abstract Algebra
2 Abstract Algebra 24 2.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 24 2.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 24 2.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 24 2.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 The General Associative Law . . . . . . . . . . . . . . . . . . 26 2.6 Identity el...
متن کاملCourse MA 2 C 02 , Hilary Term 2010
5 Introduction to Number Theory and Cryptography 72 5.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 72 5.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 72 5.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 73 5.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.5 The Fundamental Theorem of Arithmetic . . . . . . ...
متن کامل