Course 2BA1, 2008–09 Section 8: Introduction to Number Theory and Cryptography
نویسنده
چکیده
8 Introduction to Number Theory and Cryptography 125 8.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 125 8.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 125 8.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 126 8.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 129 8.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 130 8.6 The Infinitude of Primes . . . . . . . . . . . . . . . . . . . . . 131 8.7 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.8 Computing Powers in Modular Arithmetic . . . . . . . . . . . 133 8.9 The Chinese Remainder Theorem . . . . . . . . . . . . . . . . 134 8.10 A Theorem of Fermat . . . . . . . . . . . . . . . . . . . . . . . 136 8.11 The Mathematics underlying the RSA cryptographic system . 137
منابع مشابه
Course 2BA1, 2008–09 Section 4: Abstract Algebra
4 Abstract Algebra 56 4.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 56 4.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 56 4.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 56 4.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5 The General Associative Law . . . . . . . . . . . . . . . . . . 58 4.6 Identity el...
متن کاملCourse 2BA1, 2008–09 Section 2: Sets and Functions
2 Sets and Functions 10 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 10 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 14 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.6...
متن کاملCourse Ma2c03, Hilary Term 2014 Section 9: Introduction to Number Theory and Cryptography
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 . . . . . . . . . . . . ...
متن کاملCourse 2BA1: Michaelmas Term 2006 Section 5: Sets and Functions
5 Sets and Functions 1 5.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 5.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 5.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 5.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.6 Congr...
متن کاملCourse 2BA1: Michaelmas Term 2005 Section 2: Sets and Functions
2 Sets and Functions 1 2.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 2.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 2.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Congr...
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تاریخ انتشار 2009