Простые числа и криптография

1. Elementary Properties of Numbers.
1.1. Natural series of numbers. A value of number. Addition,
difference and multiplication of numbers.
1.2. Division of numbers. The greatest common divisor of
two numbers. The least common multiple.
1.3. Prime Numbers. The Sieve of Eratosthenes.
1.4. The Fundamental Theorem of Euclid
1.5. Divisibility by a Prime Number
1.6. The Unique Factorization Theorem
1.7. Divisors of an Integers
1.8. The Greatest Common Factor of Two or More Integers
1.9. The Least Common Multiple of Two or More Integers
1.10. Scales of Notation
1.11. Euler’s Totient Function
1.12. The Mo¨bius Function
2. Elementary Properties of Congruences
2.1. Congruences Modulo m
Содержание II
2.2. Solutions of Congruences
2.3. Properties of Congruences Relative to Division
2.4. Congruences with a Prime Modulus
2.5. Linear Congruences
2.6. The theorems of Fermat and Euler
2.7. Wilson’s Theorem
3. Primitive Roots modulo m
3.1. Primitive Roots Modulo p
3.2. Primitive Roots Modulo p
α, p an Odd Prime
3.3. Primitive Roots Modulo 2p
α, p an Odd Prime
4.1. Ordinary Multiplication Algorithm
5. Keys in Cryptography. Selecting Keys
6. RSA Cryptosystem. The Fixed Points of an RSA System
7. The Recognition of Primes
8. Factorization
1. Elementary Properties of Numbers I
Here we are concerned primarily with certain elementary properties
of the positive integers 1, 2, 3, 4, 5, 6, 7, . . . . We employ the word
integer or the word number in sense of positive integer. We shall
suppose that the integers are already defined, either by the process
of counting or otherwise.