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4.2 THE RSA Cryptosystem WITH PRIMES We will discuss of this algorithm is based on the process below. [2) 4.2.1 Finding the keys We use the steps below to find public key and the private key 1. select two distinct large primes p, q,r and s. 2. Calculate n= p q r s and (n) (p- 1)(- 1)(r- 1)(s-1). 3. choose a number e, such that, (e, p(n)) = 1. To find the number e, we pick number e randomly and use Euclidean algorithm to find (e,(n)) 1. Also, choose a number f, such that, (f, (n)) = 1. To find the number e, we pick number f randomly and use Euclidean algorithm to find (f.(n)) 1 4. Find d, g and Y,such that,1 s d, g <(n), Y 2 1, and e•d - p(n) + Y - 1 f g-(n) Y =1 The numbers d, g and Y and (n) are kept secret. The number d, g are the private key or decryption key.

4.2 THE RSA Cryptosystem WITH PRIMES We will discuss of this algorithm is based on the process below. [2) 4.2.1 Finding the keys We use the steps below to find public key and the private key 1. select two distinct large primes p, q,r and s. 2. Calculate n= p q r s and (n) (p- 1)(- 1)(r- 1)(s-1). 3. choose a number e, such that, (e, p(n)) = 1. To find the number e, we pick number e randomly and use Euclidean algorithm to find (e,(n)) 1. Also, choose a number f, such that, (f, (n)) = 1. To find the number e, we pick number f randomly and use Euclidean algorithm to find (f.(n)) 1 4. Find d, g and Y,such that,1 s d, g <(n), Y 2 1, and e•d - p(n) + Y - 1 f g-(n) Y =1 The numbers d, g and Y and (n) are kept secret. The number d, g are the private key or decryption key.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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this, I got it from the net if it was only 2 p and q In light of Hai, the professor asked me to ask me 4 p, q, r and s
Chapter 4 4.3 introduction 4.2 THE RSA Cryptosystem WITH PRIMES We will discuss of this algorithm is based on the process below. [2) 4.2.1 Finding the keys We use the steps below to find public key and the private key 1. select two distinct large primes p, q,r and s. 2. Calculate n = p • q r• s and ø(n) = (p - 1)(q - 1)(r - 1)(s - 1). 3. choose a number e , such that, (e, p(n)) = 1. To find the number e, we pick number e randomly and use Euclidean algorithm to find (e, o(n)) = 1. Also, choose a number f, such that, (f.o(n)) = 1. To find the number e, we pick number f randomly and use Euclidean algorithm to find (f, O(n)) = 1 4. Find d, g and Y,such that,1 < d, g < p(n), Y 2 1, and e•d - p(n) + Y - 1 f g-(n) Y = 1 The numbers d, g and Y and o(n) are kept secret. The number d, g are the private key or decryption key. 4.2.2 The Encoding process = (M mod n)/ mod n 4.2.3 The Decoding process b = (M9 mod n)a mod n %3D
Transcribed Image Text:Chapter 4 4.3 introduction 4.2 THE RSA Cryptosystem WITH PRIMES We will discuss of this algorithm is based on the process below. [2) 4.2.1 Finding the keys We use the steps below to find public key and the private key 1. select two distinct large primes p, q,r and s. 2. Calculate n = p • q r• s and ø(n) = (p - 1)(q - 1)(r - 1)(s - 1). 3. choose a number e , such that, (e, p(n)) = 1. To find the number e, we pick number e randomly and use Euclidean algorithm to find (e, o(n)) = 1. Also, choose a number f, such that, (f.o(n)) = 1. To find the number e, we pick number f randomly and use Euclidean algorithm to find (f, O(n)) = 1 4. Find d, g and Y,such that,1 < d, g < p(n), Y 2 1, and e•d - p(n) + Y - 1 f g-(n) Y = 1 The numbers d, g and Y and o(n) are kept secret. The number d, g are the private key or decryption key. 4.2.2 The Encoding process = (M mod n)/ mod n 4.2.3 The Decoding process b = (M9 mod n)a mod n %3D
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