Suppose that (n,e) is an RSA encryption key, with n = pq are larging primes and gcd(e,(p – 1)(q – 1)) =1. Furthermore, suppose that d is an inverse of e modulo (p – 1)(q – 1).Suppose that C ? Me(mod pq). In the text we showed that RSA decryption, that is the congruence Cd ? M (mod pq) holds when gcd(M,pq) = 1. Show that is decryption congruence also holds when gcd(M,pq) > 1. [Hint : Use congruences modulo p and modulo q and apply the Chinese remainder theorem]

# Suppose that (n,e) is an RSA encryption key, with n = pq

## Solution for problem 28E Chapter 4.6

Discrete Mathematics and Its Applications | 7th Edition

- Textbook Solutions
- 2901 Step-by-step solutions solved by professors and subject experts
- Get 24/7 help from StudySoup virtual teaching assistants

Discrete Mathematics and Its Applications | 7th Edition

Get Full SolutionsThis full solution covers the following key subjects: gcd, suppose, modulo, mod, RSA. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 28E from chapter: 4.6 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “Suppose that (n,e) is an RSA encryption key, with n = pq are larging primes and gcd(e,(p – 1)(q – 1)) =1. Furthermore, suppose that d is an inverse of e modulo (p – 1)(q – 1).Suppose that C ? Me(mod pq). In the text we showed that RSA decryption, that is the congruence Cd ? M (mod pq) holds when gcd(M,pq) = 1. Show that is decryption congruence also holds when gcd(M,pq) > 1. [Hint : Use congruences modulo p and modulo q and apply the Chinese remainder theorem]” is broken down into a number of easy to follow steps, and 90 words. Since the solution to 28E from 4.6 chapter was answered, more than 284 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

#### Other solutions

#### People also purchased

#### Related chapters

Enter your email below to unlock your **verified solution** to:

Suppose that (n,e) is an RSA encryption key, with n = pq