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discrete math (Number Theory) problem.

discrete math (Number Theory) problem.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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This is a discrete math (Number Theory) problem. Please explain clearly, no cursive writing.

In this problem, we will implement the RSA algorithm to encrypt and decrypt the message "148". For this exercise, you may want to use some kind of calculator that can compute the mod function. 1. Set the primes \( p \) and \( q \) as follows: \( p = 31 \) and \( q = 47 \). What are the values for \( N \) and \( \phi \)? 2. The value for \( e \) is chosen to be 11. Use Euclid’s algorithm to verify that \( e \) and \( \phi \) are relatively prime and to find \( d \), the multiplicative inverse of \( e \) mod \( \phi \). 3. Encrypt the message \( m \) by computing \( m^e \mod N \). 4. The result of the previous question is the ciphertext \( c \) that is transmitted. To decrypt the message, compute \( c^d \mod N \).
Transcribed Image Text:In this problem, we will implement the RSA algorithm to encrypt and decrypt the message "148". For this exercise, you may want to use some kind of calculator that can compute the mod function. 1. Set the primes \( p \) and \( q \) as follows: \( p = 31 \) and \( q = 47 \). What are the values for \( N \) and \( \phi \)? 2. The value for \( e \) is chosen to be 11. Use Euclid’s algorithm to verify that \( e \) and \( \phi \) are relatively prime and to find \( d \), the multiplicative inverse of \( e \) mod \( \phi \). 3. Encrypt the message \( m \) by computing \( m^e \mod N \). 4. The result of the previous question is the ciphertext \( c \) that is transmitted. To decrypt the message, compute \( c^d \mod N \).
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