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Solve for n, Q, and d. Show your work. p = 53 q = 97 e=5

Solve for n, Q, and d. Show your work. p = 53 q = 97 e=5

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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Question
**Problem Statement:** Solve for \( n \), \( \Phi \), and \( d \). Show your work. Given: - \( p = 53 \) - \( q = 97 \) - \( e = 5 \) **Solution Steps:** 1. **Calculate \( n \):** \[ n = p \times q = 53 \times 97 \] 2. **Calculate \( \Phi(n) \):** \[ \Phi(n) = (p-1) \times (q-1) = (53-1) \times (97-1) \] 3. **Calculate \( d \):** Find \( d \) such that: \[ d \times e \equiv 1 \pmod{\Phi(n)} \] This involves finding the modular inverse of \( e \) mod \( \Phi(n) \). Ensure to compute each step clearly and verify the results for accuracy.
Transcribed Image Text:**Problem Statement:** Solve for \( n \), \( \Phi \), and \( d \). Show your work. Given: - \( p = 53 \) - \( q = 97 \) - \( e = 5 \) **Solution Steps:** 1. **Calculate \( n \):** \[ n = p \times q = 53 \times 97 \] 2. **Calculate \( \Phi(n) \):** \[ \Phi(n) = (p-1) \times (q-1) = (53-1) \times (97-1) \] 3. **Calculate \( d \):** Find \( d \) such that: \[ d \times e \equiv 1 \pmod{\Phi(n)} \] This involves finding the modular inverse of \( e \) mod \( \Phi(n) \). Ensure to compute each step clearly and verify the results for accuracy.
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