8. The Rabin public-key encryption scheme is similar to RSA. Research this cryptosystem and decrypt the following ciphertext: 25292168 which was encrypted for a user with public key n 27219809.
8. The Rabin public-key encryption scheme is similar to RSA. Research this cryptosystem and decrypt the following ciphertext: 25292168 which was encrypted for a user with public key n 27219809.
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 8 please do not use a computer system generater I need to see how it's done
![### Cryptography Concepts and Problems
**7. Merkle-Hellman Knapsack Cryptosystem**
**Ciphertext:**
261, 163, 196, 172, 217, 172, 89, 142, 76, 217, 209, 172, ?
The above ciphertext was generated using the Merkle-Hellman Knapsack cryptosystem for a user with the following components:
- **Private key sequence:** \{5, 8, 17, 36, 71\}
- **Modulus (m):** 145
- **Multiplier (a):** 82
**Objective:** Obtain the plaintext message.
---
**8. Rabin Public-Key Encryption Scheme**
The Rabin public-key encryption scheme is comparable to RSA. Your task is to explore this cryptosystem and decrypt the following ciphertext:
**Ciphertext:**
25292168
This text was encrypted for a user with the public key \( n = 27219809 \).
---
**9. Mathematical Proof**
**Task:** Prove that \( 9 \mid u_{n+24} \) if and only if \( 9 \mid u_n \).
**Hint:** Use identity (1) on page 288.
---
**10. Fibonacci Identity**
**Task:** Establish the following Fibonacci identity:
\[ u_{n+8} \equiv u_n \pmod{3} \]
For solving these problems, you may need to revisit relevant concepts about cryptosystems, modular arithmetic, and Fibonacci sequences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2Ff298fa66-299e-4303-8008-5372a8669a7f%2F71tveqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Cryptography Concepts and Problems
**7. Merkle-Hellman Knapsack Cryptosystem**
**Ciphertext:**
261, 163, 196, 172, 217, 172, 89, 142, 76, 217, 209, 172, ?
The above ciphertext was generated using the Merkle-Hellman Knapsack cryptosystem for a user with the following components:
- **Private key sequence:** \{5, 8, 17, 36, 71\}
- **Modulus (m):** 145
- **Multiplier (a):** 82
**Objective:** Obtain the plaintext message.
---
**8. Rabin Public-Key Encryption Scheme**
The Rabin public-key encryption scheme is comparable to RSA. Your task is to explore this cryptosystem and decrypt the following ciphertext:
**Ciphertext:**
25292168
This text was encrypted for a user with the public key \( n = 27219809 \).
---
**9. Mathematical Proof**
**Task:** Prove that \( 9 \mid u_{n+24} \) if and only if \( 9 \mid u_n \).
**Hint:** Use identity (1) on page 288.
---
**10. Fibonacci Identity**
**Task:** Establish the following Fibonacci identity:
\[ u_{n+8} \equiv u_n \pmod{3} \]
For solving these problems, you may need to revisit relevant concepts about cryptosystems, modular arithmetic, and Fibonacci sequences.
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