7. The following ciphertext 261 163 196 172 217 172 89 142 76 217 209 172 ? was produced using the Merkle-Hellman Knapsack cryptosystem for a user with a private key that consists of the sequence {5, 8,17, 36, 71}, modulus m = message. 145, and multiplier a = 82. Obtain the plaintext 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. 9. Prove that 9 u,424 if and only if 9 u,n. Hint: Use identity (1) on page 288. 10. Establish the following Fibonacci identity:
7. The following ciphertext 261 163 196 172 217 172 89 142 76 217 209 172 ? was produced using the Merkle-Hellman Knapsack cryptosystem for a user with a private key that consists of the sequence {5, 8,17, 36, 71}, modulus m = message. 145, and multiplier a = 82. Obtain the plaintext 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. 9. Prove that 9 u,424 if and only if 9 u,n. Hint: Use identity (1) on page 288. 10. Establish the following Fibonacci identity:
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 7
![**Exercise 7: Decoding Ciphertext**
The following ciphertext:
```
261 163 196 172 217 172 89 142 76 217 209 172 ?
```
was produced using the Merkle-Hellman Knapsack cryptosystem for a user with a private key consisting of the sequence `{5, 8, 17, 36, 71}`, modulus `m = 145`, and multiplier `a = 82`. Your task is to obtain the plaintext message.
**Exercise 8: Rabin Public-Key Encryption Scheme**
The Rabin public-key encryption scheme is similar to RSA. Research this cryptosystem and decrypt the following ciphertext:
```
25292168
```
This ciphertext was encrypted for a user with public key `n = 27219809`.
**Exercise 9: Mathematical Proof**
Prove that `9 | u_{n+24}` if and only if `9 | u_n`.
*Hint:* Use identity (1) on page 288.
**Exercise 10: Fibonacci Identity**
Establish the following Fibonacci identity:
\[ u_{n+8} \equiv u_n \, (\text{mod} \, 3) \]
**Exercise 11: Fibonacci and Lucas Numbers**
Establish the following relation between Fibonacci and Lucas numbers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2F7c93566b-e046-42b7-a16a-5bd2c578b869%2Fxgsybo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 7: Decoding Ciphertext**
The following ciphertext:
```
261 163 196 172 217 172 89 142 76 217 209 172 ?
```
was produced using the Merkle-Hellman Knapsack cryptosystem for a user with a private key consisting of the sequence `{5, 8, 17, 36, 71}`, modulus `m = 145`, and multiplier `a = 82`. Your task is to obtain the plaintext message.
**Exercise 8: Rabin Public-Key Encryption Scheme**
The Rabin public-key encryption scheme is similar to RSA. Research this cryptosystem and decrypt the following ciphertext:
```
25292168
```
This ciphertext was encrypted for a user with public key `n = 27219809`.
**Exercise 9: Mathematical Proof**
Prove that `9 | u_{n+24}` if and only if `9 | u_n`.
*Hint:* Use identity (1) on page 288.
**Exercise 10: Fibonacci Identity**
Establish the following Fibonacci identity:
\[ u_{n+8} \equiv u_n \, (\text{mod} \, 3) \]
**Exercise 11: Fibonacci and Lucas Numbers**
Establish the following relation between Fibonacci and Lucas numbers.
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