Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
Bartleby Related Questions Icon

Related questions

Question

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.
expand button
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.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Computer Science
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Text book image
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Text book image
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
Text book image
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Text book image
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education