# A Classical Introduction to Cryptography Exercise BookConventional Cryptography

A Classical Introduction to Cryptography Exercise Book: Conventional Cryptography Chapter 2 Exercises Exercise 1 Weak Keys of DES We say that a DES key k is weak if DESk is an involution. Exhibit four weak keys for DES. Reminder: Let S be a finite set and let f be a bijection from S to S. The function f is an involution if f (f (x)) = x for all x E S. D Solution on page 34 Exercise 2 Semi-weak Keys of DES We say that a DES key k is semi-weak if it is not weak and if there exists a key k' such that DES,' = DESp. Exhibit four semi-weak keys for DES. D Solution on page 34 Exercise 3 Complementation Property of DES Given a bitstring x we let F denote the bitwise complement, i.e., the bitstring obtained by flipping all bits of x. EXERCISE BOOK 1 Prove that DESK(:) = DESK(x) for any x and K 2 Deduce a brute force attack against DES with average complexity of 254 DES encryptions. Hint: Assume that the adversary who is looking for K is given a plaintext block x and the two values corresponding to DESK(x) and DESK(:). D Solution on page 35 Exercise 4 3DES http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Classical Introduction to Cryptography Exercise BookConventional Cryptography

39 pages      /lp/springer-journals/a-classical-introduction-to-cryptography-exercise-book-conventional-WCWjXwyLz5
Publisher
Springer US
ISBN
978-0-387-27934-3
Pages
17 –56
DOI
10.1007/0-387-28835-X_2
Publisher site
See Chapter on Publisher Site

### Abstract

Chapter 2 Exercises Exercise 1 Weak Keys of DES We say that a DES key k is weak if DESk is an involution. Exhibit four weak keys for DES. Reminder: Let S be a finite set and let f be a bijection from S to S. The function f is an involution if f (f (x)) = x for all x E S. D Solution on page 34 Exercise 2 Semi-weak Keys of DES We say that a DES key k is semi-weak if it is not weak and if there exists a key k' such that DES,' = DESp. Exhibit four semi-weak keys for DES. D Solution on page 34 Exercise 3 Complementation Property of DES Given a bitstring x we let F denote the bitwise complement, i.e., the bitstring obtained by flipping all bits of x. EXERCISE BOOK 1 Prove that DESK(:) = DESK(x) for any x and K 2 Deduce a brute force attack against DES with average complexity of 254 DES encryptions. Hint: Assume that the adversary who is looking for K is given a plaintext block x and the two values corresponding to DESK(x) and DESK(:). D Solution on page 35 Exercise 4 3DES

Published: Jan 1, 2006

Keywords: Exhaustive Search; Block Cipher; Average Complexity; Brute Force Attack; Exercise Book