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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
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