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Chapter 4 Exercises Exercise 1 The SAFER Permutation Prove that x H (45x mod 257) mod 256 is a permutation over (0, . . . ,255). D Solution on page 97 Exercise 2 *Linear Cryptanalysis Let m be an integer such that 2m + 1 is a prime number. Let g be a generator of Z;m+l and let E be defined over Z2m by E(x) = (gx mod (2m + 1)) mod 2m. Prove that Pr[E(X) E X (mod 2)] = when X is uniformly dis- tributed. D Solution on page 97 82 EXERCISE BOOK Exercise 3 *Differential and Linear Probabilities We consider a block cipher using the following function f as a building block 1 Compute Dpf (6116,0), where 6 = 0x80000000, where 11 denotes the concatenation operation and (6116) (x, y) = 6 . x @ 6 y. 2 Compute DP~ (6116,0), where 6 = OxC0000000. 3 Compute LP~ (6116, S), where 6 = 0x00000001. 4 Compute Lpf (6116, 6), where 6 = 0x00000003. Reminder: The differential and linear probabilities of a function f are defined by Dpf(a,b) = Pr[f(X$a) = f(X)$b] and LP~ (a, b) (2 Pr[a X = b f (X)] - I)~, where X
Published: Jan 1, 2006
Keywords: Random Permutation; Block Cipher; Decryption Algorithm; Reference Paper; Active Word
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