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Chapter 3 DEDICATED CONVENTIONAL CRYPTOGRAPHIC PRIMITIVES Exercises Exercise 1 Collisions in CBC Mode We consider the encryption of an n-block message x = xlll. . . llx, by a block cipher E in CBC mode. We denote by y = ylll . 11 yn the n-block ciphertext produced by the CBC encryption mode. 1 Show that one can extract information about the plaintext if we get a collision, i.e., if yi = yj with i # j. 2 What is the probability of getting a collision when the block size of E is 64 bits? 3 For which n does this attack become useful? D Solution on page 66 Exercise 2 Collisions We iteratively pick random elements in {1,2,. . . , n) in an independent and uniformly distributed way until we obtain a collision. Denoting T the random variable corresponding to the number of trials, show that EXERCISE BOOK Hint: Letting it can be shown that XPne-n - 1. n--too 2 D Solution on page 66 Exercise 3 Expected Number of Collisions We let F : {1,2,. . . , m) 4 {1,2,. . . ,n) be a uniformly distributed random function. 1 Let N2 be the number
Published: Jan 1, 2006
Keywords: Hash Function; Success Probability; Block Cipher; Compression Function; Random Oracle Model
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