# HW3 - F such that for all a,b ∈ 1 for all public key K if...

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Homework 3 Due in Class Thursday, March 27 1 Number of Quadratic Residues Consider N = Q n i =1 p i , where each p i is a prime and for i 6 = j , p i 6 = p j . How many qudratic residues are there in Z ? N ? Why? 2 Non-Blum Integer as Modulus Can we use a modulus that is not a Blum integer in the Rabin cryptosystem? Can we use a modulus that is not a Blum integer in the Goldwasser-Micali cryptosystem? Why or why not? 3 (Optional) Malleability of Goldwasser-Micali Cryptosystem Show that there exist a non-constant function f : { 0 , 1 } × { 0 , 1 } → { 0 , 1 } and an eﬃcient (probabilistic polynomial-time) algorithm
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Unformatted text preview: F such that for all a,b ∈ { , 1 } , for all public key K , if A and B are ciphertexts of a and b under public key K , respectively, then F ( A,B ) is a ciphertext of f ( a,b ) under public key K . 4 MAC based on Encryption We construct a MAC scheme based on a good block cipher E(). Suppose the block size is ‘ . For an ‘-bit message m and an ‘-bit MAC key k , the MAC is deﬁned as the ﬁrst ‘/n bits of E k ( m ), where n is a constant. Is the above MAC scheme secure? Why or why not? 1...
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## This note was uploaded on 09/27/2010 for the course CSE 664 taught by Professor Shengzhong during the Spring '10 term at SUNY Buffalo.

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