# Cryptography: Theory and Practice

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• davidvictor
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ICS 268: Cryptography and Communication Security 10/28/2004 Homework 4 Due Tuesday , 11/09/2004 1 Hash Function Properties 1.1 Explain why the modular exponentiation function, Exp : { 0 , 1 } Z p where Exp ( x ) = g x mod p for a large prime p and g generator of Z p , is a preimage resistant hash function under the discrete logarithm assumption. 1.2 Assuming g is a generator of Z p , under the same discrete logarithm assumption, is function Exp : { 0 , 1 } → { 0 , 1 } n where Exp ( x ) = ( Exp ( x )) mod 2 n where n = | p | - 1, still a preimage resistant hash function? 1.3 Show that modular exponentiation function Exp defined as above is not second preimage resistant and also not collision resistant . 2 Authentication Scheme From A Hash Function Recall from lecture that a symmetric authentication scheme consists of an PPT algorithm KeyGen , which given a security parameter τ generates a symmetric key k which is then given to both the Client and the Server, and an interactive protocol Auth in which the Server authenticates the Client as long as both run this protocol on input k . Recall that we call

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• Fall '04
• Jarecki
• Cryptography, hash function, Cryptographic hash function, authentication scheme, symmetric authentication scheme

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