# Cryptography: Theory and Practice

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• davidvictor
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ICS 268: Cryptography and Communication Security 10/14/2004 Homework 3 Due Thursday , 10/21/2004 1 Shank’s Discrete Logarithm Algorithm : Modification Describe how to modify Shank’s “Baby Step - Giant Step” algorithm so that to compute the discrete logarithm DL g,p ( y ) for elements y of the form y = g x mod p where x is known to lie in an interval [ s, t ] s.t. 0 s < t < q where q = ord p ( g ) is the order of element g in Z * p . We want an algorithm which runs in time O ( t - s ), or, if you want to be more exact, in time O ( t - s * | p | c ) for some small constant c . Prove that your algorithm is correct. 2 Boosting a “Non-negligible Probability” Attack Show that if there is a constant d s.t. some probabilistic polynomial time algorithm A computes the discrete logarithm DL ( g, p )( y ) = x s.t. g x = y mod p with a (non-negligible) probability A ( τ ) 1 τ d for every input y , then this algorithm can be used to obtain a different probabilistic polynomial time algorithm A 0 which computes DL for every y with probability 1 - δ

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• Fall '04
• Jarecki
• Cryptography, TA, Logarithm, Discrete logarithm, Shank

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