homework 3

Cryptography: Theory and Practice

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Unformatted text preview: ICS 268: Cryptography and Communication Security 10/14/2004 Homework 3 Due Thursday , 10/21/2004 1 Shanks Discrete Logarithm Algorithm : Modification Describe how to modify Shanks 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 ( ) 1 d for every input y , then this algorithm can be used to obtain a different probabilistic polynomial time algorithm...
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This homework help was uploaded on 01/30/2008 for the course ICS 268 taught by Professor Jarecki during the Fall '04 term at UC Irvine.

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homework 3 - ICS 268: Cryptography and Communication...

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