Solutions_HW4_547 (1)

Thus applying the else we will nally nd k such that k

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Unformatted text preview: t T . Then by applying the “else” in the while loop, at most T − 1 times, we will find K such that g (K ) = y . If we look at the cycle of which y is a member, K is the node that precede y in such loop. • Suppose, on the other hand, that y is a member of a cycle with length greater than T . In this case we know there exists a zj such that the Fall 2010 Comp 547: Cryptography and Data Security 6 distance between y and zj is at most T . That is, once we found that zj , by going backwards of T steps from zj (using g −T (zj )) we will find our self on a node that precedes y in the cycle. Thus, applying the “else” we will finally find K such that (K, y ) is an edge of G. Suppose it will take m < T steps to find such zj (that is applyin...
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