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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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