11/15/2004 CSC 486 : Hem-Ogi 2.1 Proof : only if direction of Theorem 2.16 only if  By proposition 2.17, we have P  NP, One-way functions exist, 2-ary one-way functions exist  To prove the goal that One-way functions exist ) strongly noninvertible, total, commutative, associative, 2-ary one-way functions exist, we can equivalently show P  NP ) strongly noninvertible, total, commutative, associative, 2-ary one-way functions exist
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