On Yao's XOR-Lemma
Oded Goldreich, Noam Nisan and Avi Wigderson
Abstract: A fundamental Lemma of Yao states that computational weak-unpredictability of functions gets amplified if the results of several independent instances are XOR together. We survey two known proofs of Yao's Lemma and present a third alternative proof. The third proof proceeds by first proving that a function constructed by concatenating the values of the function on several independent instances is much more unpredictable, with respect to specified complexity bounds, than the original function. This statement turns out to be easier to prove than the XOR-Lemma. Using a result of Goldreich and Levin and some elementary observation, we derive the XOR-Lemma.
Keywords: One-Way Functions, Hard-Core Predicates, Direct-Sum Conjectures.
comment: received May 10th, 1996. Written in March 1995. Appears as report 95-050 of ECCC.
contact author: oded@theory.lcs.mit.edu
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