On Yao's XOR-lemma

Authors:
Oded Goldreich;Noam Nisan;Avi Wigderson
Affiliations:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Israel;Hebrew University of Jerusalem and Google, Tel Aviv;School of Mathematics of the Institute, Princeton
Venue:
Studies in complexity and cryptography
Year:
2011

Citing 14
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Abstract

A fundamental lemma of Yao states that computational weakunpredictability of Boolean predicates is amplified when 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 original 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 (1989) and some elementary observation, we derive the XOR-Lemma.