"We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consist

Menachem Kojman
Ben Gurion University of the Negev; Member, School of Mathemtics
April 6, 2011

MATHEMATICAL CONVERSATIONS

"We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consistency." -- Andre Weil

General Hardness Amplification of Predicates and Puzzles

Grant Schoenbeck
Princeton University
March 29, 2011

In this talk, I will give new proofs for the hardness amplification of fficiently samplable predicates and of weakly verifiable puzzles. More oncretely, in the first part of the talk, I will give a new proof of Yao's XOR-Lemma as well as related theorems in the cryptographic setting. This proof seems simpler than previous ones, yet immediately generalizes to statements similar in spirit such as the extraction lemma used to obtain pseudo-random generators from one-way functions [Hastad, Impagliazzo, Levin, Luby, SIAM J. on Comp. 1999].