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Chapter and Conference Paper
On Public Key Encryption from Noisy Codewords
Several well-known public key encryption schemes, including those of Alekhnovich (FOCS 2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan (STOC 2008), rely on the conjectured intractability of in...
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Chapter and Conference Paper
Sampling-Based Proofs of Almost-Periodicity Results and Algorithmic Applications
We give new and simple combinatorial proofs of almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask [7], whose almost-periodicity lemma has had far-reaching implica...
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Chapter and Conference Paper
Absolutely Sound Testing of Lifted Codes
In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of “affine-invariant” codes. Affine-invariant codes are codes whose coordinates are associ...
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Chapter and Conference Paper
A New Upper Bound on the Query Complexity for Testing Generalized Reed-Muller codes
Over a finite field \({\mathbb{F}}_q\) the (n,d,q)-Reed-Muller code is the code given by evaluations of n-variate polyn...