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Electronic Colloquium on Computational Complexity

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Reports tagged with affine:
TR10-064 | 13th April 2010
Xin Li

A New Approach to Affine Extractors and Dispersers

We study the problem of constructing affine extractors over $\mathsf{GF(2)}$. Previously the only known construction that can handle sources with arbitrarily linear entropy is due to Bourgain (and a slight modification by Yehudayoff), which relies heavily on the technique of Van der Corput differencing and a careful choice of a ... more >>>

TR10-190 | 9th December 2010
Xin Li

Improved Constructions of Three Source Extractors

We study the problem of constructing extractors for independent weak random sources. The probabilistic method shows that there exists an extractor for two independent weak random sources on $n$ bits with only logarithmic min-entropy. However, previously the best known explicit two source extractor only achieves min-entropy $0.499n$ \cite{Bourgain05}, and the ... more >>>

TR16-180 | 15th November 2016
Eshan Chattopadhyay, Xin Li

Non-Malleable Codes and Extractors for Small-Depth Circuits, and Affine Functions

Non-malleable codes were introduced by Dziembowski, Pietrzak and Wichs as an elegant relaxation of error correcting codes, where the motivation is to handle more general forms of tampering while still providing meaningful guarantees. This has led to many elegant constructions and applications in cryptography. However, most works so far only ... more >>>

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