[کتاب][B] Introduction to property testing

O Goldreich - 2017‏ - books.google.com
Property testing is concerned with the design of super-fast algorithms for the structural
analysis of large quantities of data. The aim is to unveil global features of the data, such as …

An inverse theorem for the Gowers U s+1 [N]-norm

B Green, T Tao, T Ziegler - Annals of Mathematics, 2012‏ - JSTOR
We prove the inverse conjecture for the Gowers U s+ 1 N-norm for all s≥ 1; this is new for
s≥ 4. More precisely, we establish that if f: N→− 1, 1 is a function with …

Batch codes and their applications

Y Ishai, E Kushilevitz, R Ostrovsky… - Proceedings of the thirty …, 2004‏ - dl.acm.org
A batch code encodes a string x into an m-tuple of strings, called buckets, such that each
batch of k bits from x can be decoded by reading at most one (more generally, t) bits from …

Cube testers and key recovery attacks on reduced-round MD6 and Trivium

JP Aumasson, I Dinur, W Meier, A Shamir - International Workshop on Fast …, 2009‏ - Springer
CRYPTO 2008 saw the introduction of the hash function MD6 and of cube attacks, a type of
algebraic attack applicable to cryptographic functions having a low-degree algebraic normal …

Locally testable codes and PCPs of almost-linear length

O Goldreich, M Sudan - Journal of the ACM (JACM), 2006‏ - dl.acm.org
We initiate a systematic study of locally testable codes; that is, error-correcting codes that
admit very efficient membership tests. Specifically, these are codes accompanied with tests …

Sublinear time algorithms

R Rubinfeld, A Shapira - SIAM Journal on Discrete Mathematics, 2011‏ - SIAM
Sublinear Time Algorithms Page 1 Copyright © by SIAM. Unauthorized reproduction of this article
is prohibited. SIAM J. DISCRETE MATH. c 2011 Society for Industrial and Applied Mathematics …

[HTML][HTML] Finite field models in arithmetic combinatorics–ten years on

J Wolf - Finite Fields and Their Applications, 2015‏ - Elsevier
It has been close to ten years since the publication of Green's influential survey Finite field
models in additive combinatorics [28], in which the author championed the use of high …

Algebraic property testing: the role of invariance

T Kaufman, M Sudan - Proceedings of the fortieth annual ACM …, 2008‏ - dl.acm.org
We argue that the symmetries of a property being tested play a central role in property
testing. We support this assertion in the context of algebraic functions, by examining …

Improving key recovery to 784 and 799 rounds of Trivium using optimized cube attacks

PA Fouque, T Vannet - International Workshop on Fast Software …, 2013‏ - Springer
Dinur and Shamir have described cube attacks at EUROCRYPT'09 and they have shown
how efficient they are on the stream cipher Trivium up to 767 rounds. These attacks have …

The distribution of polynomials over finite fields, with applications to the Gowers norms

B Green, T Tao - arxiv preprint arxiv:0711.3191, 2007‏ - arxiv.org
In this paper we investigate the uniform distribution properties of polynomials in many
variables and bounded degree over a fixed finite field F of prime order. Our main result is …