Key-recovery attacks on ASASA
The ASASA ASASA construction is a new design scheme introduced at Asiacrypt 2014 by
Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public …
Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public …
Bias vs structure of polynomials in large fields, and applications in information theory
A Bhowmick, S Lovett - arXiv preprint arXiv:1506.02047, 2015 - arxiv.org
Let $ f $ be a polynomial of degree $ d $ in $ n $ variables over a finite field $\mathbb {F} $.
The polynomial is said to be unbiased if the distribution of $ f (x) $ for a uniform input …
The polynomial is said to be unbiased if the distribution of $ f (x) $ for a uniform input …
Higher-order Fourier analysis and applications
Fourier analysis has been extremely useful in many areas of mathematics. In the last several
decades, it has been used extensively in theoretical computer science. Higher-order Fourier …
decades, it has been used extensively in theoretical computer science. Higher-order Fourier …
Cubic Goldreich-Levin
D Kim, A Li, J Tidor - Proceedings of the 2023 Annual ACM-SIAM …, 2023 - SIAM
In this paper, we give a cubic Goldreich-Levin algorithm which makes polynomially-many
queries to a function f: 𝔽 np→ ℂ and produces a decomposition of f as a sum of cubic …
queries to a function f: 𝔽 np→ ℂ and produces a decomposition of f as a sum of cubic …
Polynomial decompositions in polynomial time
A Bhattacharyya - European Symposium on Algorithms, 2014 - Springer
Fix a prime p. Given a positive integer k, a vector of positive integers Δ=(Δ 1, Δ 2,…, Δ k) and
a function Γ:F_p^k→F_p, we say that a function P:F_p^n→F_p is (k, Δ, Γ)-structured if there …
a function Γ:F_p^k→F_p, we say that a function P:F_p^n→F_p is (k, Δ, Γ)-structured if there …
Using higher-order Fourier analysis over general fields
A Bhattacharyya, A Bhowmick - arXiv preprint arXiv:1505.00619, 2015 - arxiv.org
Higher-order Fourier analysis, developed over prime fields, has been recently used in
different areas of computer science, including list decoding, algorithmic decomposition and …
different areas of computer science, including list decoding, algorithmic decomposition and …
Bias vs structure of polynomials in large fields, and applications in information theory
A Bhowmick, S Lovett - IEEE Transactions on Information …, 2022 - ieeexplore.ieee.org
Let be a polynomial of degree in variables over a finite field. The polynomial is said to be
unbiased if the distribution of for a uniform input is close to the uniform distribution over, and …
unbiased if the distribution of for a uniform input is close to the uniform distribution over, and …
Guest column: On testing affine-invariant properties over finite fields
A Bhattacharyya - ACM SIGACT News, 2013 - dl.acm.org
An affine-invariant property over a finite field is a property of functions over Fn/p that is
closed under all affine transformations of the domain. This class of properties includes such …
closed under all affine transformations of the domain. This class of properties includes such …
On Hitting-Set Generators for Polynomials that Vanish Rarely
The problem of constructing pseudorandom generators for polynomials of low degree is
fundamental in complexity theory and has numerous well-known applications. We study the …
fundamental in complexity theory and has numerous well-known applications. We study the …
On hitting-set generators for polynomials that vanish rarely
The problem of constructing hitting-set generators for polynomials of low degree is
fundamental in complexity theory and has numerous well-known applications. We study the …
fundamental in complexity theory and has numerous well-known applications. We study the …