The discrete Fourier transform (DFT) is a fundamental component of numerous
computational techniques in signal processing and scientific computing. The most popular …

Cryptography plays a key role in ensuring the privacy and integrity of data and the security of
computer networks. Introduction to Modern Cryptography provides a rigorous yet accessible …

We consider the sparse Fourier transform problem: given a complex vector x of length n, and
a parameter k, estimate the k largest (in magnitude) coefficients of the Fourier transform of x …

We consider the problem of computing the k-sparse approximation to the discrete Fourier
transform of an n-dimensional signal. We show: An O (k log n)-time randomized algorithm for …

We study the pseudorandomness of bounded knapsack functions over arbitrary finite
abelian groups. Previous works consider only specific families of finite abelian groups and 0 …

• We study the problem of finding a Fourier representation R of m terms for a given discrete
signal A of length N. The Fast Fourier Transform (FFT) can find the optimal N-term …

We show the following reductions from the learning with errors problem (LWE) to the
learning with rounding problem (LWR):(1) Learning the secret and (2) distinguishing …

In sparse approximation theory, the fundamental problem is to reconstruct a signal A∈ ℝ n
from linear measurements< A ψ i> with respect to a dictionary of ψ i's. Recently, there is …

In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs)
are codes that allow the recovery of each message bit from a constant number of entries of …

This paper sets new software speed records for high-security Diffie-Hellman computations,
specifically 251-bit elliptic-curve variable-base-point scalar multiplication. In one second of …