相关论文: Finding low-weight polynomial multiples using disc…
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining…
We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
Let ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this paper is…
The recently developed dynamic discretization discovery (DDD) is a powerful method that allows many time-dependent problems to become more tractable. While DDD has been applied to a variety of problems, one particular challenge has been to…
Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire)…
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
We consider message-efficient continuous random sampling from a distributed stream, where the probability of inclusion of an item in the sample is proportional to a weight associated with the item. The unweighted version, where all weights…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…