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LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith's Binary Matrix LWE
Binary matrix LWE Linear Programming Cryptanalysis
2018/8/16
We consider Galbraith's space efficient LWE variant, where the (m×n)(m×n)-matrix AA is binary. In this binary case, solving a vectorial subset sum problem over the integers allows for decryption. We s...
Other free sums are 1-way under plausible assumptions: elliptic curve discrete logs, integer factoring, and secure small-key Wegman--Carter--Shoup authentication. Yet other free sums of 1-way function...
A conjecture about Gauss sums and bentness of binomial Boolean functions
Boolean functions bent functions Walsh spectrum
2016/12/10
In this note, the polar decomposition of binary fields of even extension degree is used to reduce the evaluation of the Walsh transform of binomial Boolean functions to that of Gauss sums. In the case...
We present a general construction of a family of ordinal
sums of a sequence of structures and prove an elimination
theorem for the class of ordinal sums in an expanded language.
From this we deduce...
A LOCAL LIMIT THEOREM FOR SUMS OF INDEPENDENT RANDOM VECTORS
THEOREM FOR SUMS INDEPENDENT RANDOM
2015/9/29
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
A FUNCTIONAL HUNGARIAN CONSTRUCTION FOR SUMS OF INDEPENDENT RANDOM VARIABLES
Komlos-Major–Tusnády inequality Partial sum process Non-identically distributed variables Function classes Asymptotic equivalence of statistical experiments
2015/8/25
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremum over...
ON THE MODE OF AN EMPIRICAL HISTOGRAM FOR SUMS。
ON THE DIFFERENCE BETWEEN THE EMPIRICAL HISTOGRAM AND THE NORMAL CURVE, FOR SUMS: PART II
Histogram difference curve
2015/7/14
ON THE DIFFERENCE BETWEEN THE EMPIRICAL HISTOGRAM AND THE NORMAL CURVE, FOR SUMS: PART II.
ON THE MAXIMUM DIFFERENCE BETWEEN THE EMPIRICAL AND EXPECTED HISTOGRAMS FOR SUMS
N independent distributed random variables curve Sn probability histogram
2015/7/14
Suppose Sn
is a sum of n independent and identically
distributed random variables with E\Xl\
Uniform Renewal Theory with Applications to Expansions of Random Geometric Sums
Renewal theory random geometric sum corrected diffusion approximation
2015/7/6
Consider a sequence X = (Xn: n ≥ 1)of independent and identically distributed random variables, and an independent geometrically distributed random variable M with parameter p. The random variable SM ...
A new class of hyper-bent functions and Kloosterman sums
Bent function hyper-bent functions Walsh-Hadamard transform Dickson polynomial Kloosterman sums
2014/3/5
This paper is devoted to the characterization of hyper-bent functions. Several classes of hyper-bent functions have been studied, such as Charpin and Gong's $\sum\limits_{r\in R}\mathrm{Tr}_{1}^{n} (a...
Smoothing effect of Compound Poisson approximation to distribution of weighted sums
characteristic function concentration function compound Poisson distribution Kolmogorov norm weighted random variables.
2013/4/27
The accuracy of compound Poisson approximation to the sum $S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated.
Here $S_i$ are sums of independent or weakly dependent random variables, and $w_i$ denote weights...
Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
We give a congruence for L-functions coming from affine additive exponential sums over a finite field. Precisely, we give a congruence for certain operators coming from Dwork's theory. This congruence...
On Character Sums and Exponential Sums over Generalized Arithmetic Progressions
Character Sums Exponential Sums Generalized Arithmetic Progressions Number Theory
2012/6/19
We study upper bounds for sums of Dirichlet characters. We prove a uniform upper bound of the character sum over all proper generalized arithmetic progressions, which generalizes the classical Polya a...