Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In 2019, Gu Chunsheng introduced Integer-RLWE, a variant of RLWE devoid of some of its efficiency flaws as discussed by the authors, where n can be an arbitrary positive integer.
Abstract: In 2019, Gu Chunsheng introduced Integer-RLWE, a variant of RLWE devoid of some of its efficiency flaws. Most notably, he proposes a setting where n can be an arbitrary positive integer, contrarily to the typical construction \(n = 2^k\). In this paper, we analyze the new problem and implement the classical meet-in-the-middle and lattice-based attacks. We then use the peculiarity of the construction of n to build an improved lattice-based attack in cases where n is composite with an odd divisor. For example, for parameters \(n = 2000\) and \(q = 2^{33}\), we reduce the estimated complexity of the attack from \(2^{288}\) to \(2^{164}\). We also present reproducible experiments confirming our theoretical results.
TL;DR: A prime divisor of a composite Fermat number is called a Fermat prime, and such a prime must be congruent to 1 modulo 4, and so, by the Fermat-Girard theorem, there exists integers R and S such divisors as discussed by the authors.
Abstract: A prime dividing a composite Fermat number is called a Fermat prime divisor. Such a prime p must be congruent to 1 modulo 4, and so, by the Fermat–Girard theorem, there exists integers R and S such...
Patent•
16 Jan 2012
TL;DR: In this paper, a method for applying to the recurrence cells of a divider circuit to divide a fixed-point dividend by a fixed point divisor is described, and a set of instructions for implementing said method in a programmable medium, and/or configuring said or other programmable means is also provided.
Abstract: The present invention relates to a method for applying to the recurrence cells of a divider circuit to divide a fixed-point dividend by a fixed-point divisor. In addition, said recurrence cells and a divider circuit are provided, which divide into a base r = 2k, generating k bits in each iteration. The divisor divides a dividend x of n bits by a divisor y of m bits greater than zero, returning a quotient q of n bits and a remainder r of m bits. The present invention makes the division faster, preferably using an efficient carry propagation for addition and subtraction. The divider circuit can be easily modified in order to return more fractional bits in the quotient q. Two architectures, named for the digit recursion cell, are described. The first is for a general hardware implementation and the second is optimized for programmable logic. A set of instructions for implementing said method in a programmable medium, and/or configuring said or other programmable means is also provided. (Machine-translation by Google Translate, not legally binding)
Posted Content•
TL;DR: In this article, the authors obtain sufficient and necessary conditions for a positive divisor on a projective algebraic variety to be attracting for a holomorphic map on a line bundle.
Abstract: We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor $D$ on a projective algebraic variety $X$ to be attracting for a holomorphic map $f:X \mapsto X$.
01 Jan 2016
TL;DR: In this article, the conditional probability that an integer with exactly k prime factors has a divisor in a dyadic interval was shown to approach 0 as y → ∞ if 2(1+k logy)k log y.
Abstract: In support of a still little known, general principle according to which the structure of the set of prime factors of an integer is statistically governed by its actual cardinal, we show that, given any ɛ > 0, the conditional probability that an integer with exactly k prime factors has a divisor in a dyadic interval ]y, 2y] approaches 0 as y → ∞ if 2(1+ɛ)k logy.