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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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Patent
18 Apr 2006
TL;DR: In this article, the problem of reducing the cost of arithmetic operation and square, while avoiding inverse element operations, in a group operation of elements of a finite commutative group formed of points on an algebraic curve defined on a finite field is addressed.
Abstract: PROBLEM TO BE SOLVED: To reduce the cost of arithmetic operation and square, while avoiding inverse element operations, in a group operation of elements of a finite commutative group formed of points on an algebraic curve defined on a finite field. SOLUTION: A finite commutative group operation device includes a pseudo-inverse element operating means for calculating a pseudo-inverse element v(p), satisfying N(p)=v(p)×p [where N(p) is an element of a subfield of GF(q m ), v(p) is an element of GF(q m )] with respect to the element p of a finite field GF(q m ) [q is a prime number or a power of the prime number, m is an integer of m>1]; and a complement pseudo-inverse element operating means for calculating a complement pseudo-inverse element N(p). In the finite commutative group operation, a group operation of elements of a finite commutative group formed of points on an algebraic curve defined on GF(q m ) is performed, while avoiding an inverse element operation of a divisor in a group operation, by independently calculating a divisor and a dividend that appear in a division on GF(q m ) and associating the divisor with an expanded coordinate. The pseudo inverse element operating means calculates a pseudo-inverse element, the complement pseudo inverse element operating means calculates a complement pseudo-inverse element, the pseudo inverse element is included in a dividend, and the complement pseudo-inverse element is set as a divisor. COPYRIGHT: (C)2008,JPO&INPIT

2 citations

Patent
06 Mar 2008
TL;DR: In this paper, a carry bit from a previous iteration of the main loop determines which of the divisor or the negative value of the negative to use in the current iteration.
Abstract: In the course of performing an Elliptic Curve Scalar Multiplication operation by Additive Splitting Using Division, a main loop of an integer division operation may be performed. The integer division has a dividend and a divisor. By storing both the divisor and the negative value of the divisor, susceptibility to a Simple Power Analysis Side Channel attack is minimized. A carry bit from a previous iteration of the main loop determines which of the divisor or the negative of the divisor to use. The order of an addition operation and a shift left operations in the main loop is interchanged compared to a known integer division method and there are no negation operations in the main loop.

2 citations

Patent
24 Apr 1990
TL;DR: In this article, the upper five bits of a divisor and the upper six bits of the partial remainder of a partial remainder at present are decided by the relation of the divisors and the partial rest at present.
Abstract: PURPOSE: To save time by deciding the upper five bits of a divisor and the upper six bits of a partial remainder at present and deciding the selection of the redundant pair of quotient bits by the relation of the divisor and the partial remainder at present. CONSTITUTION: The divisor D is loaded into a register 5 and the initial partial remainder of division is loaded into the register 10. The register 10 stores the succeeding partial remainder in a redundant form of the carry output and the sum output of a carry preservation adder. However, a divided is loaded into the register 10 in a non-redundant form. The correct quotient bit generated by respective radixes -4 division is decided and selection logic is executed. The quotient bit of radix 4 division is selected from -2-+2 and the quotient bit for the next partial remainder is selected by using the divisor of five bits and the partial remainder of six bits. The addition of a negative quotient and a positive quotient is performed 'during a flight' and a complete quotient is identified. Thus, additional time is saved.

2 citations

Journal Article
TL;DR: In this paper, the Dirichlet's convolution is defined as a mapping of the set Z+ of positive integers into the power set P(Z+) such that every member of C(n) is a divisor of n. Corresponding to any general convolution C, one can define a binary relation ≤C on Z+ by "m ≤C n if and only if m ∈ C n".
Abstract: A Convolution C is a mapping of the set Z+ of positive integers into the power set P(Z+) such that every member of C(n) is a divisor of n. If for any n, D(n) is the set of all positive divisors of n , then D is called the Dirichlet’s convolution. It is well known that Z+ has the structure of a distributive lattice with respect to the division order. Corresponding to any general convolution C, one can define a binary relation ≤C on Z+ by ‘ m ≤C n if and only if m ∈ C(n)’ . In this paper we characterize Convolutions C which induce partial orders with respect to which Z+ has the structure of a semi lattice or lattice and various lattice theoretic properties are discussed in terms of convolution.

2 citations

Posted Content
TL;DR: In this article, the authors define arithmetical and dynamical degrees for dynamical systems with rational self-maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial relations in the Neron-Severi Group.
Abstract: We define arithmetical and dynamical degrees for dynamical systems with several rational maps on projective varieties, study their properties and relations, and prove the existence of a canonical height function associated with divisorial relations in the Neron-Severi Group over Global fields of characteristic zero, when the rational maps are morphisms. For such, we show that for any Weil height $h_X$ with respect to an ample divisor on a projective variety $X$, any dynamical system $\mathcal{F}$ of rational self-maps on $X$, and any $\epsilon>0$, there is a positive constant $C=C(X, h_X, f, \epsilon)$ such that $\sum_{f \in \mathcal{F}_n} h^+_X(f(P)) \leq C. k^n.(\delta_{\mathcal{F}} + \epsilon)^n . h^+_X(P)$ for all points $P$ whose $\mathcal{F}$-orbit is well defined.

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140