Filters








1,742,261 Hits in 8.9 sec

On a generalization of addition chains: Addition–multiplication chains

Hatem M. Bahig
2008 Discrete Mathematics  
We show that some notations and facts on addition chains can be generalized to addition-multiplication chains.  ...  In other words, we show that addition-multiplication chains resemble addition chains in many aspects.  ...  The aim of this paper is to show that some facts on addition chains can be generalized to addition-multiplication chains. The paper is organized as follows.  ... 
doi:10.1016/j.disc.2007.04.015 fatcat:zh7mguaisvdd3eiozfpmnq4onm

Addition Chains Meet Postage Stamps: Reducing the Number of Multiplications [article]

Jukka Kohonen, Jukka Corander
2014 arXiv   pre-print
We introduce stamp chains. A stamp chain is a finite integer sequence that is both an addition chain and an additive 2-basis, i.e., a solution to the postage stamp problem.  ...  We provide a simple method for converting known postage stamp solutions of length k into stamp chains of length k+1. Using stamp chains, we construct an algorithm that computes u(x^i) for i=1,...  ...  An extremal stamp chain (of length k) is one that attains this maximum. Example 1. A 5 = {1, 2, 4, 8, 16} is an addition chain, and in fact a minimallength addition chain ending at 16.  ... 
arXiv:1310.7090v2 fatcat:zhtznp32uvd5tdmdzkfintrame

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains [article]

Loïc Hervé
2015 arXiv   pre-print
We develop a general approach based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including a linear autoregressive model.  ...  We study properties of the Laplace transforms of non-negative additive functionals of Markov chains.  ...  We namely state general conditions ensuring the multiplicative ergodicity of an additive functional of a geometrically ergodic Markov chain.  ... 
arXiv:1506.07659v3 fatcat:gjqmfytrsbh6xkxleu62iwqsxa

EFFICIENT GENERATION OF SHORTEST ADDITION-MULTIPLICATION CHAINS

Hatem Bahig, A. Mahran
2018 Journal of the Egyptian Mathematical Society  
The aim of this paper is to generalize some results on addition chains to addition-multiplication chains. The paper concerns with generating shortest addition-multiplication chains.  ...  It first presents two methods for generating short addition-multiplication chains. Second, it presents an algorithm for generating a shortest addition-multiplication chain.  ...  For examples: Generating Shortest Addition-Multiplication Chains This section contains two subsections.  ... 
doi:10.21608/joems.2018.2691.1052 fatcat:wccvvumq4nconeoptebvqujz5a

Multiple constant multiplication by time-multiplexed mapping of addition chains

Peter Tummeltshammer, James C. Hoe, Markus Püschel
2004 Proceedings of the 41st annual conference on Design automation - DAC '04  
We propose a novel implementation of this circuit based on combining the addition chains of the constituent constants.  ...  We compare the area and latency efficiency of this addition chain based approach against a straightforward approach based on a constant table and a full multiplier.  ...  Tummeltshammer was supported through the University of Technology, Vienna, Austria by a fellowship for short-term scientific research abroad.  ... 
doi:10.1145/996566.996787 dblp:conf/dac/TummeltshammerHP04 fatcat:y46trq35afccvfsjfqqqtdxhhy

On Geometric Ergodicity of Additive and Multiplicative Transformation Based Markov Chain Monte Carlo in High Dimensions [article]

Kushal Kumar Dey, Sourabh Bhattacharya
2017 arXiv   pre-print
transformations of a one-dimensional random variable drawn from any arbitrary distribution defined on a relevant support.  ...  Two significant transformations associated with TMCMC are additive and multiplicative transformations. Combinations of additive and multiplicative transformations are also of much interest.  ...  Acknowledgment We are sincerely grateful to three anonymous reviewers whose comments led to a much improved version of our manuscript.  ... 
arXiv:1312.0915v4 fatcat:a5zxel3wajanvdtsj5digqkyau

Error detection in addition chain based ECC Point Multiplication

S. Pontarelli, G.C. Cardarilli, M. Re, A. Salsano
2009 2009 15th IEEE International On-Line Testing Symposium  
The paper takes into account the algorithm for elliptic Curve Point Multiplication based on a sequence of additions called "addition chain" and shows how suitable modifications of the algorithms used for  ...  One of the mode used to break the security of cryptosystem is the injection of a fault in the hardware realizing the cryptographic algorithm.  ...  POINT MULTIPLICATION BY MEANS OF EUCLIDEAN ADDITION CHAIN One of the methods proposed to compute the multiplication presented in equation (3) is based on the Euclidean Addition Chain [7] .  ... 
doi:10.1109/iolts.2009.5196010 dblp:conf/iolts/PontarelliCRS09 fatcat:ih77iwx7tjd6zo4zcka3llqyq4

Generalized Additive Model Multiple Imputation by Chained Equations With Package ImputeRobust

Daniel Salfran, Martin Spiess
2018 The R Journal  
We present a package for robust multiple imputation (the ImputeRobust package) that allows the use of generalized additive models for location, scale, and shape in the context of chained equations.  ...  The paper describes the basics of the imputation technique which builds on a semi-parametric regression model (GAMLSS) and the algorithms and functions provided with the corresponding package.  ...  Robust imputation with gamlss and mice The imputation method realized by the package ImputeRobust is based on a generalized additive model for location, scale and shape of the variable to be imputed.  ... 
doi:10.32614/rj-2018-014 fatcat:3zriu5o5s5b7bok5rp6qn6k4ai

Euclidean addition chains scalar multiplication on curves with efficient endomorphism

Yssouf Dosso, Fabien Herbaut, Nicolas Méloni, Pascal Véron
2018 Journal of Cryptographic Engineering  
Euclidean addition chains scalar multiplication on curves with efficient endomorphism.  ...  In order to do so we generalize results from [21] on the relation of random Euclidean chains generation and elliptic curve point distribution obtained from those chains.  ...  To obtain a proven security of n bits, that is to say to be able to guarantee that one can generate 2 n different chains computing 2 n different points, one can work with chains of length n but has to  ... 
doi:10.1007/s13389-018-0190-0 fatcat:g4eobbjb7rd3dnnxzz6dyn27rm

Effect of improved multiplication efficiency on exponentiation algorithms derived from addition chains

D. P. McCarthy
1986 Mathematics of Computation  
The interaction between the efficiency of the basic multiplication algorithm and the addition chain used to compute x" is studied.  ...  We conclude that either repeated multiplication by x or repeated squaring should be used and the provenance of each technique is established.  ...  Next we look at some exponentiation algorithms based on addition chains, (a) Repeated Multiplication by x. (c) Factor Chain.  ... 
doi:10.1090/s0025-5718-1986-0829630-0 fatcat:ppjp34bhtjb2dpmjkthvnkxppa

Effect of Improved Multiplication Efficiency on Exponentiation Algorithms Derived from Addition Chains

D. P. McCarthy
1986 Mathematics of Computation  
The interaction between the efficiency of the basic multiplication algorithm and the addition chain used to compute x" is studied.  ...  We conclude that either repeated multiplication by x or repeated squaring should be used and the provenance of each technique is established.  ...  Next we look at some exponentiation algorithms based on addition chains, (a) Repeated Multiplication by x. (c) Factor Chain.  ... 
doi:10.2307/2007998 fatcat:hamml6gsrfgofej6jvvougx7oq

Random Euclidean Addition Chain Generation and Its Application to Point Multiplication [chapter]

Fabien Herbaut, Pierre-Yvan Liardet, Nicolas Méloni, Yannick Téglia, Pascal Véron
2010 Lecture Notes in Computer Science  
In this paper, we use a similar approach. We propose to modify the key generation process using a small Euclidean addition chain c instead of a scalar k.  ...  We propose two different ways to generate short Euclidean addition chains and give a first theoretical analysis of the size and distribution of the obtained keys.  ...  This section is dedicated to a specific scalar multiplication algorithm based on Euclidean addition chains. Euclidean Addition Chains Definition 1.  ... 
doi:10.1007/978-3-642-17401-8_18 fatcat:6bj6dwcl5zhnpmgq3eb7lf47u4

Multiplicative ergodicity of laplace transforms for additive functional of markov chains with application to age-dependent branching process [article]

Loïc Hervé, Françoise Pène
2017 arXiv   pre-print
Our approach is related to the behaviour of the Laplace transform of nonnegative additive functional of Markov chains and require weak moment assumption (no exponential moment is needed).  ...  We suppose here that the lifetimes of the cells are dependent random variables, that the numbers of new cells are random and dependent.  ...  For this, we study this multiplicative ergodicity property in the context of additive functional of Markov chains with Markov kernel P and initial law µ.  ... 
arXiv:1701.00718v1 fatcat:o76o3ajvnbaoxcacqro5eag4wu

A New Method of Generating Optimal Addition Chain Based on Graph

K. Mani, M. Viswambari
2017 International Journal of Mathematical Sciences and Computing  
the move from one number to another number in the addition chain.  ...  The problem of determining correct sequence of multiplications requires in performing modular exponentiation can be elegantly formulated using the concept of addition chains.  ...  The method generates an algorithm which provides the multiplication logic using a multiplication circuit. Daniel J.  ... 
doi:10.5815/ijmsc.2017.02.04 fatcat:3xji5gyls5hl7irrsyqmpulw2m

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

Loïc Hervé, Sana Louhichi, Françoise Pène
2019 E S A I M: Probability & Statistics  
In this respect, a key property is the multiplicative ergodicity, which deals with the asymptotic behaviour of some Laplace-type transform of nonnegative additive functional of a Markov chain.  ...  We establish a spectral version of this multiplicative ergodicity property in a general framework. Our approach is based on the use of the operator perturbation method.  ...  In this model, at each step, either we follow a Markov chain Z = (Z n ) n (with probability (1 − α)) or we generate an independent random variable with distribution the invariant probability measure of  ... 
doi:10.1051/ps/2019003 fatcat:sr2hlax3tfexxcu2tlh7324omi
« Previous Showing results 1 — 15 out of 1,742,261 results