Lms Journal of Computation and Mathematics最新文献_第2页

Structure of the maximal -local geometry point-line collinearity graph 极大局部几何点线共线图的结构

Lms Journal of Computation and Mathematics Pub Date : 2016-03-01 DOI: 10.1112/S1461157016000036

P. Rowley, Ben Wright

引用次数: 0

Effective Hasse principle for the intersection of two quadrics 两二次曲线交点的有效哈塞原理

Lms Journal of Computation and Mathematics Pub Date : 2016-02-16 DOI: 10.1112/S146115701600022X

Tony Quertier

引用次数: 3

A database of genus-2 curves over the rational numbers 有理数上的二类曲线数据库

Lms Journal of Computation and Mathematics Pub Date : 2016-02-11 DOI: 10.1112/S146115701600019X

A. Booker, J. Sijsling, Andrew V. Sutherland, J. Voight, D. Yasaki

引用次数: 54

Real multiplication through explicit correspondences 通过显式对应的实乘法

Lms Journal of Computation and Mathematics Pub Date : 2016-02-05 DOI: 10.1112/S1461157016000188

Abhinav Kumar, R. E. Mukamel

引用次数: 15

A robust algorithm for estimating regression and dispersion parameters in non-stationary longitudinally correlated Com–Poisson data 非平稳纵向相关Com-Poisson数据中回归和离散参数估计的鲁棒算法

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157015000339

N. M. Khan

{"title":"A robust algorithm for estimating regression and dispersion parameters in non-stationary longitudinally correlated Com–Poisson data","authors":"N. M. Khan","doi":"10.1112/S1461157015000339","DOIUrl":"https://doi.org/10.1112/S1461157015000339","url":null,"abstract":"In recent years, Com–Poisson has emerged as one of the most popular discrete models in the analysis of count data owing to its ﬂexibility in handling diﬀerent types of dispersion. However, in a stationary longitudinal Com–Poisson count data set-up where the covariates are time independent, estimation of regression and dispersion parameters based on a generalized quasi-likelihood (GQL) approach involves some major computational diﬃculties particularly in the inversion of the joint covariance matrix. On the other hand, in practical real-life longitudinal studies, time-dependent covariates leading to non-stationary responses are more frequently encountered. This implies that further computational problems will now arise when estimating parameters under non-stationary set-ups. This paper overcomes this problem by approximating the inverse of the ill-conditioned covariance matrix in the GQL approach through a multidimensional conjugate gradient method. The performance of this novel version of the GQL approach is then assessed on simulations of AR(1) stationary and AR(1) non-stationary longitudinal Com–Poisson counts and on real-life epileptic seizure counts. However, there is not yet an algorithm to generate non-stationary longitudinal Com–Poisson counts nor a GQL algorithm to estimate the parameters under non-stationary set-ups. Thus, the paper also provides a framework to generate non-stationary AR(1) Com–Poisson counts along with the construction of a GQL equation under non-stationary set-ups.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"25-36"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157015000339","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Visualizing elements of order in the Tate–Shafarevich group of an elliptic curve 椭圆曲线的Tate-Shafarevich群中有序元素的可视化

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000243

Tom Fisher

引用次数: 1

On error distributions in ring-based LWE 基于环的LWE误差分布

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000280

W. Castryck, Ilia Iliashenko, F. Vercauteren

{"title":"On error distributions in ring-based LWE","authors":"W. Castryck, Ilia Iliashenko, F. Vercauteren","doi":"10.1112/S1461157016000280","DOIUrl":"https://doi.org/10.1112/S1461157016000280","url":null,"abstract":"Since its introduction in 2010 by Lyubashevsky, Peikert and Regev, the ring learning with errors problem (ring-LWE) has become a popular building block for cryptographic primitives, due to its great versatility and its hardness proof consisting of a (quantum) reduction from ideal lattice problems. But, for a given modulus q and degree n number field K, generating ring-LWE samples can be perceived as cumbersome, because the secret keys have to be taken from the reduction mod q of a certain fractional ideal O-K(V) subset of K called the codifferent or 'dual', rather than from the ring of integers O-K itself. This has led to various non-dual variants of ring-LWE, in which one compensates for the non-duality by scaling up the errors. We give a comparison of these versions, and revisit some unfortunate choices that have been made in the recent literature, one of which is scaling up by vertical bar Delta(K)vertical bar(1/2n) with Delta(K) the discriminant of K. As a main result, we provide, for any epsilon > 0, a family of number fields K for which this variant of ring-LWE can be broken easily as soon as the errors are scaled up by vertical bar Delta(K)vertical bar((1-epsilon)/n).","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"130-145"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

On a Li-type criterion for zero-free regions of certain Dirichlet series with real coefficients 一类实系数Dirichlet级数无零区域的li型判据

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000115

A. Bucur, A. Ernvall-Hytönen, Almasa Odžak, L. Smajlovic

引用次数: 10

An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero 无低阶零编码的GGH多线性映射的NTRU问题和密码分析算法

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000371

J. Cheon, Jinhyuck Jeong, Changmin Lee

{"title":"An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero","authors":"J. Cheon, Jinhyuck Jeong, Changmin Lee","doi":"10.1112/S1461157016000371","DOIUrl":"https://doi.org/10.1112/S1461157016000371","url":null,"abstract":"Let f and g be polynomials of a bounded Euclidean norm in the ring Z[X]/⟨X+1⟩. Given the polynomial [f/g]q ∈ Zq[X]/⟨X+1⟩, the NTRU problem is to find a, b ∈ Z[X]/⟨X + 1⟩ with a small Euclidean norm such that [a/b]q = [f/g]q. We propose an algorithm to solve the NTRU problem, which runs in 2 2 λ) time when ∥g∥, ∥f∥, and ∥g−1∥ are within some range. The main technique of our algorithm is the reduction of a problem on a field to one in a subfield. Recently, the GGH scheme, the first candidate of a (approximate) multilinear map, was found to be insecure by the Hu–Jia attack using low-level encodings of zero, but no polynomial-time attack was known without them. In the GGH scheme without low-level encodings of zero, our algorithm can be directly applied to attack this scheme if we have some top-level encodings of zero and a known pair of plaintext and ciphertext. Using our algorithm, we can construct a level-0 encoding of zero and utilize it to attack a security ground of this scheme in the quasi-polynomial time of its security parameter using the parameters suggested by [GGH13].","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"255-266"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000371","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 104

JKL-ECM: an implementation of ECM using Hessian curves JKL-ECM:一个使用Hessian曲线的ECM实现

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI: 10.1112/S1461157016000231

H. Heer, G. McGuire, Oisín Robinson

{"title":"JKL-ECM: an implementation of ECM using Hessian curves","authors":"H. Heer, G. McGuire, Oisín Robinson","doi":"10.1112/S1461157016000231","DOIUrl":"https://doi.org/10.1112/S1461157016000231","url":null,"abstract":"We present JKL-ECM, an implementation of the elliptic curve method of integer factorization which uses certain twisted Hessian curves in a family studied by Jeon, Kim and Lee. This implementation takes advantage of torsion subgroup injection for families of elliptic curves over a quartic number field, in addition to the ‘small parameter’ speedup. We produced thousands of curves with torsion $mathbb{Z}/6mathbb{Z}oplus mathbb{Z}/6mathbb{Z}$ and small parameters in twisted Hessian form, which admit curve arithmetic that is ‘almost’ as fast as that of twisted Edwards form. This allows JKL-ECM to compete with GMP-ECM for finding large prime factors. Also, JKL-ECM, based on GMP, accepts integers of arbitrary size. We classify the torsion subgroups of Hessian curves over $mathbb{Q}$ and further examine torsion properties of the curves described by Jeon, Kim and Lee. In addition, the high-performance curves with torsion $mathbb{Z}/2mathbb{Z}oplus mathbb{Z}/8mathbb{Z}$ of Bernstein et al. are completely recovered by the $mathbb{Z}/4mathbb{Z}oplus mathbb{Z}/8mathbb{Z}$ family of Jeon, Kim and Lee, and hundreds more curves are produced besides, all with small parameters and base points.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"19 1","pages":"83-99"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157016000231","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63412201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3