FAST IDEAL CUBING IN IMAGINARY QUADRATIC NUMBER AND FUNCTION FIELDS

被引：4

作者：

Imbert, Laurent ^{[1
,2
]}

Jacobson, Michael J., Jr. ^{[3
]}

Schmidt, Arthur ^{[3
]}

机构：

[1] Univ Calgary, Dept Math & Stat, CNRS, PIMS, Calgary, AB T2N 1N4, Canada

[2] Univ Montpellier 2, CNRS, LIRMM, F-34095 Montpellier, France

[3] Univ Calgary, Dept Comp Sci, Calgary, AB T2N 1N4, Canada

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2010年 / 4卷 / 02期

关键词：

Quadratic fields; quadratic function fields; hyperelliptic curves; ideal arithmetic; double base number systems; CURVES; SYSTEM;

D O I：

10.3934/amc.2010.4.237

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present algorithms for computing the cube of an ideal in an imaginary quadratic number field or function field. In addition to a version that computes a non-reduced output,we present a variation based on Shanks' NUCOMP algorithm that computes a reduced output and keeps the sizes of the intermediate operands small. Extensive numerical results are included demonstrating that in many cases our formulas,when combined with double base chains using binary and ternary exponents,lead to faster exponentiation

引用

页码：237 / 260

页数：24

共 19 条

[11] Jacobson MJ, 2009, CMS BOOKS MATH, P1
[12] An improved real-quadratic-field-based key exchange procedure
Jacobson, MJ
Scheidler, R
Williams, HC
[J]. JOURNAL OF CRYPTOLOGY, 2006, 19 (02) : 211 - 239
[13] JACOBSON MJ, 2006, INT J MATH COMPUT SC, V1, P83
[14] A DOUBLE-DIGIT LEHMER-EUCLID ALGORITHM FOR FINDING THE GCD OF LONG INTEGERS
JEBELEAN, T
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1995, 19 (1-3) : 145 - 157
[15] Lehmer D. H., 1938, Amer. Math. Monthly, V45, P227
[16] *NIST, 2007, NIST SPEC PUBL
[17] SHANKS D, 1989, NATO ADV SCI I C-MAT, V265, P163
[18] Shoup V, A library for doing number theory
[19] SUTHERLAND AV, 2007, THESIS MIT MASSACHUS

← 1 2 →