کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4636919 1340730 2006 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
How to compute modular exponentiation with large operators based on the right-to-left binary algorithm
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
How to compute modular exponentiation with large operators based on the right-to-left binary algorithm
چکیده انگلیسی

When the lengths of the operators are at least 1024 binary or 300 decimal digits, modular exponentiation can be time-consuming and is often the dominant part of the computation in many computer algebra systems. The prime approach on this computational problem is known as the square-and-multiply method, which includes two versions, i.e. the left-to-right binary algorithm and the right-to-left binary algorithm. For the past years, too many attentions have been paid to propose the fast modular exponentiation methods based on the left-to-right binary algorithm. However, extremely few attentions have been paid on developing the fast modular exponentiation methods based on the right-to-left binary algorithm. In this paper, we propose a t-fold exponent method based on the right-to-left binary algorithm. From the performance view, our t-fold exponent method is similar to the m-ary method based on the left-to-right binary algorithm. From the structure view, our t-fold exponent method offers a framework for the fast modular exponentiation methods based on the right-to-left binary algorithm. More important, it is the first but steady step to develop the fast modular exponentiation methods based on the right-to-left binary algorithm.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 176, Issue 1, 1 May 2006, Pages 280–292
نویسندگان
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