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Numerical methods for finding multiplicative inverses of a modulo N |
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| รหัสดีโอไอ | |
| Creator | 1. Bencharat Prempreesuk 2. Prapanpong Pongsriiam 3. Nairat Kanyamee |
| Title | Numerical methods for finding multiplicative inverses of a modulo N |
| Publisher | Research and Development Office, Prince of Songkla University |
| Publication Year | 2561 |
| Journal Title | Songklanakarin Journal of Science and Technology |
| Journal Vol. | 40 |
| Journal No. | 6 |
| Page no. | 1361-1367 |
| Keyword | modular multiplicative inverse, Newton's method, secant method, binary representation, Zeckendorf representation |
| URL Website | http://rdo.psu.ac.th/sjstweb/index.php |
| ISSN | 0125-3395 |
| Abstract | In this work, we propose new methods based on the root-finding methods in numerical analysis to calculate the inverse of an integer ?? modulo ?? for any positive integer ??. We apply Newton's and secant methods with a power-reduction process and Newton's and secant methods together with the binary representation and Zeckendorf representation to determine the inverse of an integer ?? modulo ??. The numerical results confirm an accuracy when compared to analytical results. In addition, the two methods with the binary and Zeckendorf representations give better CPU times than Newton's and secant methods with powerreduction, for large ??. |
