Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
US6202076A · kind A · utility
Assignee
Inventors
Key dates
| Filing date | Jan 18, 2000 |
| Grant date | Mar 13, 2001 |
| Priority date | — |
| Expiry date | Jan 18, 2020 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06F7/726
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
A scheme for arithmetic operations in finite field and group operations over elliptic curves capable of realizing a very fast implementation. According to this scheme, by using a normal basis [.alpha. .alpha.+1], the multiplicative inverse calculation and the multiplication in the finite field GF(2.sup.2n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2.sup.n). Also, by using a standard basis [1 .alpha.], the multiplication, the square calculation, and the multiplicative inverse calculation in the finite field GF(2.sup.2n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2.sup.n). These arithmetic operations can be utilized for calculating rational expressions expressing group operations over elliptic curves that are used in information security techniques such as elliptic curve cryptosystems.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.