Cryptographic method using a non-supersingular elliptic curve E in characteristic 3
US8750499B2 · kind B2 · utility
Assignee
Inventor
Key dates
| Filing date | Dec 9, 2010 |
| Grant date | Jun 10, 2014 |
| Priority date | — |
| Expiry date | Apr 9, 2033 |
Classification
- Technology area (CPC H)Electricity
- CPC primaryH04L9/3066
- WIPO fieldDigital communication
- WIPO sectorElectrical engineering
Abstract
A cryptographic method is provided of a type with public key over a non-supersingular elliptic curve E, determined by the simplified Weirstrass equation y2=x3+a·x2+b over a finite field GF(3n), with n being an integer greater than or equal to 1. The method includes associating an element t of said finite field with a point P′ of the elliptic field. The step of associating includes: obtaining a pre-determined quadratic non-residue η on GF(3n); obtaining a pre-determined point P=(zP, yP) belonging to a conic C defined by the following equation: a·η·z2−y2+b =0; obtaining a point Q=(zQ, yQ), distinct from the point P belonging to the conic C and a straight line D defined by the following equation: y=t·z+yP−t·zP; obtaining the element ξ of GF(3n) verifying the following linear equation over GF(3): −η·ξ=(η2·zQ)/a; and associating, with the element t of the finite field, the point P′ of the elliptic curve, for which the coordinates are defined by the pair (η·zQ/ξ, yQ).
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.