Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption
US7844051B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | Nov 14, 2005 |
| Grant date | Nov 30, 2010 |
| Priority date | — |
| Expiry date | Sep 30, 2029 |
Classification
- Technology area (CPC H)Electricity
- CPC primaryH04L9/3252
- WIPO fieldDigital communication
- WIPO sectorElectrical engineering
Abstract
The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.