Cryptographic applications of efficiently evaluating large degree isogenies
US8250367B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | Sep 30, 2008 |
| Grant date | Aug 21, 2012 |
| Priority date | — |
| Expiry date | Dec 29, 2030 |
Classification
- Technology area (CPC H)Electricity
- CPC primaryH04L2209/80
- WIPO fieldDigital communication
- WIPO sectorElectrical engineering
Abstract
Techniques are disclosed for representing and evaluating large prime degree isogenies for use in cryptographic signature and encryption schemes. An isogeny of prime degree 1 may be represented as an ideal in the form (1, A*alpha+B), where 1 comprises the degree of a prime number, the prime number is split into integers a and b, and alpha is a known endomorphism. For a given degree 1, integers a and b define a unique isogeny, allowing the isogeny to be stored with 3 log(1) bits of information. Techniques are also disclosed to evaluate the isogeny at a given point by decomposing the isogeny into an integer and a plurality of smaller degree isogenies, evaluating the smaller degree isogenies at the point with traditional means, and multiplying the results of the evaluations together and with the integer.
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.