Method and apparatus for public key exchange in a cryptographic system
US5463690A · kind A · utility
Assignee
Inventor
Key dates
| Filing date | Dec 14, 1993 |
| Grant date | Oct 31, 1995 |
| Priority date | — |
| Expiry date | Dec 14, 2013 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06F7/727
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
Abstract
The present invention is an elliptic curve cryptosystem that uses elliptic curves defined over finite fields comprised of special classes of numbers. Special fast classes of numbers are used to optimize the modulo arithmetic required in the enciphering and deciphering process. The class of numbers used in the present invention is generally described by the form 2.sup.q -C where C is an odd number and is relatively small, for example, no longer than the length of a computer word (16-32 bits). When a number is of this form, modulo arithmetic can be accomplished using shifts and adds only, eliminating the need for costly divisions. One subset of this fast class of numbers is known as "Mersenne" primes, and are of the form 2.sup.q -1. Another class of numbers that can be used with the present invention are known as 14 "Fermat" numbers of the form 2.sup.q +1. The present invention provides a system whose level of security is tunable. q acts as an encryption bit depth parameter, such that larger values of q provide increased security. Inversion operations normally require an elliptic curve algebra can be avoided by selecting an inversionless parameterization of the elliptic curve. Fast F…
Source: USPTO / EPO open patent data. Objective bibliographic and citation counts.