An Interoperability Consideration in Selecting Domain Parameters for Elliptic Curve Cryptography

Elliptic curve cryptography (ECC) will be an important technology for electronic privacy and authentication in the near future. There are many published specifications for elliptic curve cryptosystems, most of which contain detailed descriptions of the process for the selection of domain parameters. Selecting strong domain parameters ensures that the cryptosystem is robust to attacks. Due to a limitation in several published algorithms for doubling points on elliptic curves, some ECC implementations may produce incorrect, inconsistent, and incompatible results if domain parameters are not carefully chosen under a criterion that we describe. Few documents specify the addition or doubling of points in such a manner as to avoid this problematic situation. The safety criterion we present is not listed in any ECC specification we are aware of, although several other guidelines for domain selection are discussed in the literature. We provide a simple example of how a set of domain parameters not meeting this criterion can produce catastrophic results, and outline a simple means of testing curve parameters for interoperable safety over doubling.