Generering av elliptiske kurver for kryptografiske anvendelser

Abstract

In elliptic curve cryptography, the choice of the elliptic curve is important for security. This is because there exist elliptic curves where certain shortcuts can be made that breaks the security of elliptic curve cryptography. For this reason, several standards have been proposed to provide government institutions and the public with a set of secure elliptic curves for use in cryptography. Following the Snowden revelations, reports published by the New York Times claims knowledge of an internal memo in the NSA (National Security Agency) describing their involvement in one of the NIST (National Institute of Standards and Technology) standards. In the news article, they quote the alleged memo on the involvement of the NSA: Eventually, N.S.A. became the sole editor. . This has severely weakened the cryptographic community s trust in the NIST curves, and places higher demands for a provable random generation of proposed elliptic curves in current and future standards. It is the purpose of this thesis to consider requirements that elliptic curves should satisfy in order to be suitable for cryptographic applications. We shall give a mathematical description of why these requirements affect the security and/or technical aspects of elliptic curve cryptography. Based on these requirements, we develop a tool for generating secure elliptic curves suitable for cryptographic applications.