Reconfigurable real number field elliptic curve cryptography to improve the security

Abstract

Elliptic curve cryptography has an advantage of providing stability similar to RSA public key cryptography even when an extremely short key is used, and elliptic curve cryptography studies have been conducted on integer root based on finite field. However, if elliptic curve cryptography can be expanded to real number field, a very effective cryptographic system can be configured by selecting more diverse keys. Accordingly in this paper, a method of configuring cryptographic system using real number field coordinates on an elliptic curve is proposed. In the proposed method, keys can be selected using real number field, as well as finite field. Therefore, as the range of key selection for encryption and decryption can be expanded, there is an advantage of bringing additional improvement on safety from complexity of real number field calculation, while maintaining the advantages of existing elliptic curve cryptographic system.