Abstract: In recent years, the elliptic curve cryptography system(ECCS) plays more and more important role in the cryptography. Instead of traditional public key cryptography system that it is RSA, it is the ECCS in a lot of application areas. Therefore, there are more and more attacks on the ECCS. In this paper, we advanced the technology that improves the ECCS's safeness and keeps its good property. The technology is called "Elliptic Hyperbola Cryptography System (EHCS)". The EHCS has the same calculation complexity as ECCS, but it has excellently randomness. So EHCS can improve cryptographic safeness in theory. The EHCS has more flexible operation mode than ECCS. Therefore, the EHCS can improve information technology's safeness.

Key words: Elliptic hyperbola, EHDSA, ECDSA