Based On Elliptic Curve Cryptography, Digital Signature And Applications

With the rapid development of Internet, the problem of information security looks increasingly important. Since N.Koblitz and Miller proposed that elliptic curve could be applied in cryptographic algorithm, elliptic curve cryptosystem has become a research focus. Compared with some other public key cryptosystems, elliptic curve cryptosystem has many merits that can use smaller keys and computationally more efficient algorithms than traditional cryptographic algorithms. The security of elliptic curve cryptosystem is based on the difficulty of elliptic curve discrete logarithm. So far, the elliptic curve cryptosystem provides the highest strength-per-bit of any cryptosystem known.The digital signature is the powerful safeguard of the developing of E-business. It plays an important role in realizing the functions of identification anthentication, data integrity and denying the disavowal. PKI is an infrastructure that use public key cryptosystem, so that it can support security service and general use. The kernel component of PKI is CA(Certificate Authority).This article presents some background knowledge, including the symmetric and asymmetric encryption system in cryptography field, the developments of the elliptic curve cryptosystem and PKI. The mathematics principles of elliptic curve cryptosystem are systematically explained, including the addition rule for elliptic curve point defined over finite field. double-add basic operation implementation and scalar are studied, the security basis of the elliptic curve cryptosystem and the algorithms solving elliptic curve discrete logarithm problem is analyzed. The insecurities of two special curves over finite field are discussed, and several conditions of the secure elliptic curve are proposed.Accoding to the theory of ECC,hash and digital signature, we design the safe model based on ECDSA. Certificate Authority based on the safe model is designed and realized which can the digital certificate of the partners in E-business. The sysyem implements the hash, encryption, signature and didital envelope of sensitive information such as orders.