Public-key Cryptosystem Based On Conic Curve And Its Application In Digital Signature

Conic curve cryptography was first introduced by Prof. Cao Zhenfu. In C.Schnorr's opinion, conic curve cryptography is the most interesting topic except Elliptic curve cryptography. Compared with ECC, the computing on conic curve is much easier, and the facility of plaintext embedding is the most exciting feature of conic curve cryptography. A group modulo n on conic curve can be formed, on which we can construct cryptogram similar to RSA.Firstly, this thesis introduces the basic definition and characters of conic curve over finite field Fp and ring Z n.We closely discuss the characters of conic curve C n( a , b ) over ring Z n and prove that (C n( a , b ),⊕) can form a finite Abel field. Also, we give an algorithm for finding the basic point G on some of the conic curves over ring Z n.Secondly, we apply conic curve over ring Z nin some encryption and signature algorithms of public-key cryptosystem. A Diffie-Hellman key-exchange algorithm, an ElGamal digital signature algorithm and a multi-signature algorithm based on conic curve over ring Z n are proposed. The security of all these algorithms is based on the difficulty in factorizing large integer and computing discrete logarithm.At last, two comparisons of conic curve cryptography with ECC are made: the first is plaintext embedding and the second is computing the order of the point on the curve, and the comparing conclusion is that the conic curve cryptography has more advantages in these two fields.