Digital Signature Scheme Based On The Conic Curve Over Z_n

With the development of the computing technology of hardware and software, the classical public-key cryptosystem is faced up with growing security threats. The cryptosystem based on algebra curves, one branch of public-key cryptosystems, has aroused great interest from researchers, and corresponding standards have been issued for elliptic curve cryptosystem. Furthermore, we try to find more algebra curves except ECC, or at least more advantageous in some aspects to realize public-key cryptosystem.The dissertation makes systematic research into conic curve over residue class ring, designs a digital signature scheme on the public-key cryptography of conic curve over Z_n. The research content of this dissertation are summarized as follows:1 .The conic curve C_n(a,b) is described in two methods. Two additions are defined, proved same with each other and denoted by (?) .It is proved that the rational points of C_n(a,b) form an abelian group under the operation (?), which is denoted by (C_n(a, b),(?)).2.The dissertation discusses basic properties of the group (C_n(a,b),(?)) , including DLP, order computation, generator finding, and points out how to prove the properties of C_n(a,b) by those of C_p(a,b) and C_q(a,b), makes it possible to establish analogue over the conics for kinds of cryptographic protocols.3.The threats confronted by classical RSA are analyzed; it is proposed that the RSA public-key cryptosystem over C_n(a,b) is safer and more promising in application than the classical RSA for it can resist small encryption exponent attack and small decryption exponent attack, though for both of them, the security is based on difficulties in factorizing large integer.4.The dissertation provides the analogues of KMOV and QV over C_n(a,b). Thesecurity of these schemes is based on difficulties in factorizing large integer but than the classical RSA in resisting small encryption or decryption exponent attack.5. A digital signature scheme was designed on the public-key cryptography of conic curve over Z_n. The scheme made comprehensively use of the difficulties in factorizing Jarge integer and computing discrete logarithm, thereby increasing the performance of security. Furthermore the multiple digital signatures were designed by combining several digital signatures in conic curve over Z_n, which can be used to realize that several people sign on a same file. Then the numeric simulation for the digital signatures and the multiple digital signatures was done. Finally the numeric simulation for the RSA blind signature based on conic curve over Z_n was done.