The Research Of Implementation Technology Based On Elliptic Curve Cryptosystem And Public Key Cryptography

Elliptic Curve Cryptosystem (ECC) is based on the Mathematical problems which is called elliptic curve discrete logarithm problem (ECDLP). Compared with other public-key cryptographies, ECC not only has the higher security but also has less computation overheads, shorter key size and narrower bandwidth. Some organizations such as IEEE, ANSI, ISO, IETF SECG, have done a lot of the standardization work on algorithm of Elliptic Curve Cryptosystem and each has developed its own standard. The experts believe that ECC will become the next generation popular public key cryptography. Therefore, the study of the Elliptic Curve Cryptosystem technology has great practical significance.In the chapter 2,we first introduce the background and basic mathematic concepts related to Elliptic Curve Cryptosystem such as group, ring and field.And the whole Elliptic Curve Cryptosystem is analyzed in detail. Then the basic operation such as point add is presented based on GF ( p)or GF (2 m). Next, the algorithm of attacks to the ECDLP is analyzed, and the security criterion is proposed. The security criterion can prevent the elliptic curve from being attacked. At the same time, some algorithm to generate secure elliptic curve is listed.In the chapter 3, the scalar multiplication algorithm first is introduced. Then the improved algorithm of scalar multiplication called half sliding window algorithm is proposed. It is based on binary representation of multiplier. Next, we collect the result datum throw several experiments and represent the efficiency with chart using matlab. At last, the Digital Standard Algorithm of ECC is implemented. It is based on GF (p)and used the library of miracl.In chapter 4, the insecurity of single PIN is analyzed. Then a dual factor authentication system is designed. It combines Public Key Crypto Standard #11(PKCS#11) with EJB component technology on the basis of PIN and UsbKey digital certificate. Finally, compared with RSA,the Advantage of ECC is discussed.Then We analyze the feasibility that applying ECC on the dual factor authentication system.In the last chapter, the conclusion and deeper work are presented.