Research On Elliptic Curve Cryptosystem Discrete Logarithm Encrypted Algorithm

With the development and the application of information technology, the problem of information security becomes more and more important. Then on the basis of safe and high efficient encryption algorithm, some related network protocols are produced. Compared with some other public key cryptosystems, elliptic curve cryptosystem(ECC)has many merits, In addition to its high security ,ECC also has many other merits over the other public-key cryptosystems such as less computation overheads, shorter key size, considerable bandwidth savings, and so on. All of these merits have made it the best public-key cryptosystem that is suitable for use in future.First of all, the article discuss the currency and development trend of the cryptosystem. Second, the principle of ECC is discussed, including the mathematic foundation of ECC, basic conception of elliptic curve, constructional idea of ECC, operation on elliptic curve and so on. Third, the finite field what scalar multiplication needs is analyzed, and select OEF being the basic field of the scalar multiplication. Elliptic curve cryptosystems based on both of finite fields GF(q) and GF(2~m) have computational difficulties. In OEF field the softwareimplementation with faster arithmetic is obtained on 32bits microcomputers. Fourth, on the base of deep analysis of scalar multiplication, the paper provides a improved NAF multiplication, new algorithm improves the average applicational length of zero of binary system and ensure the least Huming weight, and decrease the quantity of point add. At last, proposes a new digital proxy multisignature based on the elliptic curve cryptosystem, The safety of this scheme is based on the elliptic curve discrete logarithm of nonsupersingular elliptic curve over finite field which has no efficient attack method by now, its safety is higher than the safety of the scheme based on finite field. And give a specific scheme, validates its correctness in theory.