Ecc-based Fast Algorithm And Signature Scheme

In this dissertation, we presented two improved algorithms which can calculate scalar multiplication on elliptic curve. Then, we analyze the digital signature algorithm of elliptic and implement this algorithm simultaneously. On second thoughts, we obtained some conclusions by investigating the algorithm. Finally, we design a new signature scheme with message recovery based on elliptic curve. The main contents of the dissertation are as follows:Chapter one summarizes current situations of elliptic curve cryptology.Chapter two introduces representation of finite field and concept of point operation on elliptic curve , extends some popular public key cryptosystem to elliptic curve cryptosystem, and give an example about elliptic curve public key cipher Algorithm. Finally, we states that choosing an appropriate parameter in elliptic curve public key cryptosystem.Chapter three studies arithmetic operations over finite field Fjm usingONB(optimal normal bases) and discuss some major fast scalar multiplication algorithms. The immediate point doubling method is used to improve k-ary algorithm and the speed of computing the repeated point doubling can be quicken. Moreover, the optimizing techniques which adopt sliding-window is applied in NAF algorithm, when the window's width is 4, Experimentation about this improved algorithm was implement efficiently.Based on above conclusions, chapter four analyzes the digital signature algorithm of elliptic and implement this algorithm by computer testing simultaneously. Later, the article presents an new computational method based on Montgomery method which was developed to reduce the computations for kP+lQ in verification process of ECDSA . In the next section, we designed a new signature scheme with message recovery based on elliptic curve. This scheme had a property that the signer'skey can simultaneously be authenticated in verifying the signature. Moreover, we also present two variants about the scheme : one is an authenticated encryption scheme that only allows a specified receiver to verify and recover the message , the other is extension based on the second scheme which can deal with the large message communication.Chapter five concludes the work in this dissertation.