The Research Of Digital Signature Schemes Based On Elliptic Curves

Information security is one of the most important problems demanding prompt solution in the information society and has become an indispensable emerging discipline in information science. Digital signature is an important technology to verify authentication, integrity and non-repudiation, so it is one of the core technologies in Information security and is one of the key technologies in the e-business and e-government. The elliptic curve cryptosystem (ECC) has the highest unit-bit security strength among the public key cryptosystems by far and has been considered to be the most universal public-key cryptosystem of the next generation.This paper mainly discusses elliptic curve signature scheme over finite fields as follows:Firstly, we analysis the internationally recognized algorithm ECDSA and other related signature algorithms. These algorithms all use the uP+vQ form in their verification step which needs to calculate two scalar multiplications. Scalar multiplications are the most time-consuming operation, so in this paper, a new algorithm that uses the uP+Q form is put forward based on the existing algorithms. It uses scalar multiplication calculation only one time so the verification step requires about half of the time ECDSA needs. Meanwhile, in the algorithm the Hash value is replaced by the Hamming weight of Hash value, so the efficiency of operations is further improved and the algorithm can prevent pseudo-signature attack.Secondly, we proposed two new ElGamal digital signature scheme based on the existing ElGamal digital signature scheme which don't need to inverse matrix during signature and verification so that the security of the signature and efficiency are improved.