Research Distributed Key Generation Protocolsand Application On Elliptic Curve Cryptography

Key generation is one of the research topics of key management. As the security of secret key constitute the foundation of all secure cryptography, it is necessary to generate the public key and secret key before any secure protocols are implemented. In order to process tasks of distributed computing, we need to improve the efficiency of key generation. Researching the distributed key generation based on elliptic curve cryptography is preferred and it is an effective method.Selecting the elliptic curve is very important in order to guarantee the correctness and security of key. Security of elliptic curve is decided by the parameter of elliptic curve. An improved algorithm of selecting elliptic curve parameter is proposed. In addition, we propose an algorithm of selecting basic point, and simulate the improved algorithm by Mathematica.After we select the security elliptic curve, we propose a distributed key generation protocol based on elliptic curve cryptography (ECC-DKG). Existing distributed key generation protocols use either cryptography based on discrete logarithm over a finite field or integer factorization. However, there are subexponential algorithms for solving this discrete logarithm problem over a finite field and the integer factorization. Elliptic curve cryptography provides a promising alternative for generating a distributed key generation protocol and no known subexponential algorithms to solve the discrete logarithm over an additive group derived from a point on an elliptic curve. We analyze the security of the ECC-DKG protocol and show that the proposed protocol is high efficient and feasible.Lastly, a scheme of broadcast Multi-Digital Signature Scheme (ECC-BMDSS) is also proposed, which overcome the disadvantage of existing protocols and implement secret sharing of broadcast mutil-digital signature. Comparing to the existing of ECDSS, the proposed scheme is high efficient and can resist many attacks.