ECC Multi - Threshold Research And Design Of Dynamic Signcryption Scheme

Elliptic Curve Cryptosystem(ECC) provides the highest strength-per-bit of any cryptosystems know so far, and the security of ECC is based on the difficulty of elliptic curve discrete logarithm problem(ECDLP). In addition to its high security, ECC also has many other good merits, such as less computation overheads, shorter key size, considerable bandwidth savings, and so on. All of those merits have made it be the best public-key cryptosystem that is suitable for use in the future.The research of this thesis focuses on designing an efficient and secure muti-threshold proactive sign-crypt scheme through ECC knowledge. For the purpose of the new signature scheme, we in advance propose a distributed proactive secret sharing scheme which is based on ECC and Lagrange formula in order to make preparation for the new sign-crypt scheme. firstly, the thesis introduces its background and up-to-date developments in domestic and international field. Some basic cryptography concepts and security algorithms, especially we make emphasis on studies of elliptic curve cryptography and digital signature algorithms, are introduced then, and seven schemes of secret sharing and five schemes of threshold group signature are analysed in detail. The analysis exposes some defects of these schemes, so some remedial measures are also shown in the paper. One of our contributions is that we propose a distributed proactive secret sharing scheme, which has many of good advantages of other schemes, and proactive property can be perfectly implemented, and no requirement of trusted center because there always are lots of disadvantages to a system with trusted center. The problems of secret updating and reuseness of member sub-secret-key are solved well by our proposed secret sharing scheme. Finally, an ECC muti-threshold proactive sign-crypt scheme without trusted center is proposed based on the former. This is another contribution to this thesis. The new proposed sign-crypt scheme have the properties of proactivness, no-reply, signcrypt, forward security, public-verification besides eight principles of threshold group signature, and for the reasons of efficiency and security, we use ECC and bilinear maps to achieve the goal. Security, computation and communication of the new scheme are also analysed, and we compare the proposed scheme with another muti-threshold group signature scheme on security and efficiency sides.We hope that our research work will benefit the development and application of proactive digitial signature.