Elliptic Curve Verifiable Secret Sharing Research

Secret sharing is an important branch of information security and cryptography. In 1979, Shamir and Blakley independently introduced Secret sharing scheme based on Lagrange interpolation polynomial and linear projective geometry, respectively. Since then much work has been put into the investigation of such schemes and gets lots of scientific achievements. With the development of modern cryptographic techniques and the increasing of the attacker's computing power, the cryptography based on finite fields can not meet the security needs. More and more researchers put into better security of elliptic curve cryptography, and get lots of schemes on elliptic curve. But in these schemes there are several problems as follows:In every secret sharing process only one secret can be shared, the system need a secure channel between the dealer and participants, and participants can not verify the validity of their shares or can only verify by themselves, which makes them may not get the correct sub-secrets. Besides, when the lifetime of the secret is too long, the adversary has enough time could compromise enough participants to reconstruct the secret.In order to overcome these problems, the paper presents a verifiable multi-secret sharing scheme on elliptic curves, two publicly verifiable multi-secret sharing schemes based on bilinear pairing, and a dynamic multi-secret sharing scheme with sub-secret updating. The main results are as follows:1. The paper presents a verifiable multi-secret sharing scheme based on elliptic curves. In the scheme participants choose the shadows by themselves, and the shadows can be reused. The scheme has verifiable property and doesn't need a secure channel. The security of the proposed scheme is based on the security of the Elliptic Curve RSA cryptosystem and the intractability of the Elliptic Curve Discrete Logarithm Problem.2. Because publicly verifiable property can detect cheater much better, the paper proposes two publicly verifiable multi-secret sharing schemes based on bilinear pairing on elliptic curves. One improves Tian's scheme, which can share several secrets in a secret sharing process. And it still has publicly verifiable property. The other is a new publicly verifiable multi-secret sharing scheme. It can not only share several secrets in one process, but also can make participants choose the shadows by themselves. The scheme is a multi-use scheme.3. The paper analyses Pang's signcryption scheme and gets it doesn't satisfy unforgeability and forward security. The paper gives a new signcryption scheme and analyses unforgeability and forward security of the new scheme.4. In view of some secrets having long lifetime, they need higher security. The paper presents a dynamic multi-secret sharing scheme based on elliptic curves cryptosystem using the new signcryption scheme. The sub-secrets of participants can update periodically. The sharing secrets and a participant can be added or deleted freely. A secure channel between participants and the dealer doesn't need because of using the new signcryption scheme in the scheme. The scheme has forward security and it's a multi-secret sharing scheme.