Research Of Secret Sharing And Threshold Cryptography

In the modern society, as the development of computer, Internet plays a more and more part in people's life. The confidentiality, integrity and availability of information must be satisfied when important data are transferred by Internet. The mean way to deal with this problem is the technique of information security. Cryptology is the core of information security.In the cryptosystem, the security of secret key decides the security of the system. The exposure of secret key would let the illegal user encrypt a message or do a signature, cause the insecurity of the cryptosystem. So how to reduce the probability of exposure of secret key by means of cryptography has an important significance.The main idea of secret sharing and threshold cryptology is to divide the secret (secret key) into several participants. Each participant has a share of the secret, only the specific numbers of participants can reconstruct the secret, less than the number of participants could not get any information about the secret. So it cannot effect the system security even some participants expose their shares. The use of secret sharing and threshold cryptology reduce the probability of the exposure of secret key.Classic secret sharing schemes are not enough to protect sensitive secret key over a long period of time. Attackers can attack secret key step by step over a long period of time, they can break several participants in a long time to get the secret key. Proactive secret sharing scheme can solve the problem of protection of sensitive secret key over a long period of time.Many classic secret sharing schemes are presented based on threshold access structure, but threshold access structure demands that all participants have the same position, right, security and reliability, but in fact each participant does not have the same position and right, so it have a important meaning to research the secret sharing scheme based on general access structure. The vector space access structure has an important place in general access structure, at the same time, the secret sharing scheme based on vector space access structure is also succinct and efficient as based on the threshold access structure. How to apply the vector space access structure to the secret sharing scheme to expand the range of application of the secret sharing scheme is worth to research. We will consider the problem in chapter 3, and give a verifiable secret sharing scheme and a publicly verifiable secret sharing scheme based on vector space access structure.Threshold cryptography is based on secret sharing. In the (t,n) -threshold scheme,n participants share the secret, each participant gives a partial signature by their secret share, any t participants' partial signatures can generate the final signature. Only the participants can have the secret shares, it can not expose the secret key even some participants are broken. In ID-based cryptography, any information about of identity could be used as public key, a third party called private key generator(PKG) can generate private key instead of CA. ID-based cryptography could take the place of CA-based cryptography. We will give an ID-based proactive threshold blind signature scheme in chapter 5.