Study Of Multi-secret Sharing Scheme

With the rapid development of information, information security will play an important role in information society. It is undoubtedly that cryptography is the core technologies. Multi-secret sharing is an important concept of encoding technology, which is the application of secret sharing. The traditional secret sharing could only share a secret, In order to share multi-secret, multi-secret secret sharing scheme is needed, which could share multi-secret during a group of participants. Multi-secret sharing is used extensively in cryptography, and electronic auction, electronic election and so on is its typical applications.During my studying period of master, how to design multi-secret sharing scheme is my main research work. The author read a large number of related books and literatures in the process of learning. Two papers were written through my own diligent study and research, the main research achievements that the author obtained were as follows.Firstly, a multi-secret share scheme was put forward which based on RSA and Chinese remainder theorem. At present, many people have researched the Shamir secret sharing scheme and the achievements that they have obtained are very much. The author proposed a multi-secret sharing scheme which based on Asmuth-Bloom threshold scheme, and the used mathematical knowledge is the Chinese remainder theorem. The RSA cryptosystem was introduced in the paper in order to increase anti-attack, which is based on the difficulty of big integer factorization. In this scheme, secret distributor can be sure whether the secret share that the participants had selected is different, participants are asked to choose again if their secret shares are equal. And because the prime which we selected is very big, we know that it is very difficult to decompose a large number, so it is not easy for attacker to steal the information.Secondly, a verifiable multi-organization multi-secret sharing scheme was put forward. Multi-organization multi-secret sharing scheme is the extension and application of the secret sharing, which can share many secrets in multiple organizations. Previous people have described and constructed the scheme, but the scheme doesn't have the verifiable process, and can not resist the intrusion effectively. By introducing discrete logarithm knowledge, a verifiable multi-organization multi-secret sharing scheme was formed by author. The solving of discrete logarithm problem is very difficult, and its introduction can make the scheme have verifiable process, it not only can resist the attacker's intrusion, but also can prevent the deception of participators effectively and determine whether the secret distributor distributed the real secret share.