The Research Of The Threshold Secret Sharing Scheme

Since the 21st century, with innovation of information technology and rapid development of the communication, human society has entered into a real information age. Especially the rapid development of the Internet, brings abundant resources and great convenience to us, at the same time, make the network also lurk various threat unprecedented. Information security will plays an important role in the information society , And cryptography technology plays a great effect in protecting information security.Human has been using password for thousands of years, the techniques of password plays an important role at that time. However, the password is a Limited password by analysis, which is Easy to be broken. Limited password refers to the safety based on the confidentiality of the algorithm. Once the algorithm is leaked, all the contents encrypted will be exposed to others. Therefore, the cryptographers propose that the algorithms can separate from the keys, this is a milestone in the cryptology.In modern cryptography, the main encryption methods are: symmetric cryptosystem (such as: DES, triple DES algorithm, AES, IDEA, etc.), public key cryptosystems(such as: RSA), elliptic curve cryptography, quantum computer and quantum cryptography. Systemic security depends on the safety of the key in the first three algorithms. Therefore, it is extremely important to protect the key. By the first single user protect the private key to the multiple users protect it together, formed a secret sharing scheme and threshold secret sharing scheme, and have been developed rapidly and applied widely.The main results of the research are as follows:(1) Make a deep research on the threshold secret sharing theory and some classical secret sharing scheme, analyzed several threshold secret sharing scheme and their weak points. Mainly analyzed the multi-secret sharing scheme of He Dawson, we founded it is a time encryption scheme and cannot resist the plotting to attack. And in the scheme of Geng, encryption cannot make arbitrary choice although the scheme can be encrypted many times, but according to the constant of polynomial composed. Therefore, propose a new multi-secret sharing scheme with security and verifiability after combined with quadratic residues. In this scheme, each participant can verify their secret share when the secret dealer distributing it, thus avoiding the fraud from the secret dealer; To prevent the secret participants cheating, each participant also can verify the secret share of the other partners; The secret share of each participant can reuse; Multi-secret can make a reconstraction in any order; Furthermore, the new scheme can withstand the conspiracy attack.(2) This text study about classical digital signature scheme, by the nature of the digital signature scheme which can verify reciprocally, we could build a verifiable multi-secret sharing scheme by combining the multi-secret sharing scheme. Each participant can customize their sub secrets, still can verify respectively. By the study to the multi-secret sharing scheme, we found that this scheme needs safe channel, therefore, we propose a new kind of secret sharing scheme based on respective verification. This scheme don't need the safe channel; The secret share of each participant is selected by themselves, it can prevent the secret dealer from cheating.