Research On Verifiable Secret Sharing

The secret sharing is an important part of the cryptography protocol. In1979, Shamir and Blakley first developed the concepts of the (t, n) threshold secretsharing (SS) scheme. However, as these schemes are discussed, there are manydrawbacks in both these secret sharing schemes as follows: 1) Only one secret can beshared during one secret sharing process; 2) Once the secret has been reconstructed, it isrequired that the dealer redistributes a fresh shadow over a security channel to everyparticipant; 3)A dishonest dealer may distribute a fake shadow to a certain participant,and then that participant would subsequently never obtain the true secret; 4)A maliciousparticipant may provide a fake share to other participants, which may make themalicious participant the only one who gets to reconstruct the true secret.To solve these problems, we choose the verifiable secret sharing(VSS) andmulti-secret sharing(MSS) as our priority research areas, this paper realizes the propertyof verification in a practical multi-secret sharing scheme, we also propose three newverifiable secret sharing schemes.The main contributions of this paper are as follows:1) In 2004, the researchers C.-C. Yang, T.-Y. Chang and M.-S. Hwang, who are fromTaiwan, China, proposed a new MSS based on the two-variable one-wayfunction(YCH Scheme). But it is a pity that this scheme doesn't have the propertyof verification. We revise the YCH scheme, the new scheme can identify thecheaters no matter if she/he is the dealer or the participant but doesn't need asecurity channel and special verification algorithm. The new scheme still has theproperties of the YCH scheme.2) We propose a new verifiable multi-secret sharing scheme based on the modularverifiable secret sharing scheme proposed by Q. Li, Z. Wang and X. Mu. Thescheme can identify the cheaters and the secret shadows can be reused.3) We analyze the scheme based on the general access structure proposed by Zhang Jian-zhong and Huang Mei-juan. In their scheme, in order to identify the cheaters,the authors have to construct a special verification algorithm. In addition, thatscheme need much computation quantity. We revise the scheme and propose a newverifiable secret sharing scheme. In our scheme, each participant chooses her/hisown shadow by her/himself, so the system doesn't need a security channel and thecost of the system can be lowered. In addition, the new scheme is a reusingscheme.4) We propose a new general verifiable secret sharing scheme based on the RSAcryptosystem and Pinch's scheme. The scheme also has many good properties.