Research Of Group Oriented Secret Sharing Technology Based On Linear Code

Secret Sharing is an important research subject of modern applied cryptography.And it is one of the important tools of protecting the secret information and critical word from being lost and destroyed.Secret sharing has the incomparable advantages in key management.What’s more,it also plays a significant role in electronic voting system and group authentication.(t,n)threshold secret sharing is a key part of secret sharing.In(t,n)threshold secret sharing scheme,a secret s will be divided into n shares and shared among n shareholders.The scheme meets:(1)any t or more than t shareholders can recover the secret(2)fewer than t shareholders cannot obtain the secret s.In traditional secret sharing system,the adversary is called Outsider if he doesn’t have any valid share.For Outsider,if he impersonates as the valid shareholder and then participates in the secret reconstruction,as a result,he can obtain the secret by collecting enough shares from other valid participants.In this paper,to cope with this kind of potential security problem in traditional secret sharing system,we give an improvement of the basic secret sharing,and propose the concept of Group Oriented Secret Sharing(GOSS):in GOSS,m(m>t)participants form a tightly couple group by generating Randomized Components(RCs).The secret can be recovered only if all m RCs are correct,which requires each participant to have a valid share in advance and participate in the secret reconstruction honestly.Then,we propose two kinds of Group Oriented Secret Sharing schemes based on linear code.The main difference between these two schemes is that they use different ways to construct the RC.Both methods have their advantages and disadvantages.The first scheme is a non-interactive and asymptotically perfect secret sharing scheme,and the second is an interactive and ideal secret sharing scheme.For the first scheme,every participant chooses the random integer independently,and binds the share with public information of all participants in a secret reconstruction to construct RC.In the secret reconstruction,RC is used to reconstruct the secret,which ensures that the outsider cannot obtain the share even he can involve in the secret reconstruction.For the second scheme,to form a tightly coupled group,all participants need to run a Random Number Selection(RNS)algorithm collectively to choose a private random number each before constructing RCs.And the sum of these random numbers must meet certain conditions.In these two schemes,by using RCs,we enhance the security of the secret reconstruction phase without any user authentication or share verification.In addition,RCs can also be applied to build other schemes in a simple way,such as multi-secret sharing,group authentication and so on.