Randomization Based Secure Secret Sharing Research In Theory And Applications

In order to implement sharing one secret to multiple users and improve robust-ness of sharing mechanism,famous cryptographers Shamir and Blakley respectively introduced the concept of(t,n)threshold secret sharing in 1979.(t,n)threshold secret sharing consists of two steps:share generation and secret reconstruction,and it includes two entities:one dealer and n shareholders.In deed,the dealer divides a secret s into n shares and sends each share to a shareholder,such that any t or more shareholders can collaborate to recover the secret while less than t shareholders cannot.Aimed at security model,access structure and application of secret sharing,the following five problems are considered.1.(t,n)threshold secret sharing can guarantee robustness in keeping the secret be-cause even if up to n-t shareholders lose their shares,the secret can still be recov-ered.However,this may lead other potential danger.Tompa and Woll proposed an illegal participant attack model to traditional(t,n)threshold secret sharing.In this model,if an illegal participant impersonates a shareholder to cooperate with other t or more legal shareholders on secret reconstruction,it can obtain the secret even though it does not have a valid share because it receives at least t valid shares from other shareholders.In order to thwart the attack,the thesis re-searches how to add an interference value into the original share to generate a new share matched with a new threshold by randomization method.In such a threshold changeable secret sharing,when an illegal participant exists in secret reconstruction,the secret will not be revealed.2.In a traditional(t,n)threshold secret sharing scheme,after each shareholder re-ceives its share from the dealer,it is supposed to keep the fixed share until the secret is recovered.However,if a secret is long-lived and it will not be recon-structed in a short period,the shareholders have to keep shares for a long time.Then,an adversary has more chances to gradually attack shareholders to capture enough shares for obtaining the secret.Therefore,traditional(t,n)threshold se-cret sharing is insufficient to protect a long-lived secret.This thesis researches how to add random value into original share and ensure the correct secret recon-struction by randomization method.3.In a(t,n)threshold secret sharing scheme,whether a secret can be recovered is totally dependent on the number of shareholders who participate in secret recon-struction.Hence,(t,n)threshold secret sharing cannot work in some applications.For example,a big company consists of some departments.The resolution of the big company shall be adopted in cooperation with representatives from each de-partment.In this case,the access structure is not just threshold.Thus,a more appropriate scheme is needed to solve such problem with the group access struc-ture.This thesis researches how to add interference values into main-share of each group to generate different sub-shares for different shareholders in a same group by randomization method.Meanwhile,in order to ensure that each sub-share is valid and can be used to represent a group,this thesis also needs to research how to eliminate effects of interference values in secret reconstruction.4.With the rapid development of network,communication patterns are not limited to 1-to-1 or 1-to-m.Group communications with m-to-m pattern become more and more popular.All the users in a group should share a session key to encrypt messages to secure communications.Secret sharing as a grouped encryption tool,this thesis tries to use secret sharing to design a group key distribution protocol with key generation center.Based on the distribution model,this thesis needs to design a highly efficient group key distribution protocol independent on mathe-matical problems.In consideration of response speed,the thesis researches how to introduce the notion of on-line/off-line into group key distribution such that the key generation center can complete a part of computations before user request.In consideration of security,the thesis researches how to add hash values into group key distribution messages to providing security by randomization method.5.As the representative application in image processing of secret sharing,extended secret image sharing is a combination of cryptography and steganography.In an extended secret image sharing scheme,the secret image is divided by an se-cret sharing method to generate noise-like shadow images.Then,each share im-age is embedded into a cover image by steganography to generate stego image which is used to kept by shareholders.Furthermore,if an extended secret image scheme can recover both secret image and cover image from stego images,it is an reversible extended secret image scheme.The thesis researches how to use generate meaningful image with high quality by randomization method in a se-cret image sharing scheme based on Chinese remainder theorem over polynomial ring.Meanwhile,the scheme can guarantee both secret image and cover image lossless reconstruction.This thesis proposes five problems of secret sharing about security model,access structure and application and tries to use randomization method to solve the problems.Randomization method means adding some interference values into original valid in-formation to generate randomized components which can be transferred during commu-nications or storage to protect the original information.Because the interference values are only utilized to protect valid information,users should eliminate effects of inter-ference values without destroying valid share during secret reconstruction.In different schemes,the detailed randomization methods are also shown in different forms.