Research On Randomized Component Based Secure Secret Reconstruction In Publilc Networks

In(t,n)secret sharing,secret can be recovered by any t or more than t shareholders.However,in public networks messages sent by participants may be eavesdropped by attackers and legal shareholders cannot verify other participant’s identity in secret reconstruction.If the number of participants is greater than t,a participant who does not own a valid share can also recover the secret by collecting components from other honest shareholders.In order to resist active attack in public networks,Harn first proposed secure secret reconstruction,which used linear combination of shares to generate Lagrange component,but this scheme is vulnerable to linear subspace attack.Miao tried to break the linear relationship among sending components by using randomized component.However,it still has information leakage and can be attacked by lattice.In view of the security threats in public networks and the vulnerabilities existing in current secure secret reconstruction that cannot resist linear subspace attack and lattice attack,this dissertation makes the following three contributions:1.In order to fix the vulnerability of lattice attack in Miao scheme,the dissertation proposes a randomized component based secure secret reconstruction on polynomial.By using a random polynomial whose degree is at least equal to the share to protect the secrecy of share,the scheme can prevent active attackers from obtaining any information about the secret by linear subspace analysis or lattice reduction in public networks.Furthermore,the scheme is perfect and ideal.2.The dissertation further promotes the randomized component based secure secret reconstruction on polynomial and proposes a more generalized secure secret reconstruction scheme on Integer Ring.The randomized component in this scheme satisfies the condition of perfect security and can resist both linear subspace attack and lattice attack in public networks.Compared with the first contribution,this scheme is not only more simple and efficient,but also still perfect and ideal.3.Due to the necessity of secure channel in public networks,the dissertation also proposes a bivariate polynomial based secure secret reconstruction,which shareholders don’t need to establish secure channel in advance.Shareholders only need to hold two shares and the bivariate polynomial can not only be used for secret reconstruction and randomized components generation,but also generate pairwise secure channel keys for shareholders.The scheme can resist all attack models we analysed in public networks.The dissertation mainly uses Chinese Remainder Theorem as the mathemetical basis for the secret reconstruction and adopts the idea of randomized component whose probability distribution range is not smaller than the share to break the relationship among sending components.It can effectively protect shareholder’s share during the secret reconstruction in public networks.Furthermore,this dissertation also proposes an efficient scheme,which don’t need to establish secure channel in advance.The scheme can use bivariate polynomial to generate the shares for both secure channel keys and randomized components calculation in secret reconstruction.