Protected Secret Sharing and its Application to Threshold Cryptography
Abstract
In the secret reconstruction of Shamir’s (t,n) secret sharing scheme (SS), shares
released by shareholders need to be protected otherwise, non-shareholders can also obtain the
secret. Key establishment protocol can establish pairwise keys for any pair of shareholders.
Then, shareholders can use these pairwise keys to protect shares in the secret reconstruction
process. However, adding a key establishment in the secret reconstruction slows down the
process significantly. Shamir’s SS is based on a univariate polynomial. Shares generated by a
bivariate polynomial enable pairwise keys to be shared between any pair of shareholders. But
we proposed a new type of SS, called protected secret sharing scheme (PSS), in which shares
of shareholders can not only be used to reconstruct the secret but also be used to protect the
secrecy of shares in the secret reconstruction process. Thus, the recovered secret is only
available to shareholders but not to non-shareholders. A basic (t,n) PSS based on a bivariate
polynomial is proposed. Furthermore, we introduce to use this basic PSS in the applications
of threshold cryptography. The PSS is unique since it protects the secrecy of the recovered
secret in a very efficient way.
Table of Contents
Introduction -- Related work -- Our scheme -- Security analysis and performance -- Application to algorithms of threshold cryptography -- Conclusion
Degree
M.S.