Efficient algorithm to construct phi function in vector space secret sharing scheme and application of secret sharing scheme in Visual Cryptography

摘要

Secret Sharing refers to a method through which a secret key K can be shared among a group of authorized participants, such that when they come together later, they can figure out the secret key K to decrypt the encrypted message. Any group which is not authorized cannot determine the secret key K. Some of the important secret schemes are Shamir Threshold Scheme, Monotone Circuit Scheme, and Brickell Vector Space Scheme. Brikell’s vector space secret sharing construction requires the existence of a function from a set of participant P in to vector space Zdp, where p is a prime number and d is a positive number. There is no known algorithm to construct such a function in general. We developed an efficient algorithm to construct function for some special secret sharing scheme. We also give an algorithm to demonstrate how a secret sharing scheme can be used in visual cryptography.