US Patent 9929860 Methods and apparatus for generalized password-based secret sharing

Generalized password-based secret sharing schemes are provided. A secret sharing method comprises obtaining a secret; obtaining fixed values from one or more parties; setting an element of a column vector of a password-based linear secret sharing scheme based on the secret; randomly selecting values from a field for additional elements of the column vector; setting remaining elements of the column vector to values that ensure that a product of a matrix and the column vector, for each fixed-share party, is equal to the corresponding fixed value; and distributing non-fixed shares to additional parties using a labeling function. In another method, a defining matrix corresponds to the secret and a field of both the secret and a plurality of shares of the secret. A given share for each party in the set is set to the corresponding obtained fixed value. A row in the defining matrix is randomly selected such that an element in the row corresponding to each party in the set is equal to the corresponding obtained fixed value.