Methods of providing multi-key encryption of a data set are provided. Operations include providing, to a first data user of the data set, a first user specific data point, providing, to a second data user of the data set, a second user specific data point, and providing, to the first data user and the second data user, at least two shared data points that, when used with either of the first user specific data point or the second user specific data point, define a component polynomial that corresponds to a component that is defined in the data set. Operations further include providing, to the first data user, a first key share point that, in combination with the first user specific data point, defines a first data user polynomial that identifies a first encryption key that is on the first data user polynomial.