Provided is an eigendecomposition cipher. Input data is formatted into a numerical representation and arranged as a data matrix. Eigendecomposition is performed on the data matrix to determine at least a first component matrix (of eigenvalues) and a second component matrix (of eigenvectors). The eigendecomposition process is modified to ensure that the first component matrix has a diagonalized matrix of eigenvalues. Provided are additional features of shaping, compression, and message generation for an eigendecomposition-based cipher. A first message is generated based upon the first component matrix. A second message is generated based upon the second component matrix. The first and second messages comprise separate indecipherable parts of the input data. The first and second messages may be transmitted or stored separately such that the source data may not be recovered without both messages.