Abstract: A homomorphic evaluation of a function is performed on input ciphertext(s), which were encrypted using an encryption scheme that includes multiple integer moduli. Each ciphertext contains one or more elements of an m-th cyclotomic number field, where m is an integer. Each ciphertext which is defined relative to one of the moduli q, each element a(X) of the m-th cyclotomic number field is represented via a matrix, with each row i of the matrix corresponding to an integer factor pi of the modulus q and each column j corresponding to a polynomial factor Fj(X) of the m-th cyclotomic polynomial ?m(X) modulo q. Content of the matrix in row i and column j corresponds to the element a(X) modulo pi and Fj(X). Performing the homomorphic evaluation of the function further includes performing operation(s) using one or more matrices from one or more of the ciphertexts.