In a fully homomorphic encryption scheme, a method is provided for performing a homomorphic operation on a data set by applying an encrypted operand supplied as a ciphertext. A data set containing ‘i’ library vectors, each with ‘j’ coefficients is subjected to a pivot operation such that each set of common ‘j’ coefficients is stored in respective library ciphertexts. A query ciphertext containing a query vector is then subjected to a homomorphic pivot operation to separate out its ‘j’ coefficients into respective pivoted query ciphertexts. A more efficient homomorphic computation can then be carried out between the ciphertexts of the pivoted forms of the query and library vectors so as to compute an encrypted set of vector differences between the query vector and each of the library vectors.