A method for encoding encrypted data for further processing includes: receiving an input data vector of length m; splitting the input data vector to k multiple vectors; multiplying each of the multiple vectors by a power of 2 to obtain k number of intermediate vectors; summing the k number of intermediate vectors to obtain a single summed vector; encrypting the single summed vector to obtain an encrypted vector; sending the encrypted vector to an operational unit to have the encrypted vector operated on to obtain a processed encrypted vector; receiving the processed encrypted vector; decrypting the received encrypted vector; dividing the processed decrypted vector by a power of 2, modulus a power of 2 to obtain multiple transitional vectors of the same dynamic range and the same length; and concatenating the multiple transitional vectors to obtain a recovered vector of length m.