1. A computer-implemented process for reducing the data size of polynomial-based fully homomorphically encrypted data, the computer-implemented process comprising: executing, by one or more processing machines in a device, programmatic code stored in a memory of the device to perform operations, the operations comprising: receiving a ciphertext at the device, the ciphertext corresponding to a public key and a plaintext polynomial bound to a message space of a polynomial-based fully homomorphic cryptographic scheme; performing a homomorphic multiplication operation using a set of at least two processing cores that support at least one of integer and finite field arithmetic, in parallel, on the ciphertext at the device to obtain a resultant ciphertext by: performing a bitwise decomposition function on the ciphertext to obtain a bitwise decomposed ciphertext, the bitwise decomposition function mapping a multi-bit data type to a sequence of bits; and performing matrix multiplication on the bitwise decomposed ciphertext and a data element that accords with an inverse bitwise decomposition of the ciphertext, the inverse bitwise decomposition mapping a sequence of bits to the multi-bit data type; outputting the resultant ciphertext.