Homomorphic Encryption with Coset Code Construction

Abstract

Homomorphic encryption enables computation on input data without decrypting it. This paper extends a construction based on scalar message codes, utilizing coset codes to pack $k$ message symbols into a ciphertext vector of length $n$. For a given field and vector length, this packing method reduces the number of ciphertext vectors required to transmit a message record. A compatible family of evaluation codes supports public addition and multiplication operations up to a predetermined degree. We prove that the scheme achieves bounded chosen-plaintext security under the coordinate-label distinguishability assumption.