\(\displaystyle \textsf{HERatio}\) : Homomorphic Encryption of Rationals Using Laurent Polynomials

In this work we present \(\displaystyle \textsf{HERatio}\) , a homomorphic encryption scheme that builds on the scheme of Brakerski, and Fan and Vercauteren. Our scheme naturally accepts Laurent polynomials as inputs, allowing it to work with rationals via their bounded base-b expansions. This eliminates the need for a specialized encoder and streamlines encryption, while maintaining comparable efficiency to BFV. To achieve this, we introduce a new variant of the Polynomial Learning With Errors (PLWE) problem which employs Laurent polynomials instead of the usual “classic” polynomials, and provide a reduction to the PLWE problem.