Recursive double-size fixed precision arithmetic

TL;DR

This paper introduces RecInt, a recursive double-size fixed precision arithmetic designed for secure, reconfigurable hardware, with a software library comparable to GMP and FPGA implementation potential.

Contribution

It presents a novel recursive data structure for fixed precision arithmetic that is efficient on both software and FPGA hardware.

Findings

Software library performance comparable to GMP

Efficient FPGA implementation of recursive integers

Recursive doubling technique for fixed size arithmetic

Abstract

This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture).