  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).
