Summary: We present in this talk an adaptation of the method of Barrett for modular arithmetic in the residue number system. First we briefly review the residue number system (RNS) for arithmetic of large integer and the state of the art for modular multiplication in RNS. We will then review and adapt to RNS the Barrett approach for modular reduction and multiplication. Finally, we will discuss some cases of interest related to scalar product and matrix multiplication modulo large integer and show some implementation results.
