Fast Modular Reduction

It is widely acknowledged that efficient modular multiplication is a key to high-performance implementation of public-key cryptography, be it classical RSA, Diffie-Hellman, or (hyper-) elliptic curve algorithms. In the recent decade, practitioners have relied mainly on two popular methods: Montgomery Multiplication and regular long-integer multiplication in combination with Barrett's modular reduction technique. In this paper, we propose a modification to Barrett's algorithm that leads to a significant reduction (25% to 75%) in multiplications and additions.