Architectures for Montgomery´s multiplication

Many public key cryptographic algorithms require modular multiplication of very large operands as their core arithmetic operation. One method to perform this operation reasonably fast is to use specialised hardware. However, larger sizes are often required to increase security. This comes at the expense of either reducing the clock rate or dramatically increasing the size and hence the cost of the system. Therefore, techniques that allow efficient and fast computation of this operation at the algorithmic level are desired. An algorithm/structure for the computation of Montgomery´s modular multiplication is presented. The modified algorithm splits the original algorithm into two multiplication operations, which can be executed in parallel. The derived architectures can be pipelined to the bit-level by interleaving multiple modular multiplication operations onto the same structure.