OPTIMIZATION TECHNIQUE FOR MODULAR MULTIPLICATION ALGORITHMS

Methods and apparatus for optimization techniques for modular multiplication algorithms. The optimization techniques may be applied to variants of modular multiplication algorithms, including variants of Montgomery multiplication algorithms and Barrett multiplication algorithms. The optimization techniques reduce the number of serial steps in Montgomery reduction and Barrett reduction. Modular multiplication operations involving products of integer inputs A and B may be performed in parallel to obtain a value C that is reduced to a residual RES. Modular multiplication and modular reduction operations may be performed in parallel. The number of serial steps in the modular reductions are reduced to L, where L serial steps, where w is a digit size in bits, and L is a number of digits of operands=[k/w].