The subject invention relates to a method and apparatus for multiplication of numbers. In a specific embodiment, the subject invention can be used to perform sequential multiplication. The subject invention also pertains to a method and apparatus for modular reduction processing of a number or product of two numbers. In a specific embodiment, sequential multiplication can be incorporated to perform modular reduction processing. The subject method and apparatus can also be utilized for modular exponentiation of large numbers. In a specific embodiment, numbers larger than or equal to 2.sup.128 or even higher can be exponentiated. For example, the subject invention can be used for exponentiation of number as large as 2.sup.1024, 2.sup.2048, 2.sup.4096, or even larger.