The present disclosure provides a system and method for performing modular exponentiation. The method may include dividing a first polynomial into a plurality of segments and generating a first product by multiplying the plurality of segments of the first polynomial with a second polynomial. The method may also include generating a second product by shifting the contents of an accumulator with a factorization base. The method may further include adding the first product and the second product to yield a first intermediate result and reducing the first intermediate result to yield a second intermediate result. The method may also include generating a public key based on, at least in part, the second intermediate result. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.