Abstract
This paper presents a new modular multiplication algorithm developed to remove division-based denormalization. In modular multiplication algorithms, the modular reduction estimates an intermediate quotient by referring to the most significant bits of the intermediate remainder since the modulus is scaled up, however, the modular multiplication results in an enlarged value that should be denormalized at the end. The denormalization has been realized by employing a division operation, which is not an efficient way in the view point of hardware implementation and processing cycles. The proposed modular multiplication is based on the scaled-modular multiplication which replaces the division-based denormalization with the Montgomery modular reduction. As a result, the hardware complexity is reduced compared to the up-to-date modular multiplication architecture.
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