Modular Multiplier Carry Prediction for Montgomery Multiplication
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Solution Overview
Problem
The RSA cryptography system's performance is hindered by the increasing number of calculations required for large key sizes, particularly in modular operations, which leads to operation time delays due to carry propagation in high radix Montgomery modular multiplication.
Innovation Solution
A modular multiplier apparatus that predicts long path carry using a medium calculation result, reducing the critical path of arithmetic operations by employing a reduction unit, a carry predictor, and an accumulator to efficiently handle modular multiplication with reduced carry propagation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If high radix Montgomery modular multiplication is used to increase operation speed, then productivity is improved, but carry propagation delay increases causing operation time to increase
Solution Approach 1:
The patent applies preliminary action by predicting the long path carry (LPC) value in advance using the medium calculation result before the final addition is completed. The carry predictor unit calculates LPC based on the medium calculation result (Si-1 + BiA) obtained during the arithmetic operation, allowing the carry value to be prepared beforehand rather than waiting for complete carry propagation through all k-bit positions.
Solution Approach 2:
The patent introduces an intermediary approach by using the medium calculation result as a basis for predicting the long path carry. Instead of directly computing the final result and then determining carry, the patent uses the intermediate medium calculation result (Si-1 + BiA) to predict LPC, which then feeds into the final accumulator to produce the result. This intermediary prediction mechanism breaks the sequential carry propagation chain.
2Productivity
If radix exponent is increased to improve operation speed, then productivity is improved, but device complexity increases due to complicated quotient determination procedure
Solution Approach 1:
The patent extracts the complicated quotient determination procedure from the critical path of the arithmetic operation. By using the pipeline method and predicting LPC based on the medium calculation result, the complex quotient determination is separated from the main multiplication flow. The system determines quotient q_i based on the predicted LPC and medium calculation result rather than through complex iterative procedures, simplifying the overall device structure while maintaining high radix operation speed.
Data Source
AI summary
Provided are a modular multiplier apparatus in which a value of a long path carry (LPC) is predicted to reduce a critical path of an arithmetic operation of Montgomery modular multiplication, and a method of reducing the critical path of the arithmetic operation. The modular multiplier apparatus for obtaining a quotient and a result of an arithmetic operation of modular multiplication by using a modulus and two arbitrary constants includes: a reduction unit for obtaining a short path carry (SPC) included when a result of a modular arithmetic operation is obtained at a current stage, by using a medium calculation result; a carry predictor for predicting a long path carry (LPC) included when the result of the modular arithmetic operation is obtained at the current stage, by using the medium calculation result; and an accumulator for accumulating the result of the modular arithmetic operation by using the SPC and the LPC, wherein the medium calculation result is obtained by adding a result of a modular arithmetic operation obtained at a previous stage and a partial product of the two constants obtained at the current stage.