Montgomery Multiplication Device With Reduced Interdependencies

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Solution Overview

Problem

Existing Montgomery multiplication techniques in cryptographic systems require a large number of processing cycles due to computational interdependencies, leading to inefficiencies in performing modular multiplications, especially when dealing with large numbers.

Innovation Solution

The technique involves precomputing auxiliary numbers associated with the modulus and Montgomery radix, computing quotients in a first stage, and using these quotients in a second stage to efficiently compute the final output, reducing interdependencies and optimizing the number of processing cycles by performing most additions concurrently with multiplications.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If traditional Montgomery multiplication is used, then the multiplication operation can be performed, but the processing cycles are excessive due to computational interdependencies

Engineering Contradiction:

Improveprocessing cyclesVSAvoidcomputational interdependencies

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The Montgomery multiplication process is divided into multiple independent stages: precomputation of auxiliary numbers, computation of quotient values, and final result computation. Each stage can be executed independently without waiting for the completion of previous stages, thereby eliminating computational interdependencies and reducing total processing cycles from 4n+5 to 5n.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Auxiliary numbers are precomputed and stored before the main multiplication operation. These auxiliary numbers (including Montgomery radix values and precomputed coefficients) are prepared in advance and can be directly used during the multiplication process, eliminating the need for real-time computation of these values and reducing overall processing time.

Inventive Principle:

Principle #10Preliminary action

2Productivity

If the number of multiplication circuits is reduced, then hardware resource usage decreases, but the processing efficiency may be affected

Engineering Contradiction:

Improvehardware circuitry utilizationVSAvoidnumber of multiplication circuits

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The computation is segmented into stages that can be executed by a limited number of multiplication circuits. By dividing the work into precomputation, quotient computation, and final computation stages, the system can achieve high hardware utilization with fewer circuits, as each circuit remains busy across different stages without requiring all circuits to operate simultaneously.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent ensures continuous utilization of multiplication circuits by pipeline the computation stages. While one set of circuits computes quotient values, another set can simultaneously compute auxiliary products, and a third set handles final accumulation. This continuous action maximizes hardware utilization without requiring a large number of circuits.

Inventive Principle:

Principle #20Continuity of useful action

Data Source

PatentUS20230244445A1Techniques and devices for efficient montgomery multiplication with reduced dependencies

Publication Date: 2023.08.03 NVIDIA CORP

AI summary

Disclosed are apparatuses, systems, and techniques to perform and facilitate fast and efficient modular computational operations, such as Montgomery multiplication with reduced interdependencies, using optimized processing resources.