Secure Conjugate Gradient Method Scaling Factor Overflow Prevention

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Solution Overview

Problem

The conjugate gradient method using a fixed-point number is prone to overflow during computation, which prevents the attainment of accurate results.

Innovation Solution

A secure conjugate gradient method computation system that employs a series of secure computation units to manipulate input values using a scaling factor D (|D| < 1) to keep intermediate values small, thereby reducing the likelihood of overflow.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If a fixed-point number is used in the conjugate gradient method, then the computational cost is reduced, but the probability of overflow increases

Engineering Contradiction:

Improvecomputational costVSAvoidoverflow probability

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent applies preliminary action by pre-multiplying intermediate computation values by a scaling factor D (where |D| < 1) before they can grow too large. This proactive scaling prevents overflow from occurring in the first place, while still allowing the use of fixed-point arithmetic to maintain low computational cost.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent changes the parameter of intermediate values by introducing a scaling factor D that multiplies these values during computation. This parameter change ensures that values remain within the representable range of fixed-point numbers, preventing overflow while maintaining computational efficiency.

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If a floating-point number is used in secure computation, then the computational accuracy is maintained, but the computational cost increases significantly

Engineering Contradiction:

Improvecomputation accuracyVSAvoidcomputational cost

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The patent changes the numerical representation parameter from floating-point to fixed-point arithmetic in secure computation. By配合 with the scaling factor D, this parameter change maintains sufficient computational accuracy while dramatically reducing the computational cost associated with floating-point operations in secure computation protocols.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentEP3982350B1Secret conjugate gradient method calculation system, secret calculation device, conjugate gradient method calculation device, secret conjugate gradient method calculation method, conjugate gradient method calculation method, and program

Publication Date: 2023.12.13 NIPPON TELEGRAPH & TELEPHONE CORP

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AI summary

An initialization unit (12) generates secret values of vectors p→0 and r→0 and a value ρ0. A first computation unit (13) generates a secret value of a D-fold value of a vector a→i-1.A second computation unit (14) generates a secret value of a D-fold value of a value γi-1. A third computation unit (15) generates a secret value of a value αi-1. A fourth computation unit (16) generates a secret value of a D-fold value of a vector d→i. A fifth computation unit (17) generates a secret value of a vector x→i. A sixth computation unit (18) generates a secret value of a vector r→i. A seventh computation unit (19) generates a secret value of a D-fold value of a value ρi. An eighth computation unit (20) generates a secret value of a value βi. A ninth computation unit (21) generates a secret value of a vector p→i.