Element Replication via Cumulative Addition

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Solution Overview

Problem

Conventional techniques require O(N) times and O(log N) stages of multiplication to replicate an element in a set, which is inefficient for secure computation, especially when dealing with ordered elements.

Innovation Solution

The method involves creating a second set by setting replication source elements to their differences and setting other elements to zero, and then using cumulative addition to replicate elements in a third set, reducing the calculation cost by leveraging small addition operations instead of multiplication.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If conventional multiplication methods are used to replicate elements in a set, then the replication can be achieved, but the calculation cost is high requiring O(N) times and O(log N) stages of multiplication

Engineering Contradiction:

Improveelement replication efficiencyVSAvoidcalculation cost

Core Design Contradiction:

ProductivityVSPower

Solution Approach 1:

The patent changes the operational parameter from multiplication to addition. By transforming the replication operation into cumulative addition using the formula b(i) = b(i-1) + a5(i), the calculation complexity is reduced from O(N) multiplication stages to O(N) addition operations, significantly improving replication efficiency while reducing computational power requirements

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent creates a simplified copy representation a5 where only replication source elements have non-zero values and other elements are set to zero. This sparse copy structure enables efficient cumulative addition to propagate replication values through the set, avoiding the need for complex multiplication operations while maintaining replication accuracy

Inventive Principle:

Principle #26Copying

2Manufacturing precision

If multiplication operations are performed to replicate elements, then the replication is accurate, but the number of calculation stages increases to O(log N)

Engineering Contradiction:

Improvereplication accuracyVSAvoidcalculation time

Core Design Contradiction:

Manufacturing precisionVSLoss of time

Solution Approach 1:

The patent substitutes the multiplication mechanical operation with addition operation. By using cumulative addition b(i) = b(i-1) + a5(i) instead of multiplication, the patent maintains replication accuracy while reducing the number of calculation stages from O(log N) multiplication stages to a single pass of O(N) addition operations, thereby reducing calculation time

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentEP3096308B1Element replication device, element replication method, and program

Publication Date: 2019.09.25 NIPPON TELEGRAPH & TELEPHONE CORP

Figure 1
Figure 2A~2C
Figure 3A~3B

AI summary

A second set including a plurality of elements a5(1), ..., a5(N) or a concealed text of the second set is obtained, where the second set is obtained by setting a replication source element a(f(h)) included in a first set to an element a(f(h))-a(f(h-1)) and setting elements other than the replication source in the first set to zero with respect to h=2, ..., M. An additive inverse of a replication source element a(f(h-1)) of which the order is before the replication source element a(f(h)) and is the closest to the replication source element a(f(h)) is -a(f(h-1)). The second set or the concealed text of the second set is used to obtain a third set or a concealed text of the third set. The third set is a set including a first element b(1)=a5(1) and i=2, ..., Nth element b(i)=b(i-1)+a5(i).