Shared Secret Re-Sharing Using Blinding Shares and Threshold Updates

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Solution Overview

Problem

Existing methods fail to efficiently generate new shares of a shared secret without altering the shared secret itself, replace compromised or lost shares, or adjust the threshold of participants required to reconstruct the shared secret, particularly in scenarios involving shared private keys.

Innovation Solution

A computer-implemented method involving a first participant generating a blinding share and obtaining intermediary shares from other participants to create new secret shares based on these and the blinding share, allowing for the generation of new shares that can increase or decrease the number of participants with valid shares, replace compromised shares, and change the threshold.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If new shares of a shared secret are generated using existing methods, then the shared secret can be updated, but the shared secret itself is altered in the process

Engineering Contradiction:

Improveability to generate new sharesVSAvoidintegrity of shared secret

Core Design Contradiction:

Adaptability or versatilityVSStability of the object's composition

Solution Approach 1:

The patent introduces a blinding secret as an intermediary element that mediates the share generation process. Each participant generates a blinding share and combines it with their existing secret share to create a new secret share. The blinding secret acts as a mediator that transforms the old shares into new shares without revealing or altering the underlying shared secret, thus resolving the contradiction between generating new shares and maintaining secret integrity

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent changes the parameter space by introducing blinding factors that operate in a separate mathematical domain. The blinding shares are generated using cryptographic parameters that are independent of the original shared secret parameters. This parameter separation allows the transformation of shares without affecting the core shared secret, enabling share updates while preserving secret stability

Inventive Principle:

Principle #35Parameter changes

2Reliability

If compromised shares are replaced, then security is improved, but the process requires complex coordination among participants

Engineering Contradiction:

Improvesecurity of shared secretVSAvoidcomplexity of share replacement process

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent enables each participant to independently generate their own blinding share and compute their new secret share autonomously. Each participant uses their existing secret share combined with their privately generated blinding share to create their new share. This self-service approach eliminates the need for complex centralized coordination during the share replacement process, reducing system complexity while maintaining security

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent segments the share replacement process into independent individual operations. Instead of requiring a coordinated group operation, each participant's share replacement is segmented into their own independent computation using their private blinding share. This segmentation allows parallel execution of share replacements without inter-dependency, simplifying the overall process complexity

Inventive Principle:

Principle #1Segmentation

3Adaptability or versatility

If the threshold of participants is changed, then the system becomes more adaptable, but the reconstruction process becomes more complex

Engineering Contradiction:

Improveflexibility of thresholdVSAvoidcomplexity of reconstruction process

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent creates a universal share structure where each new secret share is designed to work with any threshold configuration. The blinding share mechanism produces shares that are mathematically compatible with both the original threshold and new threshold requirements. This universality allows the same share structure to serve multiple threshold configurations without requiring separate reconstruction protocols for each threshold level

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS12542658B2Method of generating shares of a shared secret

Publication Date: 2026.02.03 NCHAIN LICENSING AG

AI summary

A computer-implemented method of generating shares of a shared secret, wherein each of a group of participants has a respective first secret share of the shared secret, wherein the method is performed by a first participant of the group and comprises: generating a respective blinding share of a shared blinding secret, obtaining at least a threshold number of respective intermediary shares from each of the first group of participants, wherein each respective intermediary share is generated based on a respective blinding share and a respective first secret share; generating an intermediary value based on each of the obtained intermediary shares; and generating a respective second secret share of the shared secret, wherein the respective second secret shared is generated based on the intermediary value and the respective blinding share.