Yes-and-No Secret Sharing With Hidden Access and Participant Deniability

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Solution Overview

Problem

Existing secret sharing schemes with yes and no shares are vulnerable to exploitation due to publicly known threshold access structures, allowing unauthorized reconstruction by combining sufficient yes shares, and lack participant deniability.

Innovation Solution

Implementing a secret sharing scheme with hidden access structures where yes and no shares are indistinguishable, using a random basis for vector spaces to generate shares, and a reconstruction algorithm that ensures only minimal authorized subsets can reconstruct the secret, maintaining deniability and secrecy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If a publicly known threshold access structure is used in secret sharing, then any threshold number of participants can reconstruct the secret, but the scheme becomes vulnerable to exploitation where unauthorized parties can discard no shares and combine yes shares to reconstruct the secret

Engineering Contradiction:

Improvesecret reconstruction reliabilityVSAvoidunauthorized exploitation

Core Design Contradiction:

ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The access structure information is extracted from the public domain and embedded within the secret sharing scheme itself. Each participant receives shares that encode access structure information, allowing the system to maintain reliability while preventing unauthorized exploitation by making the access structure hidden rather than public

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The scheme changes the parameter of access structure visibility from public to hidden. By encoding access structure information within the shared secrets and shares themselves, the system transforms the accessibility parameter while maintaining the functional requirement that authorized subsets can reconstruct the secret

Inventive Principle:

Principle #35Parameter changes

2Reliability

If yes shares are distributed to participants for secret reconstruction, then authorized subsets can reconstruct the secret, but participants lose deniability about whether they possess valid shares

Engineering Contradiction:

Improvesecret reconstruction capabilityVSAvoidparticipant deniability

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The scheme merges the yes share and no share into a unified share structure where both types of shares have identical mathematical forms and distributions. This merging allows participants to maintain deniability about whether their share is a yes share or no share, while the reconstruction algorithm can still reliably identify valid yes shares through algebraic verification

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The reconstruction algorithm acts as an intermediary that receives shares without knowing whether they are yes shares or no shares. The algorithm uses algebraic verification to mediate between the hidden share types and the reconstruction outcome, preserving participant deniability while ensuring reliable secret reconstruction

Inventive Principle:

Principle #24Intermediary (Mediator)

3Ease of operation

If the access structure is publicly known, then participants know which subsets can reconstruct the secret, but the scheme lacks access structure hiding security

Engineering Contradiction:

Improveparticipant knowledge of access structureVSAvoidaccess structure hiding

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

Instead of making the access structure public and relying on participant knowledge, the scheme inverts the approach by making the access structure hidden and embedded within the shares. The reconstruction algorithm inverts the traditional model by verifying share validity algebraically rather than relying on public access structure information

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS12438705B2Yes and no secret sharing with hidden access structures

Publication Date: 2025.10.07 SEAGATE TECH LLC

AI summary

A secret sharing scheme with yes and no shares and having a hidden access structure. The secret sharing scheme may include share generation in which yes shares and no shares are generated for, and distributed to, each party in the secret sharing scheme. In turn, upon an attempt to reconstruct the secret, participants in the reconstruction each provide a share, which is unknown to be a yes share or a no share to the other participants. The secret is only reconstructable if the shares used in the reconstruction include yes shares of a minimal authorized subset of the parties. However, prior to secret reconstruction, the access structure remains hidden and the participants in a reconstruction are unaware of the character of the shares provided by other participants in the reconstruction attempt.