Password-Based Secret Sharing for Secure Fixed Share Selection
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing secret sharing schemes lack the ability to securely select predetermined fixed shares without compromising security or usability, particularly in mobile device settings where key protection and flexible access control are essential.
Innovation Solution
The development of password-based secret sharing schemes that allow for the secure selection of predetermined fixed shares by adjusting polynomial coefficients in threshold and generic secret sharing schemes, ensuring both security and usability by incorporating user-defined values and auxiliary information for reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If predetermined fixed shares are selected in secret sharing schemes, then usability and flexible reconstruction policies are improved, but security of the underlying secret sharing scheme deteriorates
Solution Approach 1:
The secret is divided into multiple shares using polynomial-based secret sharing schemes, where each share contains only a portion of the secret information. This segmentation ensures that no single share reveals the complete secret, maintaining security while enabling flexible reconstruction policies where different combinations of shares can reconstruct the secret according to predefined access structures.
Solution Approach 2:
The patent modifies the polynomial coefficients in the secret sharing scheme to incorporate predetermined fixed values while maintaining the mathematical properties that ensure security. By carefully selecting and constraining specific polynomial coefficients based on fixed shares, the scheme allows usability improvements without compromising the fundamental security guarantees of the underlying cryptographic construction.
2Adaptability or versatility
If polynomial coefficients are set to depend on fixed values and secret, then flexible reconstruction policies are enabled, but complexity of the secret sharing scheme increases
Solution Approach 1:
The patent pre-determines certain polynomial coefficients based on fixed shares during the setup phase, before actual secret sharing occurs. This preliminary configuration enables flexible reconstruction policies to be embedded in the scheme structure itself, reducing the need for complex runtime decisions while maintaining adaptability for different reconstruction scenarios.
Solution Approach 2:
The scheme incorporates dynamic elements where polynomial coefficients can be selectively adjusted or constrained based on the desired reconstruction policy. This allows the system to adapt between different access structures and reconstruction requirements without requiring complete redesign, balancing flexibility with manageable complexity through parameterized configurations.
Data Source
AI summary
Methods and apparatus are provided for password-based secret sharing. An exemplary method comprises obtaining a secret; obtaining a fixed value from at least one party; setting at least one polynomial coefficient of a polynomial employed by a polynomial-based secret sharing scheme to a value that depends on the fixed value and the secret; and applying the polynomial-based secret sharing scheme to the secret to obtain a plurality of secret shares, wherein the plurality of secret shares comprises at least one fixed share derived from the at least one polynomial coefficient. Another exemplary secret sharing method comprises selecting at least one fixed share of a plurality of shares employed by an additive secret sharing scheme that splits the secret into the plurality of shares needed for reconstruction of the secret, wherein the at least one fixed share depends on the fixed value; and setting at least one masked version of the secret employed by the additive secret sharing scheme, wherein the at least one masked version of the secret depends on the at least one fixed share.