Minimum linear code construction method, secret sharing method and secret sharing system

By constructing an encoding system and vector Boolean functions over a finite field, minimal linear codes and dual codes are generated, solving the security and computational complexity problems of existing linear code sharing methods. This enables flexible access control and efficient secret recovery, making it suitable for distributed storage and blockchain key management.

CN122268585APending Publication Date: 2026-06-23XI'AN UNIVERSITY OF ARCHITECTURE AND TECHNOLOGY
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Patent Information

Application Number
CN202610497247.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-04-15
Publication Date
2026-06-23

AI Technical Summary

Technical Problem

Existing secret sharing methods based on linear codes have security and consistency issues at the access structure level, cannot meet the minimumity criterion, have high computational complexity, and are difficult to adapt to the access control requirements of complex scenarios such as distributed storage and blockchain key management.

Method used

The coding system is constructed over a finite field. The trace function and vector Boolean function are defined. The vector Boolean function with a two-to-one mapping is constructed through the Walsh spectrum property. The linear code generation expression is embedded to generate three-weighted or five-weighted minimal linear codes, ensuring that the codeword set satisfies the minimality criterion. The dual code is used to achieve secret sharing.

Benefits of technology

It achieves stability and uniqueness of the minimumity criterion for linear codes, reduces computational complexity, supports flexible access structure configuration, improves security and consistency, is suitable for large-scale and computationally limited environments, and has good engineering scalability.

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Abstract

The invention belongs to the technical field of information security and coding theories, and provides a minimum linear code construction method, a secret sharing method and a secret sharing system.The method comprises the steps that a trace function is defined in a finite field, two-to-one mapping is constructed, a vector Boolean function of a Walsh spectrum taking a finite discrete value is constructed, a codeword set is defined on the basis of the function, and a minimum linear code is obtained; embedding an output trace function into a linear code generation expression, and generating a minimum linear code which is concentrated in weight and supports no strict inclusion; and establishing one-to-one correspondence between the participants and dual code coordinates and between the minimum code word support and the minimum access structure by using the dual codes of the participants, embedding secret generation share distribution, and recovering the secrets by the participants meeting the conditions through linear combination. The system comprises four functional modules, is adaptive to scenes of distributed storage, block chain key management and the like, and realizes safe, efficient and extensible secret sharing. The method can improve the security, efficiency and flexibility of secret sharing, is adaptive to multiple scenes, and is easy to expand.
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