Secret Key Distribution via Nested Shamir Sharing
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Solution Overview
Problem
Existing methods for distributing secret keys in homomorphically encrypted messages often incur high communication costs due to the large number of partial secret keys required, which can lead to resource wastage and security risks if decrypted temporarily.
Innovation Solution
An electronic device and method utilizing a t-out-of-N secret sharing scheme, specifically Shamir's secret sharing scheme of s-out-of-(2s−1), to efficiently segment and distribute secret keys, reducing communication costs by generating and transmitting secret shares across N electronic devices while ensuring security through error inclusion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a traditional secret sharing scheme is used to distribute secret keys, then security is improved by segmenting the secret key into multiple parts, but communication cost increases due to the large number of partial secret keys that must be transmitted
Solution Approach 1:
The secret key is segmented into multiple secret shares using Shamir's secret sharing scheme, where the secret key is divided into s shares such that any t shares can reconstruct the secret key. This segmentation allows secure distribution while controlling communication overhead by optimizing the number of shares transmitted.
Solution Approach 2:
The patent applies nested secret sharing by recursively applying the secret sharing scheme multiple times. The secret key is first divided into shares at level 1, then each share is further divided into shares at level 2, and so on up to level L. This nested structure allows efficient communication by transmitting only the necessary shares at each level while maintaining security.
2Reliability
If more partial secret keys are distributed to ensure security, then reliability improves, but device complexity increases due to the larger number of keys to manage
Solution Approach 1:
The secret key management is segmented into hierarchical levels where the secret key is divided into shares at multiple levels. This segmentation reduces the number of keys each device must manage at any given time, as devices only need to store and manage their specific shares at their assigned levels rather than all possible partial keys.
Solution Approach 2:
The patent introduces a hierarchical dimension to secret key management by organizing shares into multiple levels (level 1 to level L). This dimensional organization allows complex key management to be structured in a tree-like hierarchy, simplifying the operational complexity at each node while maintaining overall security through the multi-level structure.
Data Source
AI summary
Disclosed is an electronic device which distributes secret keys by using a t-out-of-N secret sharing scheme. The electronic device includes: a communication device; a memory storing the secret key; and a processor configured to generate a plurality of secret shares corresponding to a level of 1 by segmenting the secret key corresponding to a level of zero based on a predetermined secret sharing scheme, generate a plurality of secret shares corresponding to a level of L by repeatedly performing a process of generating a plurality of secret shares corresponding to a next level by segmenting the plurality of secret shares each corresponding to the respective levels ranging from the level of 1 based on the predetermined secret sharing scheme, and transmit the plurality of secret shares corresponding to the level of L to N electronic devices through the communication device.