Shamir Secret Sharing Share Generation Device Communication Optimization
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Solution Overview
Problem
Secure computation devices using Shamir's secret sharing scheme face a significant increase in communication data when distributing shares among N devices, resulting in N times the amount of data of the plaintext, leading to inefficient data transmission.
Innovation Solution
Each share generating device applies Lagrange coefficients to reconstruct shares, reducing the total share size by dividing the share into N shares, and transmitting only the necessary calculated values, thereby minimizing the total amount of communication data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If shares are distributed among N secure computation devices using Shamir's secret sharing scheme, then secure computation can be performed, but the total amount of communication data increases to N times the amount of plaintext
Solution Approach 1:
The patent segments the traditional Shamir's secret sharing scheme into two distinct phases: a share generation phase that creates initial shares, and a share conversion phase that transforms these shares into compact representation shares. This segmentation allows the system to maintain the security properties of the original scheme while reducing communication overhead by only transmitting the compact representation shares (which are smaller than the original shares) between devices during secure computation operations.
Solution Approach 2:
The patent changes the parameter representation of shares by introducing a mathematical transformation that converts traditional Shamir shares into a compact representation. This parameter change involves expressing shares in terms of a generator element and discrete logarithms, where the compact representation stores only the essential cryptographic parameters rather than the full share data, thereby reducing communication data while preserving the ability to perform secure computations.
2Reliability
If traditional Shamir's secret sharing shares are transmitted without change, then security is maintained, but communication efficiency decreases due to large data size
Solution Approach 1:
The patent creates a cryptographic copy or representation of the original shares that preserves their security properties while occupying less space. The compact representation shares are mathematically equivalent to the original shares in terms of security guarantees, but they use a compressed format that reduces communication bandwidth requirements while maintaining the ability to reconstruct the secret through secure computation operations.
Data Source
AI summary
A share [x]i of plaintext x in accordance with Shamir's secret sharing scheme is expressed by N shares [x0]i, . . . , [xN−1]i, and each share generating device Ai obtains a function value ri=Pm(i(−))(si) of a seed si, obtains a first calculated value ζi=λ(i, i(−))[xi(−)]i+ri using a Lagrange coefficient λ(i, i(−)), a share [xi(−)]i, and the function value ri, and outputs the first calculated value ζi to a share generating device Ai(−). Each share generating device Ai accepts a second calculated value ζi(+), obtains a third calculated value zi=λ(i, i(+))[xi]i+ζi(+) using a Lagrange coefficient λ(i, i(+)), a share [xi]i, and the second calculated value ζi(+), and obtains information containing the seed si and the third calculated value zi as a share SSi of the plaintext x in secret sharing and outputs the share SSi.