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genpark-shamir-secret-sharing-polynomial-recovery-skill

mcp
Guvenlik Denetimi
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SUMMARY

Shamir's (k, n) threshold secret sharing scheme with Lagrange polynomial interpolation over prime fields

README.md

Shamir's (k, n) Secret Sharing Skill

High-efficiency, zero-dependency Python implementation of Shamir's (k, n) Threshold Secret Sharing.

Features

  • Information-Theoretic Security: Any (k - 1) shares reveal zero information regarding the underlying secret.
  • Lagrange Interpolation: Reconstructs secret in (O(k^2)) modular operations over Mersenne prime (2^{127} - 1).
  • Zero External Dependencies: Pure Python standard library (secrets).
  • Native MCP Protocol: JSON-RPC 2.0 stdio server compatible with Claude Desktop, Cursor, and Windsurf.

Architecture

graph TD
    Secret["Master Secret S"] --> Poly["Random Polynomial f(x) = S + a1*x + ... + ak-1*x^(k-1)"]
    Poly --> S1["Share (1, f(1))"]
    Poly --> S2["Share (2, f(2))"]
    Poly --> S3["Share (3, f(3))"]
    S1 & S2 & S3 --> Interp["Lagrange Interpolation at x=0"]
    Interp --> Secret

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