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