Protecting Secrets with Shamir's Method

Dividing the Secret

• We use a technique called Shamir's Secret Sharing to split the secret key into multiple parts.

• These parts, known as "shares," are distributed among the nodes in the cluster.

Reconstruction with Threshold Access

• To reconstruct the original key, a predetermined number of shares must be combined.

• This means that even if some shares are lost or some nodes become unavailable, the key can still be securely rebuilt as long as enough shares are present.

Shamir's Secret Sharing

Technical Implementation

The system implements Shamir's method using:

1. Polynomial Generation

   • Creates a random polynomial of degree t-1

   • The secret is embedded as the constant term

   • Coefficients are randomly generated

2. Share Distribution

   • Each node receives a point on the polynomial

   • Requires t shares to reconstruct (threshold)

   • Shares are encrypted during transmission

3. Key Reconstruction

   • Uses Lagrange interpolation to recover the secret

   • Only possible with threshold number of shares

   • Mathematically secure against fewer shares