Chapter 3: Secret Sharing

Learning Objectives

• State the $(t, n)$-threshold secret-sharing problem and its information-theoretic security definition
• Construct Shamir's $(t, n)$-threshold scheme via polynomial evaluation and prove perfect secrecy
• Decode a Shamir secret from $t$ shares using Lagrange interpolation over a finite field
• Construct Blakley's hyperplane scheme and recognize its equivalence up to field size
• Analyze ramp $(t, t+g, n)$-secret sharing as a rate-security tradeoff, and quantify the share-size savings
• Connect secret sharing to coded matrix multiplication (Ch 5) and secure aggregation (Ch 10)