Notes on SMPC, based on "An Introduction to Secret-Sharing-Based Secure Multiparty Computation" by D. Escudero. These are simply notes and not original content. Since this is based off of Daniel's book, I do not dive deep into each topic, instead I provide my own general introductory notes and leave it at that.

  1. The Theory of Multiparty Computation 1.1 A General Introduction to MPC 1.1.1 Adversaries and their Power Possible Corrupted Sets Type of Corruption 1.1.2 Privacy Guarantees 1.1.3 Output Guarantees 1.1.4 Different Functions to be Computed Public-Output vs Private-Output Reactive vs Non-Reactive Functionalities General vs Special-Purpose MPC 1.1.5 Efficiency Metrics 1.2 Simulation-Based Security 1.2.1 High-Level Idea 1.2.2 Interactive Agents Relevant Interactive Agents in the UC Framework 1.2.3 Interactive Systems Relevant Interactive Systems in the UC Framework Parameterized Interactive Systems 1.2.4 Security Definition Perfect Security Statistical Security Computational Security 1.2.5 The Composition Theorem 1.2.6 Some Basic Functionalities Underlying Communication Resource Arithmetic Black Box Model 1.3 Fundamental Results 1.3.1 Results for tn 1.3.2 Results for tn The Case of a Passive Adversary The Case of an Active Adversary 1.3.3 Positive Results for tn< 1.3.4 Summary of Main Results
  2. Secret-Sharing-Based MPC 2.1 Linear Secret-Sharing Schemes 2.2 MPC based on Linear Secret-Sharing Schemes 2.2.1 The Case of an Active Adversary
  3. Discussions on Honest Majority
  4. Discussions on Dishonest Majority
  5. 2.2.2 Offline-Online Paradigm