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Prologue

  • Secure 2-Party Computation
  • Secure Multi-Party Computation

Secure 2-Party Computation

SMC

Problem(informal)

A and B want to perform a fucntion f on their data. And they don't want others to know their data.

Types of Solution

  • General-purpose, e.g. Hash
  • Special-purpose, e.g. FHE

Solutions

Most general-purpose solutions are based on

  • Full Homomorphic Encryption
  • Circuit Based Solutions

Predicate-Revealing Symmetric Encryption

Equality-revealing and Order-revealing

Predicate-revealing symmetric encryption, a type of symmetric encryption where a certain predicate of encrypted plaintext(s) is revealed (even without the key)

Yao's Solution

GC + OT

If you want to know more about Yao's solution, just have a try to implement it:)

Mine implementation

This project also includes implementation of 2-Party GMW (X-Version).

Secure Multi-Party Computation

Problem(informal)

n parties have inputs ${X_1,...X_n}$, They want to perform fcuntion f over their inputs without leaking their inputs.

Application

  • Double auction
  • Statistics about compensation
  • Advertising conversion
  • MPC for cryptographic key protection
  • Government collaboration
  • Privacy-preserving analytics

Solutions

Solutions

Secret Sharing

Informal Definition:

n parties want to share a secret and only a subset of these n parties could recover it.

Constructions

we have n parties and we need t+1 parties to recover the secret s.

  • t=0
    • Everyone's share is s
  • t=n-1
    • generate n-1 random numbers ${r_1,r_2,...,r_{n-1}}$
    • the last share = $r_1 \oplus r_2 \oplus ... r_{n-1}\oplus s$
  • n-1>t>0
    • Shamir's Schem
    • only T+1 shares could confirm a unique T-degree polynomial

BGW Protocol

  • I don't understand the details and don't want to understand!

Circuit Compilers

That's a interesting topic, it tries to convert original representation algorithm to an intermediate representation. (Boolean circuit)

This part is an unfinished part of my SMC project. If I have enough time, I want to have a try!

More info: https://marsella.github.io/static/mpcsok.pdf