Chapter 1: Problem Background and Core Challenges
1.1 What Is Secret Addition
In secure multi-party computation (MPC), two parties (Alice and Bob) each hold a secret share of a binary number and wish to compute the sum of the two numbers without revealing the plaintext of either operand. Here, “secret share” refers to Boolean secret sharing: a bit x is split into two shares x₁ and x₂ such that x = x₁ ⊕ x₂, where ⊕ denotes the XOR operation. Alice holds x₁, Bob holds x₂, and each party’s share alone is a uniformly random bit from which the true value of x cannot be inferred.
