An Efficient Circuit Clause Samples

An Efficient Circuit f for Hamming Distance‌ The Hamming distance of two pass-strings pw, pwj Fn is equal to the number of locations at which the two pass-strings have the same character. More formally, d(pw, pwj) := | {j | pw[j] pwj[j], j ∈ [n]} |. We design f for Hamming distance as follows: The functionality sF is parameterized by a security parameter λ. It interacts RFE with an adversary S and two parties P0 and P1 via the following queries: • Upon receiving a query (Init, sid) from a party Pi ∈ {P0, P1}, send • Upon receiving a query (Init, sid, Pi, H, sidH ) from the adversary (Init, sid, Pi) to the adversary S. ∗ Verify that H ⊆ {P0, P1}, that Pi ∈ H, and that if a previous set H was recorded, either (1) H ∩ Hj contains only corrupted parties and sidH ƒ= sidHt , or (2) H = Hj and sidH = sidHt . ∗ Otherwise, record the pair (H, sidH ) (if it was not already recorded), output (Init, sid, sidH ) to Pi, and locally initialize a new instance adversary play the role of {P , P } − H in HF . of the original RFE functionality F denoted HF , letting the RFE RFE 0 1 RFE • Upon receiving a query from a party Pi ∈ {P0, P1}, find the set H such that P ∈ H, and forward the query to HF . Otherwise, ignore RFE the query. • Upon receiving a query from the adversary S on behalf of Pi forward the query to HF . Otherwise, ignore the query. corresponding to set H, if HF RFE is initialized and Pi ƒ∈ H, then RFE RFE