From Split Randomized Fuzzy Equality to fPAKE The Randomized Fuzzy‌ Sample Clauses

From Split Randomized Fuzzy Equality to fPAKE The Randomized Fuzzy‌. RFE Equality (RFE) functionality FP assumes authenticated channels, which an fPAKE protocol cannot do. In order to adapt RFE to our setting, we use the split functionality transformation defined by Barak et al. [BCL+05]. Barak et al. provide a generic transfor- mation from protocols which require authenticated channels to protocols which do not. In the “transformed” protocol, an adversary can engage in two separate instances of the protocol with the sender and receiver, and they will not realize that they are not talk- ing to one another. However, it does guarantee that the adversary cannot do anything 5 This is used in the argument of indistinguishability of Games G2 and G3 in Appendix C. The functionality sF is parameterized by a security parameter λ. It interacts with an adver- RFE sary S and two parties P0 and P1 via the following queries: – Initialization • Upon receiving a query (Init, sid) from a party Pi ∈ {P0, P1}, send (Init, sid, Pi) • Upon receiving a query (Init, sid, Pi, H, sidH ) from the adversary S: to the adversary S. ∗ Verify that H ⊆ {P0, P1}, that Pi ∈ H, and that if a previous set Hj was recorded, and sidH = sidHt . ∗ If verification fails, do nothing. either (1) H ∩ Hj contains only corrupted parties and sidH ƒ= sidHt , or (2) H = Hj ∗ Otherwise, record the pair (H, sidH ) (if it was not already recorded), output (Init, sid, sidH ) to Pi, and locally initialize a new instance of the original RFE func- tionality F denoted HF RFE P RFE in HF . P , letting the adversary play the role of {P0, P1} − H – 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 the query. P