Two-round UC OT ⇒ Two-round MPC in the CRS model (Garg–Srinivasan)

Free reduction · CRS model · GS18

Statement

If a two-message OT protocol secure against malicious adversaries exists in the common reference string model, every functionality has a two-round protocol in that model, over the broadcast channel, that is secure with abort against a malicious adversary corrupting any number of parties (two-round MPC) — GS18. With both rounds over the broadcast channel the abort is unanimous, as CGZ20 restate. A two-round UC-secure OT is such a protocol, since UC security implies stand-alone malicious security — Can01.

Notes

• In the common reference string model, $k$-round semi-malicious OT together with NIZK gives $k$-round malicious UC MPC for every $k\ge 2$ — BL18.
• Assuming two-round OT in the common reference string model, CGZ20 determine, for each combination of broadcast and point-to-point rounds, which of selective, unanimous and identifiable abort two-round MPC achieves against any number of malicious parties; their impossibility results hold for any correlated randomness — CGZ20.
• Two-message UC-secure OT in the common reference string model follows from DDH, QR or LWE (DDH ⇒ two-round UC-secure OT) — PVW08 — and from CDH or LPN (CDH ⇒ two-round UC-secure OT), which gives two-round malicious MPC under CDH or LPN — DGHMW20.
• Two rounds also suffice from LWE and NIZK arguments (LWE + NIZK ⇒ two-round MPC) — MW16.