Minimal Symmetric PAKE and 1-out-of-N OT from Programmable-Once Public Functions

Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); optimal round complexity: a single flow (one message from each party that can be sent in parallel) to achieve implicit authentication, or two flows to achieve explicit mutual authentication; security in the random oracle model, rather than ideal cipher or generic group model; UC security, rather than game-based. Our protocol is a generalization of the seminal EKE protocol of Bellovin & Merritt (S&P 1992). We also present a UC-secure 1-out-of-N oblivious transfer (OT) protocol, for random payloads. Its communication complexity is independent of N, meaning that N can even be exponential in the security parameter. Such a protocol can also be considered a kind of oblivious PRF (OPRF). Our protocol improves over the leading UC-secure 1-out-of-N OT construction of Masny & Rindal (CCS 2019) for all N>2, and has essentially the same cost for N=2. The new technique underlying these results is a primitive we call programmable-once public function (POPF). Intuitively, a POPF is a function whose output can be programmed by one party on exactly one point. All other outputs of the function are outside of any party's control, in a provable sense.