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

*Ian McQuoid and Mike Rosulek and Lawrence Roy*

**Abstract: **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.

**Category / Keywords: **cryptographic protocols / password-authenticated key exchange; oblivious transfer

**Original Publication**** (with minor differences): **ACM CCS 2020
**DOI: **10.1145/3372297.3417870

**Date: **received 28 Aug 2020

**Contact author: **rosulekm at eecs oregonstate edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20200828:161632 (All versions of this report)

**Short URL: **ia.cr/2020/1043

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