Publications

Recently, Boyle, Jain, Servan-Schreiber, and Srinivasan (EUROCRYPT’25) introduced the notion of simultaneous-message and succinct (SMS) secure computation. In an SMS protocol, after an initial sampling of a common reference string (CRS), two parties — Alice (with a large input) and Bob (with a small input) — can simultaneously exchange encodings of their private inputs and obtain additive shares of the output of a function evaluated over their inputs. The key requirement is succinctness: namely, the size of the CRS and each input encoding grows only poly-logarithmically in the size of Alice's input and the function output. Boyle et al., and independently Abram, Malavolta, and Roy (STOC’25), constructed SMS for all bounded-depth Boolean circuits from the plain learning with errors (LWE) assumption.

In this work, we extend the study of SMS along two new dimensions:

• Reusable SMS: In this setting, the same input encodings can be reused to compute multiple functions.

• Multiparty SMS: In the multiparty setting, we consider computations over one large input and multiple small inputs. Succinctness in this case means the size of the CRS and input encodings can grow with the total length of the small inputs (but polylogarithmically with the length of the long input and the size of the function output).

Assuming polynomial hardness of LWE (with a sub-exponential modulus-to-noise ratio), we construct reusable two-party SMS for all bounded-depth Boolean circuits with polylogarithmic communication. By additionally assuming indistinguishability obfuscation, we present a generic compiler from reusable two-party SMS to reusable multiparty SMS.