Paper 2024/1815

Succinct Randomized Encodings from Non-compact Functional Encryption, Faster and Simpler

Abstract

Succinct randomized encodings allow encoding the input $x$ of a time-$t$ uniform computation $M(x)$ in sub-linear time $o(t)$. The resulting encoding $\tilde{x}$ allows recovering the result of the computation $M(x)$, but hides any other information about $x$. Such encodings are known to have powerful applications such as reducing communication in MPC, bootstrapping advanced encryption schemes, and constructing time-lock puzzles. Until not long ago, the only known constructions were based on indistinguishability obfuscation, and in particular they were not based on standard post-quantum assumptions. In terms of efficiency, these constructions' encoding time is $\rm{polylog}(t)$, essentially the best one can hope for. Recently, a new construction was presented based on Circular Learning with Errors, an assumption similar to the one used in fully-homomorphic encryption schemes, and which is widely considered to be post-quantum resistant. However, the encoding efficiency significantly falls behind obfuscation-based scheme and is $\approx \sqrt{t} \cdot s$, where $s$ is the space of the computation. We construct, under the same assumption, succinct randomized encodings with encoding time $\approx t^{\varepsilon} \cdot s$ for arbitrarily small constant $\varepsilon<1$. Our construction is relatively simple, generic and relies on any non-compact single-key functional encryption that satisfies a natural {\em efficiency preservation} property.