Paper 2012/693
Encoding Functions with Constant Online Rate or How to Compress Garbled Circuits Keys
Benny Applebaum, Yuval Ishai, Eyal Kushilevitz, and Brent Waters
Abstract
\emph{Randomized encodings of functions} can be used to replace a ``complex'' function $f(x)$ by a ``simpler'' randomized mapping $\hat{f}(x;r)$ whose output distribution on an input $x$ encodes the value of $f(x)$ and hides any other information about $x$. One desirable feature of randomized encodings is low \emph{online complexity}. That is, the goal is to obtain a randomized encoding $\hat{f}$ of $f$ in which most of the output can be precomputed and published before seeing the input $x$. When the input $x$ is available, it remains to publish only a short string $\hat{x}$, where the online complexity of computing $\hat{x}$ is independent of (and is typically much smaller than) the complexity of computing $f$. Yao's garbled circuit construction gives rise to such randomized encodings in which the online part $\hat{x}$ consists of $n$ encryption keys of length $\kappa$ each, where $n=x$ and $\kappa$ is a security parameter. Thus, the {\em online rate} $\hat{x}/x$ of this encoding is proportional to the security parameter $\kappa$. In this paper, we show that the online rate can be dramatically improved. Specifically, we show how to encode any polynomialtime computable function $f:\bit^n\to\bit^{m(n)}$ with online rate of $1+o(1)$ and with nearly linear online computation. More concretely, the online part $\hat{x}$ consists of an $n$bit string and a single encryption key. These constructions can be based on the decisional DiffieHellman assumption (DDH), the Learning with Errors assumption (LWE), or the RSA assumption. We also present a variant of this result which applies to {\em arithmetic formulas}, where the encoding only makes use of arithmetic operations, as well as several negative results which complement our positive results. Our positive results can lead to efficiency improvements in most contexts where randomized encodings of functions are used. We demonstrate this by presenting several concrete applications. These include protocols for secure multiparty computation and for noninteractive verifiable computation in the preprocessing model which achieve, for the first time, an optimal online communication complexity, as well as noninteractive zeroknowledge proofs which simultaneously minimize the online communication and the prover's online computation.
Metadata
 Available format(s)
 Category
 Foundations
 Publication info
 Published elsewhere. This is a long version for a Crypto 2013 paper.
 Keywords
 randomized encodinggarbled circuitsecure computationverifiable computationNIZK
 Contact author(s)
 bennyap @ post tau ac il
 History
 20150215: last of 3 revisions
 20121214: received
 See all versions
 Short URL
 https://ia.cr/2012/693
 License

CC BY
BibTeX
@misc{cryptoeprint:2012/693, author = {Benny Applebaum and Yuval Ishai and Eyal Kushilevitz and Brent Waters}, title = {Encoding Functions with Constant Online Rate or How to Compress Garbled Circuits Keys}, howpublished = {Cryptology {ePrint} Archive, Paper 2012/693}, year = {2012}, url = {https://eprint.iacr.org/2012/693} }