Correlated Pseudorandom Functions from Variable-Density LPN

Abstract

Correlated secret randomness is a useful resource for many cryptographic applications. We initiate the study of pseudorandom correlation functions (PCFs) that offer the ability to securely generate virtually unbounded sources of correlated randomness using only local computation. Concretely, a PCF is a keyed function F k such that for a suitable joint key distribution (k 0 , k 1 ), the outputs (f k0 (x), f k1 (x)) are indistinguishable from instances of a given target correlation. An essential security requirement is that indistinguishability hold not only for outsiders, who observe the pairs of outputs, but also for insiders who know one of the two keys.We present efficient constructions of PCFs for a broad class of useful correlations, including oblivious transfer and multiplication triple correlations, from a variable-density variant of the Learning Parity with Noise assumption (VDLPN). We also present several cryptographic applications that motivate our efficient PCF constructions.The VDLPN assumption is independently motivated by two additional applications. First, different flavors of this assumption give rise to weak pseudorandom function candidates in depth-2 AC 0 [⊕] that can be conjectured to have subexponential security, matching the best known learning algorithms for this class. This is contrasted with the quasipolynomial security of previous (higher-depth) AC 0 [⊕] candidates. We support our conjectures by proving resilience to several classes of attacks. Second, VDLPN implies simple constructions of pseudorandom generators and weak pseudorandom functions with security against XOR related-key attacks.

CrypTen: Secure Multi-Party Computation Meets Machine Learning

“…Specifically, some use cases may require malicious security or may not provide a TTP. Possible extensions may include support for malicious security via message authentication codes [23], as well as support for Beaver triple generation via additive homomorphic encryption [55], oblivious transfer [41], or more recent methods [10] to eliminate the need for a TTP.…”

Concretely efficient secure multi-party computation protocols: survey and more

“…Another style of OT extension protocols lies in the pseudorandom correlation generator (PCG) framework [162,254]. 3 In general, the PCG-style OT extension protocols [132,134,162,256] are able to generate COT correlations with sublinear communication (i.e., Õ( √ N ) for producing N COT correlations), but need more computation than IKNP-style protocols. To simplify the following description, we now give an informal definition of COT in a vector form.…”

“…Recently, Boyle et al [256] proposed the notion of pseudorandom correlation function (PCF), and gave an efficient PCF construction for generating COT correlations under a variable-density variant of the LPN assumption (VDLPN). While PCG only allows to generate a fixed length of correlated randomness (e.g., COT) in an all at once way and does not support the stateful incremental evaluation enabled by PRG in a "stream-cipher" mode, PCF can produce correlated randomness on-the-fly and offer the ability to securely generate virtually unbounded number of correlated randomness.…”

Indistinguishability obfuscation from well-founded assumptions

“…Recently, the LPN assumption has led to a wide variety of applications (see for example, [11,14,22,35,36,63,73,88]). A comprehensive review of known attacks on LPN over large fields, for the parameter settings we are interested in, was given in [35,37]. For our parameter setting, the running time of all known attacks is Ω(2 ℓ 1−𝛿 ), for any choice of the constant 𝛿 ∈ (0, 1) and for any polynomial number of samples 𝑛(ℓ).…”

“…We refer the reader to [35,37] for a comprehensive discussion of the history and security of this assumption.…”