Correlated Pseudorandom Functions from Variable-Density LPN

Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Lisa Kohl, Peter Scholl

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review


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 {k {0}}(x), f {k {1}}(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 text{AC}{0}[ oplus] 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) text{AC}{0}[ oplus] 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.

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
EditorsSandy Irani
Number of pages12
Publication dateNov 2020
Article number9317926
ISBN (Electronic)9781728196213
Publication statusPublished - Nov 2020
Event61st Annual IEEE Symposium on Foundations of Computer Science - Durham, United States
Duration: 16 Nov 202019 Nov 2020


Conference61st Annual IEEE Symposium on Foundations of Computer Science
Country/TerritoryUnited States
Internet address


  • Cryptography, Secure computation, Learning theory, Pseudorandom functions


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