Paper 2020/1417

Correlated Pseudorandom Functions from Variable-Density LPN

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


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 $\mathsf{AC}^0[\oplus]$ 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) $\mathsf{AC}^0[\oplus]$ 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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Major revision. FOCS 2020
correlated randomnesspseudorandom correlation functionslearning parity with noiseweak pseudorandom functions
Contact author(s)
eboyle @ alum mit edu
couteau @ irif fr
niv gilboa @ gmail com
yuvali @ cs technion ac il
lisa kohl @ cwi nl
peter scholl @ cs au dk
2020-11-15: received
Short URL
Creative Commons Attribution


      author = {Elette Boyle and Geoffroy Couteau and Niv Gilboa and Yuval Ishai and Lisa Kohl and Peter Scholl},
      title = {Correlated Pseudorandom Functions from Variable-Density {LPN}},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1417},
      year = {2020},
      note = {\url{}},
      url = {}
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