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Lee, Chin Ho; Viola, Emanuele

doi:10.4086/toc.2017.v013a016

Cited by 3 publications

References 39 publications

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Correlated Pseudorandom Functions from Variable-Density LPN

Boyle

Couteau

Gilboa

et al. 2020

2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)

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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.

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Correlated Pseudorandom Functions from Variable-Density LPN

Boyle

Couteau

Gilboa

et al. 2020

2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)

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Certified Hardness vs. Randomness for Log-Space

Pyne,

Raz,

Zhan

2023

2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)

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Bounded Independence Plus Noise Fools Products

Haramaty¹,

Lee²,

Viola³

2018

SIAM J. Comput.

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Let D be a b-wise independent distribution over {0, 1} m. Let E be the "noise" distribution over {0, 1} m where the bits are independent and each bit is 1 with probability η/2. We study which tests f : {0, 1} m → [−1, 1] are ε-fooled by D + E, i.e., | E[f (D + E)] − E[f (U)]| ≤ ε where U is the uniform distribution. We show that D + E ε-fools product tests f : ({0, 1} n) k → [−1, 1] given by the product of k bounded functions on disjoint n-bit inputs with error ε = k(1 − η) Ω(b 2 /m) , where m = nk and b ≥ n. This bound is tight when b = Ω(m) and η ≥ (log k)/m. For b ≥ m 2/3 log m and any constant η the distribution D + E also 0.1-fools log-space algorithms. We develop two applications of this type of results. First, we prove communication lower bounds for decoding noisy codewords of length m split among k parties. For Reed-Solomon codes of dimension m/k where k = O(1), communication Ω(ηm) − O(log m) is required to decode one message symbol from a codeword with ηm errors, and communication O(ηm log m) suffices. Second, we obtain pseudorandom generators. We can ε-fool product tests f : ({0, 1} n) k → [−1, 1] under any permutation of the bits with seed lengths 2n +Õ(k 2 log(1/ε)) and O(n) + O(nk log 1/ε). Previous generators have seed lengths ≥ nk/2 or ≥ n √ nk. For the special case where the k bounded functions have range {0, 1} the previous generators have seed length ≥ (n + log k) log(1/ε).

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Cited by 3 publications

References 39 publications

Correlated Pseudorandom Functions from Variable-Density LPN

Correlated Pseudorandom Functions from Variable-Density LPN

Certified Hardness vs. Randomness for Log-Space

Bounded Independence Plus Noise Fools Products

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