Pseudorandom Correlation Functions

Primitives that let two parties expand short correlated keys into unbounded correlated pseudorandomness on demand, and the generators (PCGs) they extend – the machinery behind silent secure computation.

Status	Statement	Tags
	Subexponential-query PCF from sparse LPN Open in both directions, and the source paper poses it as a question rather than conjecturing an answer; the affirmative direction is this page’s reading. The one follow-up construction from sparse LPN inherits the same superpolynomial ceiling and says so. 6 open	Learning Parity With Noise Pseudorandom Correlation Functions Random Oracle Modelromassumption
	Standard-model weak PCF from sparse LPN Open, posed by the source as its second open question with an obstruction it names explicitly; the affirmative direction is this page’s reading. An independent follow-up construction reports the same random oracle as inherent to the same recursion. 6 open	Learning Parity With Noise Pseudorandom Correlation Functions Random Oracle Modelassumption
	EA-Code Distance over Rings Theorem 3.10 of the source proves the distance bound over F_2 only. Over a ring of size q its proof technique forces the rate to satisfy R much less than 1/ln q, which the source states it believes is an artefact of the argument, supported by small-parameter weight-distribution experiments over F_17 and Z_16. 5 open	Code Based Cryptography Dual Distance Learning Parity With Noise Pseudorandom Correlation Functionslower-boundadaptation (ai)
	Quasi-Abelian GV, Growing Group Named as a conjecture by the source, which says the development is out of reach of the article. It is what makes the choice of group free in the QA-SD line: resistance to every linear test, for any abelian G, reduces to it. Partially advanced in 2026 by concrete non-asymptotic bounds for particular groups, which restate the general question as open. 5 open	Code Based Cryptography Dual Distance Pseudorandom Correlation Functions Syndrome Decodinglower-boundadaptation (ai)