Obfuscation & Functional Encryption

Status	Statement	Tags
	No expanding weak quadratic PRGs Open: whether every family of quadratic Λ(n)-bounded polynomials at stretch m ≥ n^{1+ε} admits an efficient distinguisher from the same evaluations plus bounded independent noise; the paper proves only the i.i.d.-nice special case (Theorem 2) and reports, without proof, that no degree-two candidate survives its attacks experimentally. 3 open	Average Case Hardness Pseudorandom Generatorsimpossibility
	iO Overhead, Single-Output The first of the source’s named main open problems. Its main theorem gives an Omega(s/log s) additive overhead lower bound for iO on multi-output circuits under NP not in BPP – an assumption that is minimal, since a zero-overhead scheme exists if NP is in BPP. The single-output case is not covered, and the source says why: its route runs through NP-hardness of Multi-MCSP. 4 open	Black Box Separations Minimum Circuit Size Problem One Way Functionslower-boundbarrier (ai)
	Blockwise-random quadratic recovery Open: whether there is a polynomial-time algorithm that provably recovers the planted input from m = n^{1+eps} published quadratics of the blockwise-random (Lin-Matt) form, sum of a random sparse (perfect-matching) part and an independent random dense part. The paper proves this for i.i.d.-nice polynomial distributions (Theorem 2) but the blockwise-random distribution is not nice, and reports only experimental recovery via a modified semidefinite program. 5 open	Average Case Hardness Pseudorandom Generatorsassumption