I refute the 1995 dream XOR lemma conjecture by Goldreich, Nisan, and Wigderson. I also give a counterexample to the XOR lemma for low-degree polynomials.

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The hardness of the Learning Parity with Noise (LPN) problem is a foundational assumption in cryptography, forming the basis of constructions ranging from symmetric-key primitives to public-key encryption and beyond. A central open question is whether the average-case hardness of LPN can be based on worst-case complexity assumptions, as has ... more >>>

Weighted pseudorandom generators (wPRGs) were suggested by Braverman, Cohen, and Garg (STOC, 2018) as a relaxation of pseudorandom generator (PRG) used for derandomization.
We present proofs of several observations regarding wPRGs, where some of these observations are well known.

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