Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi JACM 2018) offer a general model for
deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional proof systems. A major approach for lower bounding the size of IPS refutations is the Functional Lower Bound ... more >>>

A locally decodable code (LDC) is an error correcting code that allows for recovery of any desired bit in the message based on a constant number of randomly selected bits in the possibly corrupted codeword.
A relaxed LDC requires correct recovery only in case of actual codewords, while requiring that ... more >>>

In this work, we study the worst-case to average-case hardness of the Learning with Errors problem (LWE) under an alternative measure of hardness - the maximum success probability achievable by a probabilistic polynomial-time (PPT) algorithm. Previous works by Regev (STOC 2005), Peikert (STOC 2009), and Brakerski, Peikert, Langlois, Regev, Stehle ... more >>>