The Noisy Linear Equations problem involves finding the solution to a random linear system over a finite field given noisy evaluations. This is a generalisation of various learning problems widely used in cryptography, including Learning with Errors (LWE), Learning with Rounding (LWR), and Learning Parity with Noise (LPN).

We present ... more >>>

Many hash-based proof systems check that committed words are close to Reed-Solomon codewords by testing one random combination of them. Their soundness analysis uses a proximity gap: if the combination agrees with a codeword on many positions, so do the original words, on the same positions, except for a few ... more >>>

Suppose there is an oracle $\mathcal{O}$ that computes a tiny fraction of the entries of the product of two uniformly random binary matrices over integers. We prove that there is a nearly linear-size randomized $\mathcal{O}$-oracle circuit that, with high probability, computes all the entries of the product of every pair ... more >>>