An Additive Randomized Encoding (ARE) for a distributed function f(x1,...,xn) reduces the task of securely computing f to computing the sum of locally encoded inputs.
Previous works construct AREs for simple functions such as OR with perfect security but imperfect correctness (namely, the decoder has an incorrect output with small probability), and AREs for general functions with both imperfect correctness and security.
This leaves open the existence of ARE for nontrivial functions with perfect correctness, i.e. where the sum of encodings is always decoded correctly to the function's output. We made progress on these questions, obtaining negative results.