Disclosed herein are systems, computer-implemented methods, and computer-readable media for authentication using a shared table. The method receives an authentication challenge from a first entity including an accumulator with an initial value, lists of elements in a shared table, and a list of sorting algorithms, each sorting algorithm is associated with one of the lists of elements and modified to include embedded instructions operating on the accumulator. The method then generates a temporary table for each list of elements in the shared table by copying elements from the shared table as indicated in each respective list of elements, each temporary table being associated with one sorting algorithm in the list of sorting algorithms. The method sorts each generated temporary table with the associated sorting algorithm, thereby updating the accumulator with the embedded instructions. Finally, the method transmits the updated accumulator to the first entity for verification.