1. A computer-implemented method comprising: receiving, in a peer-to-peer network, multiple sets of numerical residuals generated in accordance with multiple corresponding prime numbers; determining, based on the prime numbers, whether the sets of numerical residuals are sufficient to recover information encoded by the sets of numerical residuals; and recovering the information, when the sets of numerical residuals are sufficient, from at least a portion of the sets of numerical residuals using at least a portion of the prime numbers.