An Efficient $(n,k)$ Information Dispersal Algorithm Based on Fermat Number Transforms

The (n,k) information dispersal algorithm (IDA) is a coding technique converting a digital source file into n small digital files (shadows), and the receipt of any k out of the n shadows can losslessly reconstruct the source file. This paper presents an encoding and two decoding algorithms of (n,k) IDA via the fast Fermat number transform (FNT). The proposed encoding algorithm requires O(nlog k) arithmetic operations, and the two decoding algorithms have complexities O(nlog k) and O(klog² k) for a reasonably large file. As compared with existing work, the proposed algorithms generate significant improvement in the throughput in the low code rate k/n ≤ 1/2 settings.