An Efficient (n, k) Information Dispersal Algorithm for High Code Rate System over Fermat Fields

The (n, k) information dispersal algorithm (IDA) is the art of converting a file into n pieces of shadows, and any k out of the n shadows suffice for reconstructing the file. The IDA is applicable to the distributed communication and storage systems. This letter proposes an efficient (n, k) IDA for the case n/2≤k<;n over Fermat field GF(2^r+1). We first present the IDA under conditions of n-k in the power of 2 and n as multiple of n-k, and then extend the algorithm to the general case. For a reasonably large file, both encoder and decoder achieveΘ(nlog(n-k)) operations in processing k symbols.