Analysis and Construction of Galois Fields for Efficient Storage Reliability

Software-based Galois field implementations are used in the reliability and security components of many storage systems. Unfortunately, multiplication and division operations over Galois fields are expensive, compared to the addition. To accelerate multiplication and division, most software Galois field implementations use pre-computed look-up tables, accepting the memory overhead associated with optimizing these operations. However, the amount of available memory constrains the size of a Galois field and leads to inconsistent performance across architectures. This is especially problematic in environments with limited memory, such as sensor networks.