Network coding over the 232−5 prime field

Creating efficient finite field implementations has been an active research topic for several decades. Many applications in areas such as cryptography, signal processing, erasure coding and now also network coding depend on this research to deliver satisfactory performance. In this paper we investigate the use of prime fields with a field size of 2³² - 5, as this allows implementations which combines high field sizes and low complexity. First we introduce the algorithms needed to apply prime field arithmetics to arbitrary binary data. After this we present the initial throughput measurements from a benchmark application written in C++. These results are finally compared to different binary and binary extension field implementations. The results show that the prime field implementation offers a large field size while maintaining a very good performance. We believe that using prime fields will be useful in many network coding applications where large field sizes are required.