Network coding over the 232−5 prime field
Network coding over the 232−5 prime field
复制标题
232−5 素数域上的网络编码
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
F. Fitzek
中科院分区：
文献类型：
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作者：
M. Pedersen;J. Heide;P. Vingelmann;F. Fitzek
几十年来，创建高效的有限域实现一直是一个活跃的研究课题。密码学、信号处理、擦除编码以及网络编码等领域的许多应用都依赖于这项研究来提供令人满意的性能。在本文中，我们研究了域大小为232 - 5的素数域的使用，因为这允许实现高域大小和低复杂性的结合。首先，我们介绍了将素域算法应用于任意二进制数据所需的算法。在此之后，我们给出了用c++编写的基准测试应用程序的初始吞吐量测量结果。最后将这些结果与不同的二进制和二进制扩展字段实现进行了比较。结果表明，prime字段实现在提供大字段大小的同时保持了非常好的性能。我们相信，在许多需要大字段大小的网络编码应用程序中，使用素数字段将是有用的。
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.