文章基本信息

标题：Fast Three-Input Multipliers over Small Composite Fields for Multivariate Public Key Cryptography
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作者：Haibo Yi ; Weijian Li
期刊名称：International Journal of Security and Its Applications
印刷版ISSN：1738-9976
出版年度：2015
卷号：9
期号：9
页码：165-178
DOI：10.14257/ijsia.2015.9.9.15
出版社：SERSC
摘要：Since quantum computer attacks will be threats to the current public key cryptographic systems, there has been a growing interest in Multivariate Public Key Cryptography (MPKC), which has the potential to resist such attacks. Finite field multiplication is playing a crucial role in the implementations of multivariate cryptography and most of them use two-input multipliers. However, there exist multiple multiplications of three elements in multivariate cryptography. This motivates our work of designing three-input multipliers, which extend the improvements on multiplication of three elements in three directions. First, since multivariate cryptography can be implemented over small composite fields, our multipliers are designed over such fields. Second, since it requires multiplications of two and three elements, our multipliers can execute both of them. Third, our multipliers adapt table look-up and polynomial basis, since they are faster over specific fields, respectively. We demonstrate the improvement of our design mathematically. We implement our design on a Field-Programmable Gate Array (FPGA), which shows that our design is faster than other two-input multipliers when computing multiplication of three elements, e.g. multiplier with field size 256 is 28.4% faster. Our multipliers can accelerate multivariate cryptography and mathematical applications, e.g. TTS is 14% faster.
关键词：Three-input multiplier; Composite field; Finite field; Table look-up; ; Polynomial basis; Gaussian elimination; Solving systems of linear equations; Multivariate ; Public Key Cryptography (MPKC); Field-Programmable Gate Array (FPGA)