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Efficient characteristic 3 Galois field operations for elliptic curve cryptographic applications

机译：椭圆曲线密码应用的高效特性3 Galois现场运算

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摘要

Galois fields of characteristic 3, where the number of field elements is a power of 3, have a distinctive application in building high-security elliptic curve cryptosystems. However, they are not typically used because of their relative inefficiency in computing polynomial operations when compared to conventional prime or binary Galois fields. The purpose of this research was to design and implement characteristic 3 Galois field arithmetic algorithms with greater overall efficiency than those presented in current literature, and to evaluate their applicability to elliptic curve cryptography. The algorithms designed were tested in a C++ program and using a mapping of field element logarithms, were able to simplify the operations of polynomial multiplication, division, cubing, and modular reduction to that of basic integer operations. They thus significantly outperformed the best characteristic 3 algorithms presented in literature and showed a distinct applicability to elliptic curve cryptosystems. In conclusion, this research presents a novel method of optimizing the performance of characteristic 3 Galois fields and has major implications for the field of elliptic curve cryptography.
机译：特征3的Galois场（场元素的数量为3的幂）在构建高安全性椭圆曲线密码系统中具有独特的应用。但是，由于与常规素数或二进制Galois字段相比，它们在计算多项式运算中相对效率低下，因此通常不使用它们。这项研究的目的是设计和实现3种Galois特征算术算法，其总体效率要高于当前文献中提出的算法，并评估其在椭圆曲线密码学中的适用性。设计的算法在C ++程序中进行了测试，并使用字段元素对数的映射，能够将多项式乘法，除法，求和和模数化的运算简化为基本整数运算。因此，它们明显优于文献中提出的最佳特征3算法，并显示了对椭圆曲线密码系统的独特适用性。总之，本研究提出了一种优化特征3 Galois场性能的新颖方法，对椭圆曲线密码学领域具有重要意义。

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