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有限域上的模逆运算是许多公钥密码系统使用的算法中的核心域运算之一。该文对现有的素数域GF(p)上的模逆算法进行了改进和优化,得到了适合软硬件实现的快速算法,尤其利于快速高效的超大规模集成电路(VLSI)实现。改进后的新算法运算简单,只需用普通加减法操作,不需要模运算和任何操作数的乘法或除法,其全部运算的完成仅需一个加法器。该文同时给出了新算法的一个VLSI实现,结果显示新算法的硬件实现在速度和资源开销两方面均具有良好特性。
Modulo-inverse operations on finite fields are one of the core domain operations in the algorithms used by many public-key cryptosystems. This paper improves and optimizes the modulo-inverse algorithm in the existing prime field GF (p), and obtains a fast algorithm suitable for hardware and software implementation, especially for fast and efficient realization of very large scale integrated circuit (VLSI). The new algorithm is simple to operate. It only needs to be operated by normal addition and subtraction. It does not need the multiplication or division of the modulo operation and any operand. All the operations need only one adder. This paper also gives a VLSI implementation of the new algorithm. The results show that the hardware implementation of the new algorithm has good characteristics both in speed and resource overhead.