| 摘要: |
| 有限域的运算已经广泛应用于Reed—Solomon码、存储领域和各种加密算法中。乘法运算是其中最复杂的一种运算，有限域中的元素可以用各种基表示。文中在给出有限域元素自然基下的表示方法的基础上，推导出了域元素正则基下的表示方法，并给出了正则基下域元素的乘法运算，编写了乘法器的VHDL模型。用XILINX公司的ISE5．2软件对电路模型进行了仿真，结果表明乘法器的运算结果完全正确。 |
| 关键词: Reed-Solomon码 有限域 乘法器 自然基 正则基 VHDL语言 |
| DOI：10.3969/j.issn.1001-893X. |
| Received:February 27, 2006Revised:August 07, 2006 |
| 基金项目:华北电力大学校科研和教改项目 |
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| VHDL-based Design of a Normal Basis Multiplier in Galois Field |
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| Abstract: |
| The arithmetic operations in Galois field is central in the implementation of Reed - Solomon coders , storage and cryptographic algorithms . Multiplication is the most complicated arithmetic operation in Galois field . The elements in Galois field can be represented in several kinds of basis. In this paper , a Galois field elements are represented first by a polynomial basis. Then its elements are represented by a normal basis , and multiplication operation circuit model is presented in VHDL , which is very suited for use in VLSI systems. Finally, the circuit model is simulated by XILINX ISE 5.2, and the simulation result is correct. |
| Key words: Reed - Solomon code Galois field multiplier polynomial basis normal basis VHDL |
