一個高效率架構用於標準基底乘法器與反元運算在大域GF(2^163)

An Efficient Architecture for Using Standard Basis Multiplier and Inverse Operation in large field GF(2^163)

10.6343/ISU.2014.00334

莊水淶

反元器 ； 霍納法 ； ECC ； Inverse ； Horner Rule

義守大學資訊工程學系學位論文

2014年

碩士

陳延華

繁體中文

本論文將提出標準基底之有限體乘法器與反元器的架構，在標準基底有限體的運算中，乘法運算與反元運算是最耗時的，小域有限體可以利用建表法取代其複雜的運算，GF(2^163)所需要建的表過於龐大，還是得經過運算。因為GF(2^163)的有限體乘法的運算很複雜，本論文提出分組運算的架構，將163位元分為8個位元一組，將複雜的有限體乘法運算簡化為20次簡單的多項式運算。結合本論文新提出之乘法器與新的分解方法，發展為新的反元器架構。

This thesis presents a new two architecture for multiplication and inverse over GF(2^163) based on standard basis. A straight LUT-based multiplication requires memory of size for the Galois field of order 163 which is quite large for the fields by the National Institute of Standards and Technology (NIST). Therefore, one proposed a restriction the digit-size to 8 to design of multiplier that the result of the computing can be obtained only iterations 20 times operation, which is very much useful with respect to Network security issue that is needs high-speed applications. Moreover, this thesis is about improvement of inversion that is a part of ECC encryption system using the new proposed multiplier and factoring new method to improve the hardware architecture of inverse.