Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm

Yasuyuki NOGAMI  Shigeru SHINONAGA  Yoshitaka MORIKAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.5   pp.1200-1208
Publication Date: 2005/05/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.5.1200
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
extension field,  public-key cryptosystem,  fast implementation,  optimal extension field,  optimal normal basis,  

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This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF Fp5 is about 20% faster than those in OEF Fp5. Then, since CVMA is suitable for parallel processing, we show that TypeII AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.