2005
Generating prime degree irreducible polynomials by using irreducible all-one polynomial over F-2
ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE
- ,
- ,
- Volume
- 88
- Number
- 7
- First page
- 23
- Last page
- 32
- Language
- English
- Publishing type
- DOI
- 10.1002/ecjc.20151
- Publisher
- SCRIPTA TECHNICA-JOHN WILEY & SONS
In most of the methods of public key cryptography devised in recent years, a finite field of a large order is used as the field of definition. In contrast, there are many studies in which a higher-degree extension field of characteristic 2 is fast implemented for easier hardware realization. There are also many reports of the generation of the required higher-degree irreducible polynomial, and of the construction of a basis suited to fast implementation, such as an optimal normal basis (ONB). For generating higher-degree irreducible polynomials, there is a method in which it 2m-th degree self-reciprocal irreducible polynomial is generated from an m-th degree irreducible polynomial by a simple polynomial transformation (called the self-reciprocal transformation). This paper considers this transformation and shows that When the set of zeros of the m-th degree irreducible polynomial forms a normal basis, the set of zeros of the generated 2m-th order self-reciprocal irreducible polynomial also forms a normal base. Then it is clearly shown that there is a one-to-one correspondence between the transformed irreducible polynomial and the generated self-reciprocal irreducible polynomial. Consequently, the inverse transformation of the self-reciprocal transformation (self-reciprocal inverse transformation) can be applied to a self-reciprocal irreducible polynomial. It is shown that an m-th degree irreducible polynomial can always be generated from a 2m-th degree self-reciprocal irreducible polynomial by the self-reciprocal inverse transformation. We can use this fact for generating 1/2-degree irreducible polynomials. As an application of 1/2-degree irreducible polynomial generation, this paper proposes a method which generates a prime degree irreducible polynomial with a Type II ONB as its zeros. (c) 2005 Wiley Periodicals, Inc.
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- DOI
- https://doi.org/10.1002/ecjc.20151
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000228097900003&DestApp=WOS_CPL
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- https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=17144362464&origin=inward
- Scopus Citedby
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- ID information
-
- DOI : 10.1002/ecjc.20151
- ISSN : 1042-0967
- SCOPUS ID : 17144362464
- Web of Science ID : WOS:000228097900003