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Software implementation of finite fields of characteristic three, for use in pairing-based cryptosystems. (English) Zbl 1068.94012
Summary: In this paper, the authors examine a number of ways of implementing characteristic three arithmetic for use in cryptosystems based on the Tate pairing. Three alternative representations of the field elements are examined, and the resulting algorithms for the field addition, multiplication and cubing are compared. Issues related to the arithmetic of supersingular elliptic curves over fields of characteristic three are also examined. Details of how to compute the Tate pairing itself are not covered, since these are well documented elsewhere.

MSC:
94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14G50 Applications to coding theory and cryptography of arithmetic geometry
68P25 Data encryption (aspects in computer science)
68R01 General topics of discrete mathematics in relation to computer science
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References:
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[5] DOI: 10.2307/2007970 · Zbl 0559.10006
[6] DOI: 10.1109/18.259647 · Zbl 0801.94011
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[10] DOI: 10.1007/3-540-45455-1_26
[11] DOI: 10.1007/3-540-45682-1_29
[12] DOI: 10.1007/3-540-49649-1_6
[13] DOI: 10.1007/10722028_23
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.