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Hong, Hoon; Lee, Eunjeong; Lee, Hyang-Sook; Park, Cheol-Min

Simple and exact formula for minimum loop length in \(\mathrm{Ate}_{i }\) pairing based on Brezing-Weng curves. (English) Zbl 1271.94022

Des. Codes Cryptography 67, No. 2, 271-292 (2013).
The authors derive a formula for the minimum loop of the \(\mathrm{Ate}_i\) pairing based on some class of Brezing-Weng curves, namely Theorem 1 in the paper. Note that the \(\mathrm{Ate}_i\) pairing is one of the several pairings that have appeared in elliptic curve cryptography. The class of curves analyzed under the conditions of Theorem 1 in the paper covers almost all the interesting Brezing-Weng curves in cryptographic terms
Reviewer: Edgar Martinez-Moro (Soria)

Cited in 6 Documents

MSC:

94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)

Keywords:

pairing-based cryptosystem; elliptic curves; Miller algorithm

Software:

ECPP
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References:

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