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Electronics and Telecommunications Research Institute (한국전자통신연구원)
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Efficient Computation of Eta Pairing over Binary Field with Vandermonde Matrix

  • Shirase, Masaaki (School of Systems Information Science, Future University Hakodate) ;
  • Takagi, Tsuyoshi (School of Systems Information Science, Future University Hakodate) ;
  • Choi, Doo-Ho (Software & Content Research Laboratory, ETRI) ;
  • Han, Dong-Guk (Software & Content Research Laboratory, ETRI) ;
  • Kim, Ho-Won (Department of Computer Engineering Information, Pusan National University)
  • Received : 2008.05.31
  • Accepted : 2008.12.24
  • Published : 2009.04.30
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Abstract

This paper provides an efficient algorithm for computing the ${\eta}_T$ pairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy a modified multiplication in $F_{2^{4n}}$ using the Vandermonde matrix. For F, G ${\in}$ $F_{2^{4n}}$ the proposed multiplication method computes ${\beta}{\cdot}F{\cdot}G$ instead of $F{\cdot}G$ with some ${\beta}$ ${\in}$ $F^*_{2n}$ because ${\beta}$ is eliminated by the final exponentiation of the ${\eta}_T$ pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in $F_{2^n}$ as n ${\rightarrow}$ ${\infty}$, while the cost of the previously fastest Karatsuba method is 9 multiplications in $F_{2^n}$. Consequently, the cost of the ${\eta}_T$ pairing computation is reduced by 14.3%.

Keywords

Acknowledgement

Grant : Development of the Technology of Side Channel Attack Countermeasure Primitives and Security Validation

Supported by : IITA

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