TY - GEN

T1 - An efficient residue group multiplication for the η T pairing over

AU - Sasaki, Yuta

AU - Nishina, Satsuki

AU - Shirase, Masaaki

AU - Takagi, Tsuyoshi

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2009

Y1 - 2009

N2 - When we implement the η T pairing, which is one of the fastest pairings, we need multiplications in a base field and in a group G. We have previously regarded elements in G as those in to implement the η T pairing. Gorla et al. proposed a multiplication algorithm in that takes 5 multiplications in , namely 15 multiplications in . This algorithm then reaches the theoretical lower bound of the number of multiplications. On the other hand, we may also regard elements in G as those in the residue group in which βa is equivalent to a for and . This paper proposes an algorithm for computing a multiplication in the residue group. Its cost is asymptotically 12 multiplications in as m → ∞, which reaches beyond the lower bound the algorithm of Gorla et al. reaches. The proposed algorithm is especially effective when multiplication in the finite field is implemented using a basic method such as shift-and-add.

AB - When we implement the η T pairing, which is one of the fastest pairings, we need multiplications in a base field and in a group G. We have previously regarded elements in G as those in to implement the η T pairing. Gorla et al. proposed a multiplication algorithm in that takes 5 multiplications in , namely 15 multiplications in . This algorithm then reaches the theoretical lower bound of the number of multiplications. On the other hand, we may also regard elements in G as those in the residue group in which βa is equivalent to a for and . This paper proposes an algorithm for computing a multiplication in the residue group. Its cost is asymptotically 12 multiplications in as m → ∞, which reaches beyond the lower bound the algorithm of Gorla et al. reaches. The proposed algorithm is especially effective when multiplication in the finite field is implemented using a basic method such as shift-and-add.

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U2 - 10.1007/978-3-642-05445-7_23

DO - 10.1007/978-3-642-05445-7_23

M3 - Conference contribution

AN - SCOPUS:70549104843

SN - 3642054439

SN - 9783642054433

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 364

EP - 375

BT - Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers

T2 - 16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009

Y2 - 13 August 2009 through 14 August 2009

ER -