TY - GEN

T1 - Efficient pairings on twisted elliptic curve

AU - Nogami, Yasuyuki

AU - Sakemi, Yumi

AU - Akane, Masataka

AU - Morikawa, Yoshitaka

PY - 2008

Y1 - 2008

N2 - This paper proposes an efficient implementation of Ate pairing on twisted elliptic curve. Suppose that a pairing-friendly elliptic curve E has a twisted elliptic curve E′ of degree d, and let Ψd be an isomorphic map from E′ (double struck F signpe) to the corresponding subgroup of E(double struck F signpk). Then, consider double struck G sign′1 = Ψd -1(double struck G sign1) and double struck G sign′2 = Ψd-1(double struck G sign2) for double struck G sign1, double struck G sign2 at Ate pairing α. Let P ∈ double struck G sign 1, Q ∈ double struck G sign2, P′ ∈ double struck G sign′1 and Q′ ∈ double struck G sign′2, the authors have shown α(Q, P) = f t-1,Q,(P)(pk - 1)/r = ft-1,Q′(P′) (pk - 1)/r. This paper shows that this new Ate pairing, namely cross twisted (Xt) Ate pairing, provides an quite efficient implementation.

AB - This paper proposes an efficient implementation of Ate pairing on twisted elliptic curve. Suppose that a pairing-friendly elliptic curve E has a twisted elliptic curve E′ of degree d, and let Ψd be an isomorphic map from E′ (double struck F signpe) to the corresponding subgroup of E(double struck F signpk). Then, consider double struck G sign′1 = Ψd -1(double struck G sign1) and double struck G sign′2 = Ψd-1(double struck G sign2) for double struck G sign1, double struck G sign2 at Ate pairing α. Let P ∈ double struck G sign 1, Q ∈ double struck G sign2, P′ ∈ double struck G sign′1 and Q′ ∈ double struck G sign′2, the authors have shown α(Q, P) = f t-1,Q,(P)(pk - 1)/r = ft-1,Q′(P′) (pk - 1)/r. This paper shows that this new Ate pairing, namely cross twisted (Xt) Ate pairing, provides an quite efficient implementation.

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U2 - 10.1109/ICCIT.2008.172

DO - 10.1109/ICCIT.2008.172

M3 - Conference contribution

AN - SCOPUS:57849134187

SN - 9780769534077

T3 - Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

SP - 430

EP - 439

BT - Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

T2 - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

Y2 - 11 November 2008 through 13 November 2008

ER -