Efficient Pairings on Twisted Elliptic Curve

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 psi d be an isomorphic map from E'(F pc ) to the corresponding subgroup of E(F pk ). Then,consider...

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Bibliographic Details
Main Authors: Nogami, Y., Akane, M., Sakemi, Y., Morikawa, Y.
Format: Conference Proceeding
Language:English
Subjects:
Acceleration
Ate pairing
Authentication
Communication networks
Elliptic curve cryptography
Elliptic curves
implementation
Information technology
twist
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Summary: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 psi d be an isomorphic map from E'(F pc ) to the corresponding subgroup of E(F pk ). Then,consider G' 1 = psi d -1 (G 1 ) and G' 2 = psi d -1 (G 2 ) for G 1 ,G 2 at Ate pairing alpha. Let P isin G 1 , Q isin ,G 2 , P' isin G' 1 and Q' isin G' 2 , the authors have shown alpha(Q, P) = f t-1,Q (P) ( p K -1)/r = f t-1,Q' (P') ( p K -1)/r .This paper shows that this new Ate pairing, namely cross twisted (Xt) Ate pairing, provides an quite efficient implementation.
DOI:10.1109/ICCIT.2008.172