Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve

Masataka Akane; Yasuyuki Nogami; Yoshitaka Morikawa

doi:10.1587/transfun.E92.A.508

Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve

Masataka Akane, Yasuyuki Nogami, Yoshitaka Morikawa

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y² = x³ + a, a ∈ F_p. For the curve, an isomorphic substitution from G₂ C E(F_p¹²) into G ₂ in subfield-twisted elliptic curve E(Fp2 ) speeds up scalar multiplications over G₂ and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.

Original language	English
Pages (from-to)	508-516
Number of pages	9
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E92-A
Issue number	2
DOIs	https://doi.org/10.1587/transfun.E92.A.508
Publication status	Published - Feb 2009

Keywords

Ate pairing
Fast computing
Subfield arithmetic operation
Twist

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1587/transfun.E92.A.508

Cite this

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title = "Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve",

abstract = "This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2 = x3 + a, a ∈ Fp. For the curve, an isomorphic substitution from G2 C E(Fp12) into G 2 in subfield-twisted elliptic curve E(Fp2 ) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.",

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AU - Morikawa, Yoshitaka

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N2 - This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2 = x3 + a, a ∈ Fp. For the curve, an isomorphic substitution from G2 C E(Fp12) into G 2 in subfield-twisted elliptic curve E(Fp2 ) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.

AB - This paper presents implementation techniques of fast Ate pairing of embedding degree 12. In this case, we have no trouble in finding a prime order pairing friendly curve E such as the Barreto-Naehrig curve y2 = x3 + a, a ∈ Fp. For the curve, an isomorphic substitution from G2 C E(Fp12) into G 2 in subfield-twisted elliptic curve E(Fp2 ) speeds up scalar multiplications over G2 and wipes out denominator calculations in Miller's algorithm. This paper mainly provides about 30% improvement of the Miller's algorithm calculation using proper subfield arithmetic operations. Moreover, we also provide the efficient parameter settings of the BN curves. When p is a 254-bit prime, the embedding degree is 12, and the processor is Pentium4 (3.6 GHz), it is shown that the proposed algorithm computes Ate pairing in 13.3 milli-seconds including final exponentiation.

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Fast Ate pairing computation of embedding degree 12 using subfield-twisted elliptic curve

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Keywords

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