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

Masataka Akane, Yasuyuki Nogami, Yoshitaka Morikawa

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)508-516
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number2
Publication statusPublished - Feb 2009


  • 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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