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.
| 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 | |
| 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