Abstract
It is said that the lower bound of the number of iterations of Miller's algorithm for pairing calculation is log2 r/φ(k), where φ(·) is the Euler's function, r is the group order, and k is the embedding degree. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from ⌊log2 r⌋ to ⌊log2(t-1)⌋, where t is the Frobenius trace. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ." For such a curve, this paper gives integer variable χ-based Ate (Xate) pairing that achieves the lower bound. In the case of the well-known Barreto-Naehrig pairing-friendly curve, it reduces the number of loops to ⌊log 2χ⌋. Then, this paper optimizes Xate pairing for Barreto-Naehrig curve and shows its efficiency based on some simulation results.
Original language | English |
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Pages (from-to) | 1859-1867 |
Number of pages | 9 |
Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
Volume | E92-A |
Issue number | 8 |
DOIs | |
Publication status | Published - Aug 2009 |
Keywords
- Ate pairing
- Miller's algorithm
ASJC Scopus subject areas
- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics