# Pairing arithmetic device, pairing arithmetic method and recording medium having pairing arithmetic program recorded thereon

Contact: |
Mototaka Senda, Ph.D. |

Phone: |
(1)510-468-3372 |

E-mail: |
ousvo@okayama-u.ac.jp |

**Patent number: US8477934**

### Description

A pairing arithmetic device is provided with a CPU which calculates pairing e(S,Q), with F as a rational function calculated using S∈G_{1}, Q∈G_{2}, a predetermined integer variable as χ, and an algorithm (MMA) of a mirror with respect to multi-pairing as F. The order r, the trace t of the Frobenius endomorphism map/image Φ_{p} are specified using the integer variable χ according to the degree of embedding k. The CPU carries out the arithmetic operation by means of: an inputting means which inputs the aforementioned integer variable χ, the rational point S, and the rational point Q into their respective predetermined registers; a calculating means which calculates F; a calculating means which calculates values at a rational point Q(x_{Q},y_{Q}) on a straight line which passes through predetermined rational points; a calculating means which calculates f_{χ,s}(Q) using F and the aforementioned value; and a calculating means which uses f_{χ,s}(Q) to calculate the pairing e(S,Q) as a [83].performing machining, e.g. cylindrical grinding.

- Category：
- Computer and IT

- Keyword：
- Digital group signature