Okayama University

Yumi Sakemi

Yoshitaka Morikawa

Yasuyuki Nogami

Masataka Akane

Hiroaki Nasu

Provided are a pairing computation device, a pairing computation method, and a pairing computation program all of which enable fast pairing computation. The pairing computation device includes, where:

Pairing computation device, pairing computation method, and pairing computation program

There is provided a pairing computation device provided with a CPU which computes pairing e(S,Q) with S&#x3b5;G, Q&#x3b5;G, &#x3c7; being a given integer variable, and F being a rational function calculated using Miller's algorithm with respect to multi-pairing (MMA). An order r, a trace t of the Frobenius endomorphism &#x3c6;are specified preliminarily using the integer variable &#x3c7; according to an embedding degree k. The CPU performs pairing computation by means of: an input unit which inputs the integer variable &#x3c7;, the rational point S, and the rational point Q into respective predetermined registers; a computation unit which computes F; a computation unit which computes a value at a rational point Q(x, y) of a straight line passing through given rational points; a computation unit which computes f'(Q) using the aforementioned F and the value; and a computation unit which computes the pairing e(S,Q) using aforementioned f&#x2032;(Q) as [F83]. [F83]()=().

Pairing computation device, pairing computation method and recording medium storing pairing computation program

Provided are a scalar multiplier and a scalar multiplication program for performing a scalar multiplication at a high speed. In computing a scalar multiplication [s]P of a rational point P of an additive group E(F) including rational points on an elliptic curve where a characteristic p, an order r, and a trace t of a Frobenius endomorphism at an embedding degree k=12 using an integer variable &#x3c7; are given by: p(&#x3c7;)=36&#x3c7;&#x2212;36&#x3c7;+24&#x3c7;&#x2212;6&#x3c7;+1, r(&#x3c7;)=36&#x3c7;&#x2212;36&#x3c7;+18&#x3c7;&#x2212;6&#x3c7;+1=p(&#x3c7;)+1&#x2212;t(&#x3c7;), t(&#x3c7;)=6&#x3c7;+1, the scalar multiplication [s]P is computed as: [s]P=([A]&#x3c6;'+[B])P, using a Frobenius map &#x3c6;&#x2032;given by: [p]P=&#x3c6;&#x2032;(P) assuming that a twist degree d is 6 and a positive integer e is 2 where k=d&#xd7;e.

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Okayama, Japan

Yumi Sakemi