The Tate Pairing Via Elliptic Nets
The Tate Pairing Via Elliptic Nets
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DOI：
10.1007/978-3-540-73489-5_19
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发表时间：
2007-07
期刊：
影响因子：
--
通讯作者：
Katherine E. Stange
中科院分区：
文献类型：
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作者：
Katherine E. Stange
We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from ℤnto a ring that satisfy a certain recurrence relation. We explain how an elliptic net is associated to an elliptic curve and reflects its group structure. Then we give a formula for the Tate pairing in terms of values of the net. Using the recurrence relation we can calculate these values in linear time. Computing the Tate pairing is the bottleneck to efficient pairing-based cryptography. The new algorithm has time complexity comparable to Miller’s algorithm, and should yield to further optimisation.
