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Inverting the Final exponentiation of Tate pairings on ordinary elliptic curves using faults
Tate pairing Ate pairing final exponentiation
2016/1/4
The calculation of the Tate pairing on ordinary curves involves two major steps: the Miller Loop (ML) followed by the Final Exponentiation (FE). The first step for achieving a full pairing inversion w...
FINDING COMPOSITE ORDER ORDINARY ELLIPTIC CURVES USING THE COCKS-PINCH METHOD
Cocks-Pinch method ordinary elliptic curves order setting
2009/11/18
We apply the Cocks-Pinch method to obtain pairing-friendly com-
posite order groups with prescribed embedding degree associated to ordinary
elliptic curves, and we show that new security issues aris...
On the final exponentiation for calculating pairings on ordinary elliptic curves
Tate pairing addition chains
2009/6/10
When using pairing-friendly ordinary elliptic curves to com-
pute the Tate and related pairings, the computation consists of two main
components, the Miller loop and the so-called final exponentiati...
ON THE EXISTENCE OF DISTORTION MAPS ON ORDINARY ELLIPTIC CURVES
cryptography Decision Diffie-Hellman
2008/11/13
An important problem in cryptography is the so called Decision Diffie-Hellman problem (henceforth abbreviated
DDH). The problem is to distinguish triples of the form (ga, gb, gab) from arbitrary trip...