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I am trying to read a paper in cryptography. In key generation phase, paper give a definition for bilinear like G and Gt be two cyclic groups of prime order p

$e: G * G \to G_t$. be a map with the following properties: enter image description here

and in one place i found a definition like enter image description here

my doubt is in the last part. Specifically in m.e(g1,gn)^t suppose m is any message, g1=3,gn=13 t=6 (for more information v=5,gi=10.no problem whether all the value assumptions are true or not). then how can i compute e(g1,gn)^t part? sorry for my bad math notation

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According to PBC manual, Pairing functions, map $\hat e(,)$ (without t-power) could be calculated as follows:

pairing_pp_t pp;
pairing_pp_init(pp, g1, pairing);
pairing_pp_apply(r1, gn, pp); // r1 = e(g1, gn)
pairing_pp_clear(pp);

Before calculating the map, pairing parameters must be initialized.

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  • $\begingroup$ you did in program. But can you tell on example did by hand. I mean with numerical value?. Some where i found that e(3,11)=3 mod 11. Is it correct. if not can you explain with this kind of example? sorry for i am being a disturbance to you :P keep in mind that my exact problem is e(g1,gn)^t @Vadym Fedyukovych $\endgroup$ – John Mathew Dec 7 '15 at 4:30
  • $\begingroup$ printf(r1); @John Mathew $\endgroup$ – Vadym Fedyukovych Jan 3 '16 at 10:36

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