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This work is based on the proposal of a deterministic randomness extractor ofa random Diffie-Hellman element defined over two prime order multiplicativesubgroups of a finite fields $\mathbb{F}_{p^n}$, $G_1$ and $G_2$. We show thatthe least significant bits of a random element in $G_1*G_2$, areindistinguishable from a uniform bit-string of the same length.  One of the main application of this extractor is to replace the use of hashfunctions in pairing by the use of a good deterministic randomness extractor.

Multi-sources Randomness Extraction over Finite Fields and Elliptic Curve