Multi-sources Randomness Extraction over Finite Fields and Elliptic Curve
This addresses a cryptographic need for secure randomness extraction in pairing-based systems, but it appears incremental as it builds on existing extractor proposals.
The paper tackles the problem of extracting randomness from Diffie-Hellman elements over finite fields, showing that the least significant bits are indistinguishable from uniform bit-strings, enabling the replacement of hash functions in pairings.
This work is based on the proposal of a deterministic randomness extractor of a random Diffie-Hellman element defined over two prime order multiplicative subgroups of a finite fields $\mathbb{F}_{p^n}$, $G_1$ and $G_2$. We show that the least significant bits of a random element in $G_1*G_2$, are indistinguishable from a uniform bit-string of the same length. One of the main application of this extractor is to replace the use of hash functions in pairing by the use of a good deterministic randomness extractor.