Journal of Cryptology
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extractors for binary elliptic curves
Designs, Codes and Cryptography
The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Optimal Randomness Extraction from a Diffie-Hellman Element
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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A deterministic extractor for an elliptic curve, that converts a uniformly random point on the curve to a random k-bit-string with a distribution close to uniform, is an important tool in cryptography. Such extractors can be used for example in key derivation functions, in key exchange protocols and to design cryptographically secure pseudorandom number generator. In this paper, we present a simple and efficient deterministic extractor for an elliptic curve E defined over Fq,n, where q is prime and n is a positive integer. Our extractor, denoted by Dk, for a given random point P on E, outputs the k-first Fq-coordinates of the abscissa of the point P. This extractor confirms the two conjectures stated by R. R. Farashahi and R. Pellikaan in and by R. R. Farashahi, A. Sidorenko and R. Pellikaan in, related to the extraction of bits from coordinates of a point of an elliptic curve.