Introduction to finite fields and their applications
Introduction to finite fields and their applications
A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
The Newton Polygon of Plane Curves with Many Rational Points
Designs, Codes and Cryptography
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Elliptic Scalar Multiplication Using Point Halving
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Designs, Codes and Cryptography
Cryptographic implications of Hess' generalized GHS attack
Applicable Algebra in Engineering, Communication and Computing
Efficient pseudorandom generators based on the DDH assumption
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
A security analysis of the NIST SP 800-90 elliptic curve random number generator
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
The Twist-AUgmented technique for key exchange
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
On the use of financial data as a random beacon
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
On randomness extraction in elliptic curves
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
International Journal of Applied Cryptography
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We propose a simple and efficient deterministic extractor for an ordinary elliptic curve E, defined over $$\mathbb{F}_{2^n}$$ , where n = 2驴 and 驴 is a positive integer. Our extractor, for a given point P on E, outputs the first $${\mathbb{F}}_{2^\ell}$$ -coefficient of the abscissa of the point P. We also propose a deterministic extractor for the main subgroup G of E, where E has minimal 2-torsion. We show that if a point P is chosen uniformly at random in G, the bits extracted from the point P are indistinguishable from a uniformly random bit-string of length 驴.