How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A pseudo-random bit generator based on elliptic logarithms
Proceedings on Advances in cryptology---CRYPTO '86
A note on the x-coordinate of points on an elliptic curve in characteristic two
Information Processing Letters
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Extractors for binary elliptic curves
Designs, Codes and Cryptography
Security Analysis of DRBG Using HMAC in NIST SP 800-90
Information Security Applications
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
Efficient, secure, private distance bounding without key updates
Proceedings of the sixth ACM conference on Security and privacy in wireless and mobile networks
Splittable pseudorandom number generators using cryptographic hashing
Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
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An elliptic curve random number generator (ECRNG) has been approved in a NIST standard and proposed for ANSI and SECG draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional Diffie-Hellman problem and the hardness of two newer problems, the x-logarithm problem and the truncated point problem. The x-logarithm problem is shown to be hard if the decisional Diffie-Hellman problem is hard, although the reduction is not tight. The truncated point problem is shown to be solvable when the minimum amount of bits allowed in NIST standards are truncated, thereby making it insecure for applications such as stream ciphers. Nevertheless, it is argued that for nonce and key generation this distinguishability is harmless.