Advances in Cryptology - CRYPTO 2007

Volume 4622 of the series Lecture Notes in Computer Science pp 466-481

A Security Analysis of the NIST SP 800-90 Elliptic Curve Random Number Generator

  • Daniel R. L. BrownAffiliated withCerticom Research
  • , Kristian GjøsteenAffiliated withDepartment of Mathematical Sciences, Norwegian, University of Science and Technology, NO-7491 Trondheim


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.


Random Number Generation Elliptic Curve Cryptography