Sammendrag
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.
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