Zufallszahl

Random Number Generators

A good source of random numbers is essential for many crypto operations

"A real fair random number generator"

• The key feature of a good random number generator is the non-predictability of the generated numbers
• This means that hardware support for generating entropy is essential

Hardware random number generators

Hardware random number generators in operating systems or standalone components collect entropy from various random events mostly by using the (low bits of the) time an event occurs as an entropy source.

• The entropy is merged into an entropy pool and in some implementations there is some bookkeeping about the number of random bits available.

When Random Number Generators Fail

Random number generators can fail

• returning predictable non-random numbers
• if not enough entropy is available when random numbers should be generated
• This typically occurs for embedded devices and virtual machines

Embedded devices lack some entropy sources other devices have

• No persistent clock, so boot-time is not contributing to the initial RNG state
• No hard-disk: No entropy from hard-disk timing, no way to store entropy between reboots

Virtual machines

Virtual machines emulate some hardware components so that the generated entropy is over-estimated

• The most critical component that has been shown to return wrong results is an emulated environment is the timing source (Engblom, 2011).

Typically the most vulnerable time where low-entropy situations occur is shortly after a reboot

• Unfortunately many operating system installers create cryptographic keys shortly after a reboot (Heninger, Durumeric, Wustrow, & Halderman, 2012).

Another problem is that OpenSSL seeds its internal random generator only seldomly from the hardware random number generator of the operating system.

• This can lead to situations where a daemon that is started at a time when entropy is low keeps this low-entropy situation for hours leading to predictable session keys (Heninger, Durumeric, Wustrow, & Halderman, 2012).

For systems where – during the lifetime of the keys – it is expected that low-entropy situations occur, RSA keys should be preferred over DSA keys

For DSA, if there is ever insufficient entropy at the time keys are used for signing this may lead to repeated ephemeral keys.

• An attacker who can guess an ephemeral private key used in such a signature can compromise the DSA secret key.
• For RSA this can lead to discovery of encrypted plaintext or forged signatures but not to the compromise of the secret key (Heninger, Durumeric, Wustrow, & Halderman, 2012).