Some Thoughts On Secure Random Numbers

Many protocols and cryptographic primitives such as DSA rely on secure random numbers. For example, the Signal messenger and it’s quite intricate protocol was recently analyzed and a paper about the analyses published[1]. The authors wrote that they “do not consider faulty/malicious random number generators” in their threat model, but also state that if “[…] generated randomness is compromised or bad, Signal offers no protection”. Secure random numbers are the most common weakness. A compromised random number generator used widely even allows for bulk data collection and decryption[2].

In my mind this problem is relatively easy to avoid. For one, protocols can be modified to  not to leak raw output of the random number generator, which makes practical attacks on the rng much harder. For example, instead of sending a nonce consisting of raw rng output, which would give an eavesdropper information to determine the state of the rng, one could use the sha512 of the rng output. To ensure that this is correctly implemented the protocol participants can exchange the raw rng output later once secure communication has been established and ensure that indeed the nonce that was used was sha512(rng) and not raw rng output itself. For primitives that require random numbers for operation (e.g., signing) one can use the secure hash of the message and private-key for a unique, deterministic and secure random number (this is used by ed25519, IIRC). My point is that most of these problems seem avoidable and systems can be hardened to not completely fail even if the random number generator has been compromised.

The other point is that random numbers should be generated by the OS and incorporate as many different sources as possible. Linux, OpenBSD and other operating systems offer APIs that return secure random numbers collected from various sources of entropy in the system. The latest generation of x86 chips even has RNG instructions that generate secure random numbers (caveats: [3,4]). I think the more entropy from difference sources the better (caveat: [5]), and personally I think systems like HAVEGED can be helpful as an additional source of entropy. One counter argument that I heard was that nobody knows how good this cpu entropy really is, and that entropy extracted from hard-disk latency (and similar). However, for other sources of entropy we don’t know that either. The most sensible paper showing entropy extraction from disk drive latency[6] shows that technically only for certain drives, and I’m willing to wager that all of these results will look quite differently for modern SSD drives. As far as I know quantifying the goodness of entropy sources on computers is an open research problem. I think adding entropy from cpu sources like HAVEGED does is helpful, especially in situations like device startup and other situations where there’s not a lot of entropy available from other sources.


[1] Katriel Cohn-Gordon, Cas Cremers, Benjamin Dowling, Luke Garratt, and Douglas Stebila, “A Formal Security Analysis of the Signal Messaging Protocol”,

[2] Daniel J. Bernstein, Tanja Lange, Ruben Niederhagen. “Dual EC: a standardized back door.” Pages 256–281 in The new codebreakers: essays dedicated to David Kahn on the occasion of his 85th birthday, edited by Peter Y. A. Ryan, David Naccache, Jean-Jacques Quisquater. Lecture Notes in Computer Science 9100, Springer, 2015. ISBN 978-3-662-49300-7.


[4] Becker, CHES’13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems,Pages 197-214, DOI 10.1007/978-3-642-40349-1_12,


[6] D. Davis, R. Ihaka, and P. Fenstermacher, “Cryptographic Randomness from Air Turbulience in Disk Drives,” Advances in Cryptology — CRYPTO ’94 Proceedings, Springer-Verlag, 1994, pp. 114–120.

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