The security of commit-and-reveal protocols is well understood, and has certain flaws. Basically, the protocol is insecure to the extent that an adversary who controls b of the authorities gets to choose among 2^b outcomes for the result of the protocol. However, an attacker who is not a dirauth should not be able to influence the outcome at all.
We believe that this system offers sufficient security especially compared to the current situation. More secure solutions require much more advanced crypto and more complex protocols so this seems like an acceptable solution for now.
Here are some examples of possible future directions:
- Schemes based on threshold signatures (e.g. see [HOPPER])
- Unicorn scheme by Lenstra et al. [UNICORN]
- Schemes based on Verifiable Delay Functions [VDFS]
For more alternative approaches on collaborative random number generation also see the discussion at [RNGMESSAGING].
The reveal phase lasts 12 hours, and most authorities will send their reveal value on the first round of the reveal phase. This means that an attacker can predict the final shared random value about 12 hours before it's generated.
This does not pose a problem for the HSDir hash ring, since we impose an higher uptime restriction on HSDir nodes, so 12 hours predictability is not an issue.
Any other protocols using the shared random value from this system should be aware of this property.
This design is not immune to certain partition attacks. We believe they don't offer much gain to an attacker as they are very easy to detect and difficult to pull off since an attacker would need to compromise a directory authority at the very least. Also, because of the byzantine general problem, it's very hard (even impossible in some cases) to protect against all such attacks. Nevertheless, this section describes all possible partition attack and how to detect them.
A malicious directory authority could send only its commit to one single authority which results in that authority having an extra commit value for the shared random calculation that the others don't have. Since the consensus needs majority, this won't affect the final SRV value. However, the attacker, using this attack, could remove a single directory authority from the consensus decision at 24:00 when the SRV is computed.
An attacker could also partition the authorities by sending two different commitment values to different authorities during the commit phase.
All of the above is fairly easy to detect. Commitment values in the vote coming from an authority should NEVER be different between authorities. If so, this means an attack is ongoing or very bad bug (highly unlikely).
Let's consider Alice, a malicious directory authority. Alice could wait until the last reveal round, and reveal its value to half of the authorities. That would partition the authorities into two sets: the ones who think that the shared random value should contain this new reveal, and the rest who don't know about it. This would result in a tie and two different shared random value.
A similar attack is possible. For example, two rounds before the end of the reveal phase, Alice could advertise her reveal value to only half of the dirauths. This way, in the last reveal phase round, half of the dirauths will include that reveal value in their votes and the others will not. In the end of the reveal phase, half of the dirauths will calculate a different shared randomness value than the others.
We claim that this attack is not particularly fruitful: Alice ends up having two shared random values to choose from which is a fundamental problem of commit-and-reveal protocols as well (since the last person can always abort or reveal). The attacker can also sabotage the consensus, but there are other ways this can be done with the current voting system.
Furthermore, we claim that such an attack is very noisy and detectable. First of all, it requires the authority to sabotage two consensuses which will cause quite some noise. Furthermore, the authority needs to send different votes to different auths which is detectable. Like the commit phase attack, the detection here is to make sure that the commitment values in a vote coming from an authority are always the same for each authority.