5
$\begingroup$

I am looking for an analysis of practical mix networks with server downtime.

For example, if a message is supposed to go from A -> B -> C -> D, what happens if B wants to send the message but C is offline temporarily?

This could be a stop-and-go mix network so holding onto a message longer is OK, but I am wondering whether there's any paper analyzing this sort of thing? For instance, how does it affect anonymity, how does B know when to retry sending it, etc?

Or what if C goes offline permanently, is the message lost? Is there a mix network protocol for resilience in this case?

$\endgroup$
  • $\begingroup$ If B wants to send to C and C is offline, then B cannot send. This has no impact on anonymity, because B not sending doesn't reduce anonymity. If C is permanently offline, then the mix cannot complete. But, I don't feel like I'm answering your question, perhaps you could clarify? $\endgroup$ – Alpha Bravo Aug 8 '18 at 15:06
  • $\begingroup$ Maybe you're asking whether the mixnet can work if C doesn't participate (for whatever reason). That depends on the particular mixnet you're using. For onion routing, where the ciphertext is of the form $enc(pk_A, enc(pk_B, enc(pk_C, enc(pk_D, m))))$, the mixnet cannot work, because C doesn't participate, hence, the layer of the onion encrypted by $pk_C$ cannot be removed. By comparison, for a re-encryption mixnet, the mixnet works, since B can just send to D. The resulting reduction in anonymity corresponds to reducing the number of mix nodes from four to three. $\endgroup$ – Alpha Bravo Aug 8 '18 at 15:11
  • $\begingroup$ I'm wondering two things, 1) what happens if C goes offline temporarily (say for a day), does that have implications on anonymity? I think the answer can be made to be "no" but am wondering if there are research papers on it. And also 2) if C were to go offline permanently, the message could be lost at B, so are there mix nets that take this into account and ensure better resiliency? $\endgroup$ – Some Guy Aug 10 '18 at 3:29
0
$\begingroup$

It depends on your choice of mixnet, as to whether a mixnet is resilient in the case that C doesn't participate (for whatever reason, including system failures and adversarial behavior by C).

For onion routing, where the ciphertext is of the form

  • $enc(pk_A,enc(pk_B,enc(pk_C,enc(pk_D,m))))$,

the mixnet is not resilient, because $enc(pk_C,enc(pk_D,m))$ cannot be decrypted without participation of C.

By comparison, for a re-encryption mixnet, where the ciphertext is of the form

  • $enc(pk,m)$,

the mixnet works, since B can skip C and send directly to D. The resulting reduction in anonymity corresponds to reducing the number of mix nodes from four to three.

$\endgroup$
  • $\begingroup$ In response to crypto.stackexchange.com/questions/61228/… (I don't have enough reputation to comment above): 1) if B waits for C to come online, then there's no loss of anonymity (the proof would embrace the idea that waiting for a computation doesn't harm security), and 2) why would B loss a message? $\endgroup$ – Alpha Bravo Aug 10 '18 at 8:51
  • $\begingroup$ For 2 I mean that if C goes offline permanently before the message gets to it, then it gets stuck at B. That's a problem if you want to ensure a high level of messages get through (say 99.9% or whatever). I think you could just send the message twice through different routes, but am wondering if there's a paper that has analyzed this problem, because does sending the same message twice have anonymity concerns, and are there other alternatives to get redundancy? $\endgroup$ – Some Guy Aug 10 '18 at 19:10
  • $\begingroup$ As explained above, using a re-encryption mixnet, it doesn't matter if C goes offline, because it isn't needed. By comparison, it is needed for onion routing. $\endgroup$ – Alpha Bravo Aug 15 '18 at 10:10
  • $\begingroup$ Regarding "sending the same message twice," this doesn't create any anonymity concerns. Sending a message once, twice, or arbitrarily many times makes no difference, the message is out there, whether it was put out there more than once makes no difference. $\endgroup$ – Alpha Bravo Aug 15 '18 at 10:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.