As per "The Stability and the Security of the Tangle", how will IOTA ensure that all honest nodes are continuously using their hashing power?

Question

As per the recently released The Stability and the Security of the Tangle, a 2018 ICUBE - University of Strasbourg "study of the stability and the security of the distributed data structure at the base of the IOTA protocol, called the Tangle", a proof is provided that either:

(1) All the honest nodes must constantly use all their hashing power to validate the main chain (similarly to the bitcoin protocol)

(2) Or some kind of authority must be provided to avoid this kind of attack (like in the current version of the IOTA where a coordinator is used).

Skipping to the conclusion of this landmark study on the tangle reveals the following conclusion:

6 Conclusion

We presented a model to analyze the Tangle and we used it to study the average confirmation time and the average number of unconfirmed transaction over the time.

Then, we defined the notion of assiduous honest majority that captures the fact that the honest nodes have more hashing power than the adversarial nodes and that all this hashing power is constantly used to create transactions. We proved that for any tip selection algorithm that has a maximal deterministic tip selection (which is the case for all currently known TSA), the assiduous honest majority assumption is necessary to prevent a double-spending attack on the Tangle.

Our analyze shows that honest nodes cannot stay at rest, and should be continuously signing transactions (even empty ones) to increase the weight of their local main sub-DAG. If not, their available hashing power cannot be used to measure the security of the protocol, like we see for the Bitcoin protocol. Indeed, having a huge number of honest nodes with a very large amount of hashing power cannot prevent an adversary from attacking the Tangle if the honest nodes are not using this hashing power. This conclusion may seem intuitive, but the fact that it is true for all tip selection algorithms (that have a deterministic maximal TSA) is something new that have not been proved before.

I would like to highlight the following profound observations:

for any tip selection algorithm ... the assiduous honest majority assumption is necessary to prevent a double-spending attack on the Tangle.

and

Our analyze shows that honest nodes cannot stay at rest, and should be continuously signing transactions (even empty ones) to increase the weight of their local main sub-DAG.

and

If not, their available hashing power cannot be used to measure the security of the protocol, like we see for the Bitcoin protocol

and finally

having a huge number of honest nodes with a very large amount of hashing power cannot prevent an adversary from attacking the Tangle if the honest nodes are not using this hashing power

Given that IOTA is committed to removing The Coordinator, how will IOTA ensure that all honest nodes are continuously using their hashing power?

@ben75 has answered that the 'Assiduous Honest Majority' must not be misunderstood. Here it is for clarification and for the record:

Assiduous Honest Majority Assumption

The cumulative weight and the score can be used by a node to select its main DAG. However, even if it is true that a heavy sub-DAG is harder to generate than a light one, there is no relation yet in the protocol between the weight of sites and the hashing power capacity of honest nodes.

We define the assiduous honest majority assumption as the fact that the hashing power of honest nodes is constantly used to generate sites and that it is strictly greater than the hashing power of the adversary. In fact, without this assumption, it is not relevant to look at the hashing power of the honest nodes if they do not constantly use it to generates new sites.

Thus, under this assumption, the cumulative weight of the honest DAG grows according to the hashing power of the honest nodes, and the probability that an adversary generates more sites than the honest nodes in a given period of time tends to 0 as the duration of the period tends to infinity. Conversely, without this assumption, an adversary may be able to generates more sites than the honest nodes, even with less available hashing power

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The document is also available through this source: https://hal.archives-ouvertes.fr/hal-01716111v2

Answer 1

The paper referenced in the question try to demonstrate that the tangle cannot resist to a 51% attack. Nothing really new here.

The position of the Iota Foundation is to favorise a stable organic growth of honest transactions (as founders said multiple times on discord, reddit, ...)

Some members of the community suggested to include a spammer on IRI nodes to artificially increase the tps. (suggestion discussed on discord a few weeks ago)

IMO, the referenced paper is a bit misleading in it's formulation (as demonstrated by the question of the OP). An not very attentive reader may understand that ALL honest nodes MUST constantly use their full hashing power to secure the network. But the paper talks in fact of assiduous honest majority (of nodes) : a concept equivalent to the cumulative hash power invested in honest transactions.

In other words the conclusion of this paper is something like : "With the currently proposed tip selection algorithms, the total hashing power invested in honest transactions MUST be greater than the total hashing power invested by an attacker to prevent double spend."

Answer 2

My paper states that any tip selection that uses the weight of sites to select tips are subject to double-spending attack if the amount of hashing power used by nodes to generates honest sites is smaller than the hashing power of an adversary. This is not very surprising as ben75 said this is just the non-resistance to 51% attack.

About the implication "all honest nodes must constantly... " this is true if you want to maximize the cumulative hash power invested in honest transactions but not a necessary condition as ben75 pointed out.

Also I want to say about the other choice "Or some kind of authority must be provided..." that this can mean very different things. Of course the coordinator is one possible choice, but having another decentralized way of resolving conflicts is another one.

I think everyone wants to avoid the first solution where every node is spamming to secure the network so other solutions must be investigated.