Step-by-step: the road to Fleming, 3: Sybil resilience simulations

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fleming
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#1

Aim

As part of our focus on evaluating the design of the SAFE Network for Fleming, we took a good hard look at Sybil resilience.

The main objective of this work was to clearly map out the extent to which the Network is resilient to Sybil attacks.

This knowledge would then provide us with certain constraints that we’d need to take account of in developing other aspects of the Network design.

Assumptions

We’ll start by describing the Network according to a set of assumptions. This creates a model that lets us run simulations and analyse the system’s response to perturbations in the parameters.

Uniform work

We define the concept of iteration as being the point at which all nodes in the Network have completed one unit of work (w).

In a real network, the pace at which useful work is carried out by different nodes may vary. However, this simplification allows for a uniform description of the Network. We’ve also assumed that minor variations between different nodes will cancel each other out, because this allows us to gain good insight in the trends of the system at a macro scale.

Ageing

Since node ageing is the main weapon against Sybil attacks on SAFE, we now have to simulate ageing in order to measure its effectiveness.

In the fully featured SAFE Network, node ageing will use proxies for the amount of work done by a node to estimate how much useful work each node has contributed to the Network. It will then age nodes logarithmically: in other words, every time a node has done twice the amount of work it has previously completed, it will gain 1 age.

For this model, we assume that these proxies are perfect. This means that the age of each node is equal to log_2(w): the logarithm of the number of work units they’ve done. Because of the uniform work assumption, this is equivalent to saying that their age is log_2(n) where n is the number of iterations for which they’ve been a member of the Network.

Nodes leaving

To simulate the probability of nodes leaving the Network at any point in time, we use an exponential decay approximation.

This approximation appears to be sensible as these trends were measured in existing peer-to-peer networks such as gnutella.

We use the simplest expression of this exponential decay available to us by assuming:
Prob(node leaving) = 1 / w where w is the amount of work done by this node.

We don’t try to tweak any constants to fit a hypothetical reality as we are mainly interested in the trends. We’re not attempting to provide precise definitions of w or what actually constitutes a single work unit here. This means that we can simply make deductions based on the macro-impact of certain decisions according to the trends observed in the system.

Later, we’ll be able to build a more precise picture by estimating values for these constants based on the actual behaviour of live test networks.

Nodes joining

We’re also considering one idea for reducing the possible impact of an attempted Sybil Attack: the Network should only accept joining nodes on its own terms (i.e. if it needs the extra-capacity that these nodes could offer).

Such a measure would prevent any entity from immediately offering nodes that would cover a high percentage of the Network because they have a malicious intent to take over.

In our simulations, we are considering that such a measure be put in place so that nodes only get accepted as the Network needs more capacity.

We should be clear that this exercise does not include any simulation of how data will perform. Instead, the rate of growth of the Network is simply defined as the rate at which the data stored in the Network grows.

In some simulations, we consider the steady-state (where the number of nodes in the Network is not changing). In others, we look into the impact of varying growth rates on the system.

For the steady-state case, any node leaving the Network is immediately replaced with a node of age 4 joining the Network. The reasoning behind this is that if a joining node starts at age 4, it will avoid immediate churn in the Network.

Variables

The main point of modelling the Network’s Sybil resilience is to inform the design work. Here are some levers we can action to influence the design:

Node ageing

To a large extent, node ageing was designed as a Sybil resiliance mechanism so:

  • How does it accomplish its task?
  • What is its impact?

Section size

  • How many nodes should there be in any given section of the network?

This particular design decision has ramifications on many aspects of the design of the Network. For instance, a larger section will lead to fewer hops through the Network when communicating messages across the Network. On the other hand, a larger section may mean that the number of nodes that can be communicated with directly by any given node grows beyond what’s technically feasible. For this reason, other aspects of our design work interplay with this decision.

  • Being mindful of this, what is the impact of the minimum section size on sybil resilience alone?

Number of Elders per section

In the SAFE Network, Elders are the oldest nodes in any given section. They are trusted with important tasks such as reaching consensus on events happening in their section. No individual Elder is ever trusted, but a quorum of elders can make decision together on behalf of their entire section.

Varying how many Elders constitute a quorum may impact Sybil resilience. In a way, reducing the number of Elders may centralize the decision-making power within a section.
So we have to answer this unintuitive question: what is the right balance of centralization that will make our decentralized system the most secure?

Note that it may seem that considering some level of centralization as a measure against Sybil attacks goes against the principles of the Network. It isn’t actually the case: rather than a binary decision, centralization vs decentralization can be seen as more of a slider. Our aim is to pick the setting on that slider that makes the Network the most fit to deliver on its fundamentals overall.

Like the section size, the number of Elders per section has wide reaching implications on the design of the Network overall.

For its two main components, having a bigger group means that the consensus algorithm (PARSEC) needs to scale to a larger number of participants.

Beneath a certain number, having less Elders may negatively impact the reliable delivery of messages through the Network if connectivity between nodes is limited.

Threat models

The main attack vector we are considering in this document is Sybil attacks: in other words, where an attacker creates many pseudonymous identities in an attempt to gain more influence on the Network.

We considered two different scenarios:

Botnet attack

In one scenario, the attacker gets hold of a botnet. In such a case, we can assume that the financial cost of maintaining an attack for a long time is rather low to the attacker. Practically, it’s more the opportunity cost of not using the botnet for other nefarious purposes that may be more lucrative.

For this reason, we allowed a botnet attacker to provide a larger proportion of nodes to the Network (20% of all joining nodes in our simulations).

We are also interested in observing the behaviour of such an attack over a relatively long time period.

The attacker will also like face the same challenges with the reliability of his nodes as any other: therefore, our simulation assumes that the attacker’s nodes will leave the Network at the same rate as any other node.

Datacenter attack

Another possible situation consists of using a large amount of reliable compute power in an attempt to target the Network. For instance, an attacker could run their own datacenter or simply rent a server farm for a certain amount of time.

The financial cost of such an attack is higher to the attacker, particularly when maintaining that compute power over time. Therefore, we’re more interested in observing the impact of such an attack over a relatively short time period - but with the optimal amount of compute power needed to maximise Network disruption. We saw that an attacker who provides above 5% of all nodes joining the Network didn’t improve the prospects of an attack significantly, so this is the magic number that we chose for our simulations.

Simulations

Picking a network size and number of iterations

In most of our simulations, we picked a time horizon of 20,000 iterations with 100,000 nodes. These values were picked so that the simulations could run in a reasonable time (i.e: ~1 hour).

By running one simulation with 100,000 nodes and another one with 200,000 nodes, we could see that the impact of the number of nodes was quite limited. This meant that we could use the results we obtained with 100,000 nodes in various conditions and extrapolate the trends for larger networks.

All of the curves in this blogpost are representing the same thing, so we will use this opportunity for giving a short explanation about them:

On the x axis, we have the number of iterations. With a network of age 12 (the Network has been running for 2^12 iterations until now, so a minority of older nodes have age 12 and most nodes are younger), 20K iterations represent about 5 times the original amount of work done by the Network. In this case, the Network’s starting age is 20 so 20K iterations represent about 2% of the entire lifetime of the Network.
On the y axis, we have information about the proportion of nodes in any section. The distribution varies over the entire Network, so the black curve represents the average, the blue and pink curves represent half a standard deviation and a full standard deviation away from the average (to give an idea of the spread). The green curve represents the percentage of malicious Elders in the section in the entire Network that has the most malicious elders.

Because any Section that has 33% of its Elders as malicious means that they can stall progress in that Section, a very simple way to interpret this curve is that the earlier the green curve crosses the 33% percentage line, the worse this set of parameters is at fending off a Sybil attack.

By this measure, the particular conditions we picked here are terrible.

Of course, this is to be expected as this choice of parameters was totally arbitrary and simply used as a starting point. Continuing this post, we will show how a more careful choice of parameters leads to much better results.

Conditions:

Variable Value
Number of iterations 20K
Initial number of nodes {100K, 200K}
Initial network age 20
Network growth static
Minimum section size 10
Ratio of elders to min section size 100%
Attack vector 20% botnet

Figures with varying total number of nodes in the network

N: 100K N: 200K
100K 200K

Picking an initial network age

We played with a few different values for the initial network age. Let’s focus here on two different ages: 12 and 16. Note that these represent the logarithm of the amount of work done, so a network of age 16 has done 16 times more work (i.e: 2^(16-12)) than a network of age 12.

The general trend is quite predictable:

For a network of age 12, the amount of work done by the oldest existing members is 2^12 == 4096 work units. This means that a time horizon of 20,000 represents ~5 times more work than has been done by the oldest Elders.

For a network of age 16, the entire duration we’re looking at represents 1/3 of the work done by the oldest Elders. This means that we learn less about how the Network would behave in the long run.

Since we are looking for high-level trends, it is better for us to mostly use a younger network here (age 12). This allows us to extrapolate the results to older networks by keeping the amount of work an adversary puts in proportional to the amount of work did before that adversary joined.

In other words, using a young network means we can easily (with fewer computations) create situations where an adversary is able to take over the Network. This helps us to see what can be done to mitigate such attacks.

Conditions

Variable Value
Number of iterations 20K
Initial number of nodes 100K
Initial network age {12, 16}
Network growth static
Minimum section size 50
Ratio of elders to min section size 100%
Attack vector 20% botnet

Figures with varying starting age

age: 12 age: 16
age12 age16

Impact of network growth

We simulated network growth so that we could measure its impact on the Network.

Everything else being equal, we compared a static network with two networks: one that grew 7 times and another that grew 50 times during the duration of the simulation.

Note that since we simulated an attacker that keeps providing 20% of all new nodes, we assumed that the rate of resources provided by the attacker was able to match the network growth.

Given the dramatic difference in network growth, we observed that the impact on Network behaviour wasn’t as high as we may have predicted.

Roughly, a network that is growing very fast behaves similarly to a network with a lower initial age as the ratio of existing nodes to the nodes the attacker provides decreases with the growth rate.

Because simulating network growth makes the simulations slower and we saw that the trends weren’t massively different, we decided to use a network with static size in any further simulation.

Conditions

Variable Value
Number of iterations 20K
Initial number of nodes 100K
Initial network age 12
Network growth {static, 7X, 50X}
Minimum section size 50
Ratio of elders to min section size 100%
Attack vector 20% botnet

Figures with varying network growth

static 7X 50X
static 7X 50X

Impact of the section size

With the number of nodes and the initial network age decided, it was time to start looking into the impact of variables that we have control over when designing the SAFE Network.

We did a few simulations with varying values for the minimum section size.

The result is pretty significant! With this set of parameters, a network with sections of size 10 will not be able to withold a 20% Sybil attack for any stretch of time. But increasing the section size to 100 drastically reduces the probabilty of a section being owned by the attacker.

The spread of ratio of elders per section becomes much tighter across the Network, which means that it becomes considerably harder for an attacker to control 1/3 of any given section.

At this stage, we didn’t test a minimum section size larger than 100 as we thought that there may be scaling limitations by going beyond this order of magnitude. Now it’s time to explore other ways to reduce the impact of a Sybil attack.

Conditions

Variable Value
Number of iterations 20K
Initial number of nodes 100K
Initial network age 12
Network growth static
Minimum section size {10, 50, 100}
Ratio of elders to min section size 100%
Attack vector 20% botnet

Figures with varying minimum section size

10 50 100
size10 size50 size100

Reducing the number of Elders per section

One idea that we explored was to reduce the number of Elders in each section. This is closer to what is specified in the current Network specifications.

We ran various simulations. Here is a sample of 3 simulations with various number of Elders per section under two different attack vectors: the 20% botnet and the 5% datacenter attack.

The most important feature of these graphs is the delay happening for around 5000 iterations (around twice the age of the Network) when reducing the number of Elders.

It’s important to remember that however powerful any attacker is, their nodes must first catch up with the age of the existing Elders before they can pose a threat. Because there are now only 10% Elders, the attacker must wait for their nodes to become one of the 10% oldest nodes.

With this information, it’s quite obvious that if we were to assume a technical limitation of ~100 nodes per section, having only ~10 Elders per section is much better than having mostly Elders in the network.

It is also better for scalability of the Network to have less Elders per section as Elders are much more connected than simple Adult nodes.

Conditions

Variable Value
Number of iterations 20K
Initial number of nodes 100K
Initial network age 12
Network growth static
Minimum section size 100
Ratio of elders to min section size {10%, 17%, 17%, 30%, 50%, 100%}
Attack vector {20% botnet, 5% datacenter}

Figures with number of elders per section

20% botnet
10 17 100
10elders 17elders size100
5% datacenter
10 30 50
10datacenter 30datacenter 50datacenter

Scaling up

So far, we saw that a low ratio of Elders (~10%) is good as it imposes a delay before any kind of attacker is able to do any damage to the Network.

We don’t have hard numbers that say that 100 nodes per section represents the largest number that is technically possible. But we’ll know what is technically acceptable when we have more data from the testnets.

So - assuming this limit of 100 isn’t a real limitation in any way, how can we improve Sybil resilience of the Network?

To investigate further, we ran some simulations with larger sections - but this time, we kept the ratio of Elders to Adults at 10%. (A lower ratio means more concentration of power between Elders, which may have other undesirable consequences even without considering the impact on Sybil attacks).

These simulations showed very clearly that given 10% of Elders, the larger the section, the more resilient our network would be to Sybil attacks.

Conditions

Variable Value
Number of iterations 20K
Initial number of nodes 100K
Initial network age 12
Network growth static
Minimum section size {100, 300, 500}
Ratio of elders to min section size 10%
Attack vector 20% botnet

Figures with increasing section size and fixed elders ratio

100 200 300
10elders 200section 300section

Conclusions

To summarise, these simulations have been invaluable to the design of the SAFE Network. While we can’t come up with a strict number for any specific variable without considering the scope of the wider Network, there are nonetheless some conclusions that we can make from:

  • Node ageing mitigates Sybil attacks by forcing an attacker to maintain an attack for longer before they can participate in the decision making process.
  • A larger Section size reduces the probability of owning any Section of the Network with a relatively low proportion of nodes.
  • A smaller fraction of Elders adds a delay between the time an attacker starts providing nodes to the Network and the time before they can theoretically control a Section.

A ratio of 10% of elders per Section seems to be striking a good balance between the scalability cost of having large Sections, the scalability cost of having many elders and the impact on Sybil resilience.

As an order of magnitude, a minimum section size of ~100 seems to be required to be able to significantly affect the ability for an attacker to perform a Sybil attack. A larger Section (as far as connectivity permits) seems to only improve the Sybil resilience properties of the system.

With this knowledge, we can use information we will gain in future testnets (for instance: what’s the relationship between the number of Elders and the scalability of the Network as a whole) to decide of exact numbers while being aware of how they impact Sybil resilience of the system.

Of course, we are standing on the shoulders of giants when performing simulations of the network in this community. For instance, this post and this one already contained a treasure trove of information on how the Network would behave under a variety of circumstances. What we wanted to investigate here was specifically the impact of how exactly we define node ageing on Sybil resilience of the systems, which is why we went ahead and performed these new simulations.
These kind of topics are a place were the power of the community can definitely bring a lot, so if you fancy running your own simulations under various conditions and sharing the results with your own analysis, feel free to have a look at the code we used to produce this data.

In the next post in this series, we aim to shift the focus to another one of the “big questions” we’ve been discussing on the road to Fleming: “Network restarts”.

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SAFE Network Dev Update - March 21, 2019
The road to SAFE Fleming
#2

Awesome work. It’s lovely to see the impact of some of the questions in the back of my mind, and very comforting that they are being modeled.

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#3

I will repeat what I already said, but a section should accept a node when:

  • the node passes the resource proof
  • and a slot for a new node is available in the section

The condition should not depend on the remaining free space. The aim is to get a larger network to be able to sustain sybil attacks, by diluting attackers’ nodes.

In rust simulations there was a parameter that allowed to observe the influence of the number of young nodes in a section. Is there anything similar in the new simulations?

I don’t agree. An attacker is more motivated for maintaining its nodes than a casual user. This is a supplementary reason for not rejecting users willing to enter the network.

In this condition, I agree that simulating a static network is the same as simulating a growing one.

But I think this is a bias in favor of rejecting new nodes because in the real world an attacker will have a fixed number of nodes available and not a number proportional to the network size. And it is obvious that a growing network will be more likely to sustain this attack.

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#4

Supposing an attacker launched a successful Sybil attack and managed to control more than a third of the nodes, by what mechanism could he influence the network. I’m not referring to the ‘what’ - altering votes, blocking messages, stealing coins - but the ‘how’. How would the attacker obtain sufficient visibility into the workings of the network to go about doing these things? I can see how bringing the network down might be possible by reprogramming the vault software and getting more and more corrupted vaults to join, but how would you go about stealing a Safecoin?

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#5

Not though, if 100% of the growth was the attacker or colluding attackers. So add 100million nodes to a thousand node network and voila, after some time you win. I say this to try and show the argument that an attacker with say a botnet that can flood huge amounts of nodes is an issue. ageing helps here with desktop botnets (they don’t live long enough), data helps with IOT botnets (they have too few resources), but it is an issue of there was a google attack or some of those “silly” things folk talk about. There is much more to this, but a huge network with a high % of colluding attackers is not necessarily safer than a smaller network with a small % of colluding attackers. There is definitely a balance.

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#6

That would only stall the section, the bad folk need 2/3 of the sections elders (not easy). If they do malicious stuff then malice detection will get them (they need to sign messages, so we have proof of malice). There are many more points, but this is all where the network fundamentals work well. They cannot tell nodes to delete data (as we don’t delete), they may block access in some ways, but they are achieving nothing there, but costing themselves safecoin.

Safecoin itself is a different story that the RFC will explain exactly why a section takeover does not harm safecoin. Well it should anyway :wink:

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#7

So the only real danger from a Sybil attack is the possibility that over time an attacker could bring the network down? Obviously that’s quite a big one :wink: but are there any other things such an attacker could do? It strikes me that even before Malice Detection, their options would be limited by the difficulty in actually seeing what they’re doing.

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#8

That is the main one, there are likely subtle attacks we have yet to see, but the current simplifications of the code and introduction of chains and parsec mean our toolkit is quite large and should be powerful in combating such attacks, but we cannot be complacent just yet. I would like to take a bit of time after Fleming to dive right down into vandalism attacks as well as any attack that can mutate the network or safecoin issuance etc.

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#9

But that would be true also in stress period, when the network needs new vaults to increase available free space. So, this isn’t an argument to accept vaults only when the network needs them.

On contrary if the network accepts vaults permanently, then the network will be bigger when an attacker decides to launch the offensive, so it will harder to control or disrupt a section.

But if the attack happens at the very beginning when the network is still small (like your figures), we can’t do anything about it, accepting nodes only when the network needs them will only delay the inevitable. The only defense is to let it grow rapidly to reduce the initial window when an attack could be successful.

I will need to revive my old rust simulations to prove it. The problem is that I don’t really have time for it right now.

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#10

The point is that would not be continuous and also it would not be unlimited new nodes. In fact it would make such attacks last much longer as the network will actively not allow surge joins of any player, including bad actors.

EDIT (added quote) Yes this is true, the larger the network the better, or at least the total age of the network all node ages added) is the measure of the strength of the network, so the younger the weaker for sure.

I very much appreciate your work in this area and the debates. I did push internally for the Engineers to re-read those threads as they are very important. So please do accept thanks and if you do get time, there will be plenty of opportunities to debate this prior to full launch for sure. Thanks again

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#11

Great work as usual Maidsafe team.

Question re:sybil attacks, how much does a combination of a 5% datacenter together with a 20% botnet attack affect these estimates? Is such a scenario even likely? I’m sure you’ve thought about it and curious as to your thoughts.

Re:how does the network accept new nodes - Accepting new nodes based on space could limit the growth of the network assuming that there’s no upper limit to a vault size and that a node that was just accepted joined with a vast storage capacity. There’s an egalitarian simplicity to TFA’s proposed [accepting nodes if there’s a slot for one] in that no matter how far above the minimum resources requirements a node has gone (i.e., means of node owner), they do not affect the subsequent chance of a node of more meager means (but that meets the requirements) to join the network. Not to mention that nodes with large vaults attached (per the previous assumptions) could limit the growth of sections size, which could be detrimental to sybil resistance per your results.

I agree that there’s a balance (to David’s point), but an attacker would likely be more persistent in waiting for space to be available (more datacenter than botnet) while casual then honest nodes are more likely to quit participation attempts faster, thus increasing the proportion of potentially malicious nodes among the pool of new nodes waiting to join.

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#12

This seems intuitive when thought of in comparison to proof-of-work. PoW is more sybil resistant the more work is being done by the network. If PoW were sharded in to groups, those groups would each be more vulnerable to an attack than as a whole. Bitcoin puts the decentralisation slider to max by having only one work pool.

Nice write up Pierre!

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#13

No its not about 5 times since each age represents twice the one before it.
2^12 = 4096 (age 12)
2^13 = 8192 (age 13)
2^14 = 16384 (age 14)
and 20K would be about age 14.25
So not 5 times but approx 1.1875 increase in age.

Not consistent in your terminology. Is age represented by twice the work than the age previous or directly proportional to the work (is age = amt_of_work/constant)

It is 16 times the work to go from age 12 to age 16. NOT 16 times older since that would be age 12 to age 28.

Here you are equating “older” and “work”. You say “16 times older” but then say it is +4 older. Which is it? It is 16 times the work and +4 older

And remember that work is not related to time since there could be x amount of work for 10 seconds then 5x for the next 10 seconds and then x/4 for the next.

I am highlighting this because it is easy to bring this inconsistency into your simulation and end up with skewed results.

Agreed. I would modify it though in that as the ability for a section to accept a node but not need it, there should be an increased rejection ratio. Actually even when a section needs a node there should be some rejection of nodes too making it more difficult and raising the cost to an attacker and only some minor inconvenience of time to a legit person adding a node

In the case where the section does not need a new node and say there are 10 free slots capable to be filled

  • at 10 available slots say a node has a 90% chance of being accepted
  • at 9 available then 80% chance
  • etc and at 1 available there is a 10% chance of being accepted.

Of course another function could be used to determine change of acceptance/rejection.

The reason I am following is to prevent an attacker flooding the network and has all their nodes accepted even though the various sections are not needing them and this prevents others from joining for a long time. So by rejecting it gives more chance over time for others to be accepted.

On another note there was the concept mentioned by the dev team/David of a queue for each section where the section may not need a node but any new ones put into a queue till needed. This means the attacker has a very high cost to keep their nodes running but gaining no age or farming. The other good people are less likely to be disadvantage since they are using spare resources and not trying to keep thousands of nodes waiting in a queue.

Absolutely they are motivated to remain on line for as long as possible.

Except maybe the botnet where the computers in the botnet will be switched off perhaps faster than any good node since the owners of those computers are not even aware of being in a bot net or the safe network. And so just turn off their computers when it suits them and not when it suits the attacker.

An attacker is likely to run up their nodes in a very short amount of time, so new nodes in that could and likely be 99-100% attacker and <1% others.

But the botnet nodes as I said above will live on average a lot less than people running up legit nodes. But for a datacentre the nodes being added will simply continue till they are accepted and during that time frame the others will be a very low percentage (maybe as bad as I suggested above). Which is why I suggested a balance between what @tfa suggested and what is being suggested here.

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#14

Sorry just a slightly overloaded usage of “age”, here age means linear time. That is, “age” as used colloquially, so 2^14.24/2^12, not “node age”. So effectively equivalent to work for constant work rate. This is since in this context we’re interested in wall clock time

Thanks for pointing it out, yes precision of terminology is important to convey the meaning. It’s a delicate balance depending on the target audience

Correct. There is some wiggle room how to define “work” though, and we might end up with something that is fairly uniform in time.

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#15

This I think is a mistake and trying to include time. My point was that there is no suitable relationship between work done and time. There is obviously going to be times (pun intended) when the relationship seems to be there but in the long term it will not exist.

This is especially important when comparing one section to another. There is no reason to consider that work versus time will be consistent between sections.

Thus no simulation can use a supposed relation between time and work, and there should be no reason for any simulation to consider real time at all. Maybe for a human comfort report it could loosely say work versus time over a long period is somewhat consistent, but in reality that is just an illusion.

Can I suggest you use work for amount of work done (# of events) and age for node age. So for the illusionary “network time” then work done or #events is used rather than time or age.

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#16

Just for clarity might be worth noting internally the line was getting drawn at 1/3rd itself cos once at 1/3rd members, they can stall, then they can also selectively stall certain Blocks/events and allow certain other events that benefit them such as influence membership in the section to take the ratio from 1/3rd to 2/3rd potentially.

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#17

Not consistent in your terminology.

Thanks for pointing this out @neo, I’ve edited the couple of places where I used “age” ambiguously to say “amount of work” instead, which is what I meant.

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#18

Thank you for the explanation!
To be clear (the statistic lessons I got are a long time ago and restricted):

On the y axis, we have information about the proportion of nodes in any section. The distribution varies over the entire Network, so the black curve represents the average, the blue and pink curves represent half a standard deviation and a full standard deviation away from the average (to give an idea of the spread).

That is the ‘malicious / total’-proportion of nodes of the mean section? And 1 full standard deviation is the proportion of the ‘34.1%’-th section above and below that, like here?: https://en.wikipedia.org/wiki/Standard_deviation#/media/File:Standard_deviation_diagram.svg

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#20

Some thoughts of different Sybil attack preventions, without necessary technical knowlege. :slight_smile:

The solutions below are based on the following restrictions:
No budget, time, knowlege, technical or any other restrictions, everything else equal.
The following should be seen as inspiration and not as technical advise! :joy:

Invitation only up to, example 200k nodes . Controlled growth up to when the network reaches, example 200k nodes, similar to how the alpha test networks works.

Dynamic network growth allowance , somewhat in my mind, reverse similar, to Bitcoin halving. In the beginning the network could be restrictive with adding peers as a safety measurement, when network gets older it would be getting closer to zero limit in growth rate. The negative would be that it would limit a network that might need to grow fast in the beginning.

Neighbour overwatch, example every 200 iterations. For every, example 200 work iterations, a neighbour overwatch would occur.

Lets say that when a section have made, example 200 work iterations, then they will demand to check some previous work of a neighbour section. The goal would be to give added security boost without affecting performance too much and also be able to give lower section sizes. In worst case a malice actor could disrupt a section for awhile but would eventually go bust.

Dynamic proof of stake .
Similar to dynamic network growth, when the network is young it would demand a higher stake of coins, the stake size would reduce as the network gets older.

Keep up the amazing work, you guys are amazing. :slight_smile:

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#21

Yes it’s the usual standard deviation as defined by the square root of the variance. The distribution is quite likely to be close to a normal distribution so the rule (empirical rule) you’re referring to probably holds.

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