David Rosenthal: Bitcoin's Lightning Network

Discussions of cryptocurrencies and other blockchain technologies are bedeviled by a nearly universal assumption that attributes that are possible to achieve in theory are guaranteed to be realized in practice. Examples include decentralization and anonymity.

Back in June David Gerard asked :

How good a business is running a Lightning Network node? LNBig provides 49.6% ($3.7 million in bitcoins) of the Lightning Network’s total channel liquidity funding — that just sits there, locked in the channels until they’re closed. They see 300 transactions a day, for total earnings on that $3.7 million of … $20 a month . They also spent $1000 in channel-opening fees.

Even if the Lightning Network worked (which it doesn't ), and were decentralized (which it isn't ), Gerard's point was that the transaction fees were woefully inadequate to cover the costs of running a node. Now, A Cryptoeconomic Traffic Analysis of Bitcoin’s Lightning Network by the Hungarian team of Ferenc Béres, István A. Seres, and András A. Benczúr supports Gerard's conclusion with a detailed analysis.

Below the fold, some commentary.

As usual, Bitcoin enthusiasts are taken in by the hype. As Béres et al write :

LN’s core value proposition is that Bitcoin users can send low-value payments instantly in a privacy-preserving manner with negligible fees, which has led to quite a widespread adoption of LN among Bitcoin users.

Béres et al built a simulation and calibrated it against the public information they could find about the Lightning Network. Experiments they ran using their simulation led them to conclude that the "negligible fees" are massively subsidized by the large Lightning nodes. From their abstract :

Our findings on the estimated revenue from transaction fees are in line with the widespread opinion that participation is economically irrational for the majority of the large routing nodes who currently hold the network together. Either traffic or transaction fees must increase by orders of magnitude to make payment routing economically viable. We give worst-case estimates for the potential fee increase by assuming strong price competition among the routers. We also estimate how current channel structures and pricing policies respond to a potential increase in traffic, and show examples of nodes who are estimated to operate with economically feasible revenue.

And, because the Lightning Network isn't decentralized, "privacy-preserving" is a myth. Béres et al 's second conclusion is :

Our second set of findings considers privacy. Even if transactions are onion routed, strong statistical evidence on payment source and destination can be inferred, as many transaction paths only consist of a single intermediary by the side effect of LN’s small-world nature.

Negligible Fees

Because Bitcoin failed to achieve Satoshi Nakamoto's goal of supporting " small, casual payments ", the major goal of the Lightning Network was to impose much lower fees than the Bitcoin blockchain. But Béres et al find that the only non-subsidized major node charges fees similar to those for Bitcoin itself :

Based on our findings, the annual RoI is way below 5% for almost all relevant entities. The only exception is rompert.com, who indeed applies orders of magnitude higher fees than others. It is interesting to see that despite its high transaction fees, it has the highest daily traffic in the simulation. Note that rompert.com applies base fees close to on chain fees, which may invalidate the assumptions of our simulator if participants fall back to on-chain rather than paying rompert.com routing fees.

And again :

The reason behind low annual RoI is low transaction fees. Table 1 shows that for forwarding α= 60,000 Satoshis, most of these entities ask for less then 100 Satoshis, which is less than 0.2% of the payment value. Very low fees may uphold LN’s core value proposition, but they are economically irrational for the central routers holding the network together. Based on our simulations, for several routers (e.g., LNBIG.com, yalls.org, ln1.satoshilabs.com, etc.), fees should be in the range of a few thousand Satoshis to reach a 5% annual RoI, that is approximately the magnitude of on-chain transaction fees (1,000-2,000 Satoshis)

Source

In other words, most transactions pay only around 10% of the cost of their routing. This greater than Uber level of subsidy could make business sense only in the context of investing in a future monopoly capable of massively raising prices. But prices are capped by transaction fees on the Bitcoin blockchain, making it impossible.

Even with this level of subsidy, the network doesn't work well. Béres et al estimate that the network attempts about 7,000 transactions per day. They simulated lower and higher transaction rates and summarize the rates of failed transactions in Figure 22. Note that at 7,000 transactions per day one-third of them fail. This is not a practical payment system.

Privacy-Preserving

Why do so many transactions fail? Presumably, the reason is that their selected route was incapable of transmitting them. Ideally, the network would dynamically re-route them along paths that were capable. But dynamic routing, such as IP's, in networks such as Lightning is an exceptionally difficult computational problem. Because as each transaction passes through a channel it changes the ability of the channel to accept subsequent transactions, it is a version of the Canadian Traveller Problem . Finding the best path is PSPACE-complete .

So the Lightning Network punts on the routing problem. As Béres et al write :

LN applies source routing, meaning that it is always the sender who decides the payment route towards the intended recipient. Packets are onion routed, which means that intermediary nodes only know the identity of their immediate predecessor and successor in the route. Therefore, from a privacy perspective, nodes are incentivized to avoid single-intermediary paths, as in those cases intermediaries are potentially able to identify both the sender and the receiver.

Because the sender has imperfect information as to the state of the network, and even more so as to the state each of their selected hops will be in when the transaction arrives there, their incentives are inimical to privacy. As Béres et al note :

By our discussion, high node degrees and long payment paths are compulsory for privacy. First, payments from low degree nodes are vulnerable,as the immediate predecessor or successor set is too small and can allow privacy attacks for example by investigating possible channel balances. Second, the majority of payments should be long, otherwise an intermediary has strong statistical evidence for the source or the destination of a large number its routed payments.

Even in theory, the combination of source and onion routing provides a fairly weak version of privacy, similar to that provided by coin mixing :

Although the intermediary knows the sender and receiver if it knows that the payment is single-hop, the onion routing technique used in LN provides a weaker notion privacy called plausible deniability. By onion routing, an intermediary has no information on its position in the path and the sender node can claim that the payment was routed from one of its neighbors.

But, both because senders have imperfect information about the state of the network, and because each hop in the route imposes fees, senders in practice choose short routes via the small number of large, well-connected router nodes such as LNBIG.com. LNBIG.com supplies about half the total liquidity of the network, and owns at least 25 router nodes. As shown in Figure 22 above :

The average shortest path length of LN is around 2.8, meaning that most payment routes involve one or two intermediaries. This phenomenon is further exacerbated by the client software, which prefers choosing shortest paths, resulting in a considerable fraction of single-hop transactions.

Béres et al observe that :

Simulations reveal that on average 17% of the payments are single-hop payments, ... By increasing the fraction of merchants among receivers, this fraction increases to 37%, meaning that strong statistical evidence can be gathered on the payment source and destination through the router node for more than one third of the LN payments. We note that in practice, the ratio of de-anonymizable transactions might be even larger, since payments with longer routes can also be de-anonymized if all the router nodes correspond to the same company.

As for example with LNBIG.com. This all leads Béres et al to conclude :

the topological properties of LN make a considerable fraction of payments easily de-anonymizable. However, with the present fee structure, paths can be obfuscated by injecting extra hops with low cost to enhance payment privacy.

In other words, in order for Lightning Network to provide privacy, it must be massively over-capitalized. If fees are high enough that running a router node is economically rational, privacy cannot be provided because the additional hops needed would both be too expensive and would increase the already high probability of transaction failure.