What's Smart about Smart Contracts: Bitcoin Maxi Edition

Day 6: Rubin's Bitcoin Advent Calendar

Welcome to day 6 of my Bitcoin Advent Calendar. You can see an index of all the posts here or subscribe at judica.org/join to get new posts in your inbox

Now that we’ve established the four pillars of Privacy, Decentralization, Self Custody, and Scalability, let’s get into smart contracts. But first…

DOES BITCOIN HAVE SMART CONTRACTS?

There is a lot of fuss around if bitcoin has or doesn’t have smart contracts, and this is usually people talking past one another. Bitcoin does have enough functionality to create certain smart contracts. But Bitcoin does not “have Smart Contracts” in the same way that, say, Ethereum “has” Smart Contracts. Sure, one can argue that because Ethereum is weaker in terms of its fulfillment of the four pillars, it doesn’t really have smart contracts either. But almost undeniably there is something happening in the Ethereum Ecosystem that isn’t happening for Bitcoin – yet.

Often, Bitcoin Boosters will say that the types of things happening on Ethereum aren’t desirable at all and are just scams. Many of these Boosters then go on to promote projects of similar dubious nature… but that’s off topic for this post! While there are many projects that frankly suck, there are also many projects on Ethereum that are relevant to the interests of Bitcoiners! Examples of projects that advance Ethereum’s realization of these 4 pillars that would be difficult to build on Bitcoin include: Gnosis Safe for Custody; Tornado Cash for Privacy; Optimistic/Zero Knowledge Rollups for scalability; SmartPool for on-chain mining pool coordination. It’s claimed that any time something of value proves out in the other ecosystems, Bitcoin can easily just incorporate the highlights.

My position is somewhat unique on this matter: Smart Contracts aren’t something you build on top of a layer with good decentralization, privacy, scalability, and self custody – Smart Contracts are a central part of what makes achieving those pillars possible! In other words, we need a Smart Contract ecosystem that enables broad innovation in order to make our four pillars robust. This is not the same as saying we need the Ethereum VM, but we do need something to be different than the status quo today to empower builders to create new tools on top of Bitcoin. This differs from a traditional Bitcoiner perspective which is more along the lines of once we improve our (insert generic property here); then we can consider figuring out how to add more smart contracts.

That bar sucks it’s too crowded

Another reason sometimes given for not wanting smart contracts is that they’re too expensive and won’t scale. While this is a valid concern, the story around fees is somewhat interesting. You may have seen people complain about high fees on other platforms and say therefore it sucks and should die. It’s a bit like saying a crowded bar is no good. Obviously, if people are at the bar it is good. That your enjoyment is less is solely because you’re antisocial. On other platforms, there are users paying exorbiant fees to do transactions… but would they be doing them if they weren’t getting commensurate value? Let’s have a look at some data from cryptofees¹.

Clearly a lot of folks are willing to pay for Ethereum and projects on top of it. Bitcoin is ultimately a business, and it relies on its customers paying fees to incentivize the production of blocks. More fees, more incentive to provide security for Bitcoin. It’s a little problematic, therefore, when users are getting more utility from (by virtue of how much they are spending) other chains than Bitcoin².

Although we need to be careful to not hurt Bitcoin’s essential properties, it’s clear that smart contracts provide massive leverage for incentivizing users to do transactions to pay for block production, without which Bitcoin falls apart.

Capitalist or Communist?

The last point I’ll leave you with is perhaps a bit charged / “problematic”, but I think it’s a good one. Bitcoin is a bit like America. Ethereum is a bit like China. Provisionally, America is the Free Market Capitalism country and China is the State Controlled Communist Markets country. In practice, if you visit a market in China there seems to be a lot more capitalism than in the US. Tons and tons of small businesses, operating with (seemingly) little regulation. On the other hand, in San Francisco you can spend $200k trying to get permits for an Ice Cream shop and fail. On the flip side, in the states once you’re successful and operating it’s pretty darn hard for the government to substantial interfere. In China, your CEO might vanish for a few weeks like Jack Ma.

Bitcoin is a bit like America. Building on it is incredibly hard, but if you figure it out and crack the code it’s supposed to work forever and devs bend backwards to ensure your use case won’t break.

Ethereum is a bit like China. Building on it is incredibly easy – at first – but if what you’re doing violates the “social order” your thing will get rekt by king VB with EIPscallibur. Examples of this include the removal of refunds for clearing space which bricked a popular gas fee arbitrage token.

Now, obviously this description is tinged with preference. I love America. Best country in the world (or, rather, terrible country, just better than all the other terrible countries). However, Bitcoin is not America and Ethereum is not China. There can be a middle road, and benefits from such an approach as well. Smart contracts seem to be really good at enabling permissionless innovation. Permissionless innovation is great for capitalism! Capitalism is great for improving utility of users and coordinating people. Wouldn’t it be nice if building on Bitcoin didn’t require getting proposals passed the developer “commitiburo” and more innovators picked Bitcoin as the best chain to build new ideas on top of? Obivously we don’t want to sacrifice the other parts that make Bitcoin great, but we can still entertain the types of economic benefits we would see by enabling more permissionless innovation. Because ultimately, and perhaps tautologically…

The best platform for capitalism wins

As described, Bitcoin has certain positive and negative properties. Ethereum too. At the end of the day, in aggregate, what “matters” is what participants choose to use and rely on through a free market selection process. That’s why despite not offfering the playground of Ethereum, Bitcoin has something that people value more: stability. However, stability and stagnation are two sides of the same coin. Stagnate for too long and competitors will eat your lunch. And perhaps the stability that makes Bitcoin unique will eventually be convincingly present in other ecosystems, despite Bitcoin’s head start in that endeavor.

Spooky Scary!

In the coming posts we’ll review the concepts more in depth, the state of the art research for Bitcoin Smart Contracts, and get into some examples of useful Bitcoin contracts.

Pillars of Bitcoin: Privacy

Day 5: Rubin's Bitcoin Advent Calendar

Welcome to day 5 of my Bitcoin Advent Calendar. You can see an index of all the posts here or subscribe at judica.org/join to get new posts in your inbox

Privacy is foundational to Bitcoin. Fundamentally, we care about censorship resistance so folks can’t stop you from doing activity they can tell you’re doing… but what if they couldn’t tell you were doing anything at all? The more private a system is, the better it is at ensuring that all participants are free to do as they wish.

Unfortunately, privacy is one of the most difficult things to achieve in the universe. For every action there is an equal and opposite reaction; if one wants to make an action, how can one ensure the reaction is not observable? And if one masks the reaction, how can one hide the masking?

Privacy exists in a delicate position in our society. America is hands down the leader in rights to privacy of any society, but citizens still face a barrage of assaults against their privacy. Privacy from the government also differs from privacy from corporations, and the corporations often times can be in cahoots with the government. Some regulatory regimes (e.g., the EU) claim to be “better on privacy” than America, but have overall a weaker sense of individual rights than in America (so they may be better at the privilege of privacy, but not at the right to it).

Why is privacy so delicate? In part, because unlike speech there’s no explicit enumerated right to privacy¹. Privacy is an unenumerated right under the American constitution. What this means is that legally we do believe it to be a right because it seems to be implied by other constitutional protections that could not exist without it (e.g., the right to not be searched without due process). Because there’s not explicit protection of privacy, it’s a constant battle to determine what constitutes an violation of privacy. For example, if your house is extra hot because you’re growing pot in it (or hint hint Bitcoin mining), can police use thermal cameras to detect it and then establish probable cause to get a warrant and raid your house? See Kyllo v. United States, that’s an illegal search baby! However it’s possible that this line would erode over time as the expectation of privacy changes – if everyone had thermal camera sunglasses and could see your pot growing plain as day, maybe it’d be unreasonable to think you’re private!

Cryptographic research has yielded amazing tools for creating provable privacy for digital actions. For example, it’s possible to send a digital message in a manner such that only the intended recipient can read it. And as long as your spying adversary isn’t standing over either of your shoulders looking at your screen (or more realistically, running a scanning program on all your data like the one Apple said they might be doing earlier this year), the only people who will know the contents of the message are you and the recipient.

The government kinda sorta hates this stuff!

Because the bad guys can use it! But, because America is super free privacy loving country, citizens still have a basically unlimited protected right to use whatever privacy technology they want. Many politicians have mentioned wanting backdoors into software, but none have truly succeeded to introduce much truly limiting. Not to mention you can’t make math illegal, which is all that cryptography is. Alphabet soup agencies resort to trying to insert backdoors, but these are still subject to public review and the information revealed could only really be used legally for big “national security issues” like against a group with a pre-existing warrant, but the general collection of information would be illegal under the expectation of privacy right. At least in theory – Snowden showed us that mass data collection does still happen… But cryptography gets better, and open-source supply chain devices become better, so inserting backdoors in the code becomes harder and harder.

So great, probably solved for Bitcoin, right? Just Crypto It. Not quite. While systems like ZCash do exist that make transactions much more private, they take up more space, so they decrease the availability of block space… however, perhaps with better privacy, there’s less ability to discriminate against different transaction sources, so less decentralization is needed to guarantee censorship resistance.

This points to another conflict, which arises with privacy: auditability v.s. transparency v.s. Deniability.

An auditable system means that anyone can verify the history of all transactions and check for validity transparently. Many bitcoiners have a preference for “elementary school math”, where validating the transaction record requires very basic math in the code, and not much else. However, if you go to a fully encrypted form, you might no longer be able to easily check important rules like the amount of coins not being increased through a crypto backdoor. This type of auditability where you could “do it by hand on a calculator” we’ll call transparency, since you can see everything! If it were encrypted, it would be opaquely auditable. You could tell it’s valid, but not the specific transfers that happened. Maybe no one person is going to look through all the data, but across all humanity someone is bound to audit at least the transactions they’re involved in.

Deniability stands in contrast to either of these properties. If, say, a government agency comes to you and says “hey, we know you controlled key X, please show us all transactions that X was involved in”, a deniable system would allow you to produce any answer, making such a query useless. However, if a system was strongly deniable like that, it would be very hard to audit because the audit could potentially turn up differing results. So Bitcoin transactions aren’t particularly deniable by default.

One of the drawbacks of Bitcoin’s auditability is that the auditability is forever. So if you have a lapse of privacy, all your old information can be checked. So let’s say you bought a coffee in 2021, and in 2055 the government decides all coffee drinkers are going to go to jail to pay for their drug use sins, then your old cafe might be able to reveal you as a customer. Bitcoin never forgets.

It’s My Data and I want it Private Now

Therefore it’s an urgent priority to make Bitcoin as private as possible as soon as possible in order to keep users safe now and forever, or else the fundamental usability of the system is at risk. However, compromising on auditability or decentralization would be unpopular, so it’s not as simple as adding ZCash and increasing block space.

There are a lot of different pathways Bitcoin can take to increase privacy. For example, the lightning network can mask and make many payments ephemeral, as well as adding deniability if one continually signs false histories of revoked txns. Sidechains can add all sorts of privacy primitives, if they want. And on-chain techniques like swaps or joins can be used to make the base privacy better as well.

In future posts we’ll explore how covenants can have a role in improving privacy!

Pillars of Bitcoin: Decentralization

Day 4: Rubin's Bitcoin Advent Calendar

Welcome to day 4 of my Bitcoin Advent Calendar. You can see an index of all the posts here or subscribe at judica.org/join to get new posts in your inbox

Many may have tried, but few have successfully characterized what “being decentralized” means in an objective / quantitative sense. Instead, we’re left with soft “know it when I see it”s.

Decentralization may be a pillar of Bitcoin with a lotta fanfare, but it’s still just a means to an end. It’s about the Pantheon, not the pillars! A system can be very decentralized and still kinda suck. Much like pillars with no roof won’t keep the rain out!

Got Gas?

For a more than slightly contrived example, imagine a pre-internet driver navigating gas stations prices. Kind of “decentralized”, right? Users/purchasers operate on local information to see pricing and make a decent decision, and sellers operate on local information to stay competitive. Over time the network should “converge” a sellers learn who has better prices throughout town, but from the perspective of an individual purchaser it’s really hard for them to determine within their remaining tank range/willingness to drive across town for a dollar who has the best prices. So while the market works as a decentralized pricing system, it’s not highly consistent!

It’s Hard; No CAP

Computer network nerds have three rules for keeping their jobs: consistency, availability, and partition tolerance. What do these mean in practice? Thinking back to our gas analogy, gas stations are very available (you can always get gas at some price), they’re strongly partition tolerant (i.e., if you can’t see other gas station’s advertised prices you won’t know if it’s better, but you can still get gas). But the pricing might be all over the map! No consistency!

It’s really hard to achieve all three properties – there even exist proofs of its impossibility. Instead, engineers make tradeoffs to achieve different amounts of guarantee across the properties.

For Bitcoin we care a lot about consistency¹. If I send money to Alice, I should not be able to send it to Bob. We also care a lot about partition tolerance. If some group of participants should shunt themselves out from others, the system should still operate? So do we inherently care less about availability? Well, kinda! If the “blockchain is closed” and you can’t transact, at least you still have your money. And technologies like Lightning Network can help bridge the gaps if the Bitcoin blockchain is unavailable that you can still fully confirm transactions as long as it comes back eventually.

So, interestingly, Availability seems like the property we need to care about the least… but it’s one of the main reasons we need decentralization! That’s because even though we might have a design that elevates the other two properties, it doesn’t mean that availability is unimportant. And availability is not one monolithic level, there are many different types of availability fault one might experience on a network. For example, you might experience reduced or no availability if:

1. The network doesn’t have blockspace at your price
2. The internet is down
3. Your usual peers are offline
4. Theres a fire at a major data center
5. Your battery on your phone dies
6. A big solar flare happens
7. An evil government changes your DNS records to your mining pool and you don’t know the IP address
8. An evil government runs the network entirely and doesn’t like your transactions so they get censored.

Some of these problems, decentralization can help us with! Some, decentralization can’t help with. And some are caused by decentralization. Uh oh!

For example…

A fire a major data center can be defrayed by being more decentralized – a fire can only spread so far! The other data centers should be fine, since Bitcoin is partition tolerant, the overall network is available.

If a big solar flare happens, there’s not much any of us can do if all the internet is down and our devices got fried. Too catastrophic… We can recover eventually, your metal seed plates will be fine, but hopefully someone had some Faraday cage shielded backups.

If blockspace is too expensive, decentralization may be the cause!

In order to keep the network decentralization friendly, Bitcoin uses far less bandwidth and storage than a centralized system (like Google) could use. This ensures that participants on the network need not be particularly well resourced or well connected to be a meaningful, full participant in the Bitcoin Network.

That’s because of another availability issue: censorship. Bitcoin fundamentally stands as a fuck-you to the entrenched powers that be. As such, Bitcoin uses decentralization to guarantee censorship-resistance against state actors. While there’s been much ink scaled about the censorship of scalability v.s. the censorship of state actors, Bitcoin is hyper focused on providing some form of “equal protection”.

Everyone hates that you lose availability from high tx prices, and all are equally affected². Everyone hates solar flares, and all are equally affected. But with state actor censorship, enemies of the state, be they Jews, Conservative Non-Profits, Black Americans, Gazan Chocolatiers, People who believe things posted on *******’s Twitter Account etc, can be picked apart and subjected to selective abuses. If anyone can run a node (and hopefully miner), and most people don’t have a political agenda, we can maybe protect individuals of any background.

As such, Bitcoin’s decentralization is focused on censorship-resistance, even at the expense of on-chain availability.

The Neverending Story

The story doesn’t end there. Decentralization, as we noted earlier, is very tough to quantify. Even if we can’t quantify it, we can still reason about decentralization efficiency. Given the “costs of decentralization”, how much censorship resistance do we get? Can we decrease the costs and achieve the same amount? Can we keep the cost the same and gain more censorship resistance? Or… do we need to increase the costs, because we’re not censorship resistant enough? Stay tuned for future posts we’re we’ll see if we can’t do something about it!

Pillars of Bitcoin: Self Custody

Day 3: Rubin's Bitcoin Advent Calendar

Welcome to day 3 of my Bitcoin Advent Calendar. You can see an index of all the posts here or subscribe at judica.org/join to get new posts in your inbox

Not your keys, not your coin. A simple maxim often repeated by Bitcoiners, but an important one. Why?

That thing about the gold standard you probably heard before:

In the existing financial system, your assets aren’t really your assets. Let’s suppose you own a share of Google. You don’t really own that share, you own a virtual claim and the actual certificate sits somewhere with a corporation like The Depository Trust & Clearing Corporation (DTCC). So what? Why does it matter who holds the paper?

The U.S. Dollar is a great example of why you should care. One dollar used to represent an amount of Gold you could redeem for real physical bite-it-to-see-its-pure gold. This was a promise of course, the paper dollar did not have the actual gold in it. This was all good and dandy until in 1933, Executive Order 6102 was put in place which made the holding of physical gold illegal. Get arrested and go to jail illegal. EO 6102 mandated that all Gold be turned in to the Federal Reserve. This was quickly followed by a devaluing of the redemptive value of the dollar in Gold by the government from $20.67 per troy ounce to $35 as a “one time” move¹. Today a troy ounce costs around $1,800. This is because in 1971 an Executive Order was put through that ended the dollar’s gold backing entirely.

What’s this got to do with Bitcoin?

If Bitcoin is held in accounts at regulated entities like exchanges a similar act to 6102 could make redeeming actual bitcoin impossible for users of those services. Suppose those users are forced to receive in place of their exchange Bitcoin a Bitcoin Note that is backed by bitcoin. And then one day, the amount of Bitcoin per Bitcoin Note can be reduced – or worse, completely unlinked.

If this happens, all is lost. Bitcoin is fundamentally about a monetary standard for the world where no self-important rulers can manipulate the currency. Self custody is a requirement for Bitcoin to avoid these sorts of takeovers.

OK, OK, I’ll keep my coins off exchange…

Just fixing your behavior isn’t enough, to keep Bitcoin functional you need most users to follow suit. Yet many users today do choose to keep some or all of their Bitcoin on centralized services (yours truly included!).

This is for two main reasons:

1. Game Theory: we can’t do anything about this. As long as not too many other people are using an exchange for custody, it doesn’t matter if you are since a regulatory takeover won’t be too effective. So selfishly, you may as well benefit from the ease of keeping your coin on a service (assuming it is easier) rather than taking responsibility for your own assets. Likewise if no-one else is self custodying there’s not much advantage for you to be either.
2. Software freakin’ sucks for self custody! We can fix this. Although the quality of wallets has improved dramatically from Bitcoin’s early days, it’s still incredibly difficult to do well. Further, self-custody solutions don’t have solid options for handling many common needs such as inheritance, spending limits, and more.

If we work on strengthening the fully self-sovereign self-custody options that Bitcoin users have at their disposal, we can help more Bitcoin users to choose to keep their funds themselves and achieve “herd immunity” against future executive order 6102s. If we self custody in great number, we don’t permit them the immediate victory over most users. You can’t arrest everyone, not easily at least.

in short…

PLEBZ

TOGETHER

STRONK

Pillars of Bitcoin: Scalability

Day 2: Rubin's Bitcoin Advent Calendar

Welcome to day 2 of my Bitcoin Advent Calendar. You can see an index of all the posts here or subscribe at judica.org/join to get new posts in your inbox

This is the first of four posts in an advent mini-series about four fundamental pillars of Bitcoin. I know, I know, a series within a series. What am I, nuts? But it’s important that we begin our journey by setting the stage with a few big picture objectives for Bitcoin before we get into why Smart Contracts matter.

After all, we’re trying to build the hardest money possible, not Crypto Kitties… right?

The four pillars I’ve chosen to focus on are Scalability, Self Custody, Decentralization, and Privacy. Are there other properties that are also important? Sure. Might there be a “more fundamental” name for each pillar? Ok. But generally I find that these 4 categories are different enough from one another and capture a very wide swath of what Bitcoin is and not overly specific or overly general. Otherwise we’d just have one pillar for Bitcoin: “To Fix This”.

Now onto the content.

Scalability is a controversy generating issue. Throughout Bitcoin’s history there have been acerbic disagreements about what sort of scale is required and how to accomplish it. Back then I even helped create a conference series, Scaling Bitcoin, where people got to present to/shout at each other in person!

But why is scalability so important? And why does it generate controversy?

Famously, certain folks have remarked that, “you can’t buy coffee with Bitcoin” because fees would be too high. This is an issue that’s easy to empathize with; if transactions cost $10 who wants to do that for a $5 coffee – No One!

The common response is that Bitcoin isn’t for trivial purposes like buying a cup of coffee, it’s The Hardest And Most Sound Money To Ever Exist And If You Buy Coffee With It You Are Stupid.

There’s some truth to that. Bitcoin doesn’t need to function to enable your trivial day to day purchases, it needs to exist to help you take self-sovereign control over your money! Forget about your coffee, stack sats, survive hyperinflation, avoid the pod, don’t eat the bugs. Capiche?

So what’s the rub? Well, if Bitcoin is to really be the vaccine against autocratic rulers and corrupt financial systems, it needs to protect everyone, not just elite sat-stackers who can afford to use it. Scalability represents our desire for Bitcoin to be affordable for all who could benefit from it. Many who live under abusive or corrupt regimes today might already be priced out. Imagine earning 1000 satoshis per day and spending 300 satoshis to do a transaction. Real bummer. And what if fees go up? There’s also the insulting concept of dust in Bitcoin, 546 satoshis, currently about $0.30. Some people work hard just to earn that much! Where do you think people who fall on this low end of the economic spectrum live… in the freest of the free western countries? No, they’re Congolese children mining cobalt. Maybe it’s OK that they’re priced out: Bitcoin preserves wealth (and freedom), it doesn’t create it. And just having cheaper fees isn’t going to free the child workers. But still, wouldn’t you rather have Bitcoin be able to benefit anyone who might have the need to use it, regardless of net worth?

Good news: there are techniques that exist today for scaling access to Bitcoin. Bad news: they all have different tradeoffs.

Just Make the Blocks Bigger Bro

Early on in Bitcoin’s history a contingency of Bitcoiners felt strongly that Bitcoin should scale by increasing the size of Blocks to accommodate more transactions per second and keeping fees low. While mild block size increases (e.g., as done with SegWit) are probably ok, the ever-increasing block size would threaten Bitcoin’s decentralization and make it harder for anyone to be able to run and audit the system. And if you can’t run and audit Bitcoin yourself, you might as well be using the legacy financial system.

There are some efficiency improvements that can shrink transactions marginally, contributing to an effectively larger block. But Blockspace will always be scarce, no matter how space efficient transactions are.

Lightning Network

The Lightning Network is a very popular means of scaling bitcoin. It makes a second layer on top of Bitcoin where you can make cheaper and lower latency payments. It functions sort of like the equivalent of Venmo versus Bank Wire Transfers. You set up a “payment channel” with a counterparty, and are able to make many cheap payments between you and the counterparty. You can even route payments through friend’s channels if you don’t have a direct link. A few major downsides to this approach are as follows:

1. That it requires an active online presence and ability to get bitcoin transactions confirmed (which still costs money!)
2. It requires some form of durable storage any time you make a transaction.
3. That in order to receive funds, you have to have someone loan you the “potential” capital (think credit worthiness, which requires some sort of reputation system and identities).

In countries like El Salvador, which have begun adopting Bitcoin as legal tender, many users of the Lightning Network are doing so through a centralized service provider which doesn’t protect users from the types of abuse possible in current banking paradigms. In theory, this central service provider isn’t there because the El Salvador government is some kind of soon-to-be dictatorship, but rather because solving the problems of capital loan, regular online presence, and durable storage are hard problems for citizens of a poor country.

Sidechains

Another popular approach is to make federated sidechains, such as RootStock, Liquid, Nomic, or ThorChain, etc. A Federated Sidechain is essentially a “fancy multisig”, where funds are sent into the custody of a set of entities (usually such that many independent entities would have to collude to steal funds). The federation then runs some sort of cryptocurrency backed by the deposits. Users are granted virtual bitcoin on the sidechain which they can use in accordance with the rules of the sidechain. Eventually they may request that whatever balance they have on the sidechain be sent out of the sidechain and into a normal bitcoin address of their choosing. This achieves a sort of scalability because the base layer does not have to validate or store any of the transactions occurring on the sidechain. However, the tradeoff is severe: the funds are completely owned by the Federation, which means that users are not guaranteed to be able to access their funds. It’s basically a bank with a cool API.

This post doesn’t end in a fun or upbeat way: we want everyone to be able to access and benefit from Bitcoin; we can’t get everyone for access in the obvious way of bigger blocks or we risk unravelling Bitcoin’s core guarantees; and the solutions using layers on top of bitcoin reduce some of the core properties that make Bitcoin valuable to society in the first place. Some of these tradeoffs may be acceptable in certain cases, but we must always strive to support the most users with the strongest Hard Money properties we can.

In future posts we’ll see how more sophisticated smart contracts could improve Bitcoin’s scalability, or at least provide a different set of tradeoffs compared to the solutions above.