We all wish we had the time to sit down and read all about Bitcoin, but we can listen almost anywhere. So let me read it for you. This is a crypto Kana me quick read welcome back everybody to the crypto Kana me. I am guys Swan the guy who is read more about Bitcoin than anybody else, you know. No, and we are diving in this week. We're starting off the week with a technical discussion on something that is going to be important to tomorrow's interview. We've got Max hillebrand on this show tomorrow if everything goes well, hopefully all the scheduling works out, but I'm really excited to pick his brain about a couple of things. He's been diving into recently, but to set the stage will go back over a lot of this tomorrow in brief. But to set the stage we're going to read a piece by Aaron then veered mm on bitcoin magazine.com. And this is a really great piece all about Tap Root, which we've not covered yet on the show. So let's go ahead and dive into the piece and then we'll talk about it afterward and it is titled Taproot is coming what it is and how it will benefit Bitcoin. Bitcoin users May before long be able to benefit from a trick called Taproot first proposed by Bitcoin core contributor and former block stream CTO Gregory Maxwell Taproot would expand on Bitcoins smart contract flexibility while offering more privacy in doing so even the most complex smart contracts would own the blockchain typically be indistinguishable from Euler transactions while a big undertaking. This is not just Theory several of the most prolific Bitcoin core contributors including Peter Wella Anthony towns Johnson Lau Jonas, Nick and Drew palestra Tim roughing Rusty Russell and indeed Gregory Maxwell are working on a schnorrer signature proposal that would include Taproot all-in-one protocol upgrade. Here's what Taproot is and how it works. P2 sh All Bitcoins are essentially locked up in scripts a couple of lines of code embedded in a transaction included in the blockchain that Define how the coins can be spent in the next transaction spending conditions, usually involve providing a signature to prove ownership of the coins, but other well-known conditions, for example, include time logs coins can only be spent after a specific block height or date. Or multisig coins can only be spent if some number of private keys out of a set of private Keys provide signatures. Different conditions can be mixed and matched to create complex types of smart contracts an example of such a contract could be that coins can be spent if both Alice and Bob sign or if Alice alone signs after a week has passed or if Bob alone signs while also providing a secret number whichever of these three conditions is met first is how the coins are spent. Since 2012 scripts or the conditions are often not publicly visible at first only the new owner of the coins knows how they can be spent this is done with a trick called P2, sh pay to script hash where initially only a hash of the script is included in the blockchain this seemingly random scrambled number holds the coins. When the owner spins the coins he reveals the whole script as well as the solution to the script at the same time. Anyone can then use the initial hash to check that the supplied script was indeed the original script locking up the coins and can immediately conclude that the requirements of the script were met still when the coins are spent. It's currently necessary to reveal all of the possible. Is it could have been met including the conditions? That weren't met? This has two main downsides one its data heavy especially if there are many conditions into it's bad for privacy. Everyone learns all the different ways in which funds could have been spent which can for example reveal what kind of wallet was used and perhaps even more mast masked or Merkel eyes abstract syntax tree is a proposed solution that uses Merkle trees a decades-old compact data structure invented by cryptographer Ralph Merkle to work around these two downsides in short all the different conditions under which the funds can be spent are individually hashed as opposed to combined into a single hash and included in a Merkle tree, which ultimately uses a single hash the Merkel route this Merkel route quote locks up the coins. The unique benefit is that if any of the data in the Merkle tree is revealed the Merkel root and some additional data called the Merkel path can be used to verify that that specific data was included in the Merkle tree the rest of the Merkle tree remains hashed and hidden. With Mast this means that only the condition that is met needs to be revealed. If in the initial example above Alice alone spins the funds after a week. She just reveals that condition in the Merkel path. No one learns that the money could have also been spent by Alice and Bob together or by Bob alone if he'd added a secret number. This makes Mast more data efficient than complex P2, sh smart contracts and adds privacy to boot yet with schnoor Taproot can do even better a transaction can hide that a masked structure existed at all. snore - nor signature scheme has long been on the wish list of many Bitcoin developers and is currently in development to be deployed as a soft Fork protocol upgrade many cryptographers consider the schnoor signature scheme to be the best in the field as its mathematical properties offer a strong level of correctness. It doesn't suffer from malleability and is relatively fast to verify as its best-known benefit in the context of Bitcoin schnur's quote linear math allows for Signature aggregation several signatures in the same transaction can be combined into one a similar trick could be applied to multisig transactions combining both public keys and signatures into threshold public keys and threshold signatures a multisig transaction can be made indistinguishable. or from any regular transaction in the signature scheme can be used in even more interesting ways. For example, it's possible to use data to tweak both a private key and a public key as a simplified example a private key and its corresponding public key can be tweaked by multiplying both by 2. The private key x 2 and the public key times two would still correspond and the private key times to could still sign messages that could be verified with the public key times to anyone unaware that the original key pair was tweaked wouldn't even see any difference the tweaked keys look like any other key pair. This is what enables Taproot. Taproot Tap Root is based on an interesting realization. No matter how complex almost any Mast construction could or should include a condition that allows all participants to agree on the outcome and simply sign off on a settlement transaction together in the earlier example, if Bob knows Alice can buy herself claim all the funds next week, you might as well cooperate with her now to sign off together. In many typical smart contract setups, he would even be penalized if he doesn't the complexity really just serves to keep everyone honest. Taproot resembles Mast and always includes a condition where all participants can cooperate to spin the funds the Co-operative close by utilizing schnoor signatures. This is where it gets interesting first off. The Co-operative clothes would utilize schnur's threshold trick to make it look like a regular transaction from one person to another so the public keys of all participants are added together resulting in the Threshold public key corresponding with this threshold public key the combination of all participants signatures their threshold signature allows them to spin the funds so far so good, but spending the funds as if it were a normal transaction is the only thing they can do no Mast like structures yet. That's where the other schnoor trick comes in. All the alternative ways in which the funds can be spent the non-cooperative outcomes are this time combined into a different script this script then is hashed and used to tweak the threshold public key rather than public key times to as used in the earlier example this result in a threshold public key times script. We're still simplifying here this threshold public key. Times script corresponds, of course to a threshold signature. I'm script. Now if the money is spent cooperatively all participants combine their signatures into the threshold signature and tweak it with the script the resulting threshold signature times script allows them to spend the funds yet and importantly to the outside world all this would still just look like a regular public key and a regular signature in other words a regular transaction. Only if a Cooperative close proves impossible the threshold public key can be shown for what it really is tweaked in this case both the original threshold public key and the script are revealed. This proves that the threshold public key times the script was tweaked with this specific script. So like the hash and P2 sh The Tweak proves to the world that the funds should be spendable. Well, if the alternative conditions as specified in this script are met and like with P2, sh these conditions are of course immediately met to spend the funds alternatively instead of tweaking the threshold public key with script the threshold public key can be tweaked with a Merkel root of a Merkle tree that includes all the different conditions under which the funds can be spent a masked structure to And the funds then only the spending condition that's been met needs to be revealed. As such Taproot offers all the benefits of Mast while under normal circumstances, no one will ever know that a regular transaction was hiding such a complex smart contract as a fallback. This is a general outline of the Taproot concept implementation specifics may vary for more details read the original Taproot proposal by Gregory Maxwell or watch this presentation by Peter. Wela. All right, and that concludes Aaron Van Buren's Taproot article on bitcoin magazine. Let's go ahead and hit our sponsor and I really want to dive into this one for anyone who has a podcast anchor cannot be beaten particularly for trying to get off the ground. Their entire platform is free. This includes unlimited hosting both in audio that you upload and how much your listeners download I have uploaded an Library of audio now and I've never paid anchor a dime. In fact, they connect me with other sponsors and have run an ad consistently on my show. So they've paid me for exposure to my audience that's really hard to beat even if we ignore that I can record directly in the app or my browser. I don't need any other software. If I don't want it I can edit at sound effects clips and they automatically published to all of the top podcasting platforms. I never ever had to do a thing. So if you were thinking of starting a show or already have a podcast, there's no better platform out there check out anchor by downloading the app or go to Anchor dot f m-- today. All right. Thank you to bitcoin magazine for allowing me to continue to read these articles. There's so much great stuff and another huge. Thank you to Aaron van Werdum for the continuous amazing work that he puts out. They are unbelievably lucky to have him so and as well as I am we have had him on the show in the past you have actually listen to that interview we go into a lot of great stuff and he has so many so many he's just a notion of Articles to dig through and I've been consistently Old that his lightning Network series that I read on the show way back when in like episode 40 something is one of the best explanations and like dives into the lightning Network that you can get and it's pretty damn thorough and amazing. So I highly recommend all of that stuff. I'll have those links in the show notes along with the Bitcoin magazine article, but let's talk about Taproot. So this piece goes through there's a lot of people working on these Nor and Taproot proposals right now and it really is it's kind of funny that all these things were slowly piled on top of each other and till and like kind of during the work on all of these soft Forks. We've got multiple layers of additional use of this technology because Mast is a huge Improvement in and of itself so go back to let's go back to the beginning. I'm going to kind of re-explain hopefully more simply some of these About some of these things that I know particularly in audio hearing all of these terms can make it really confusing to follow but P2, sh. Hey the script hash. It just means that you were paying to a hash just a fingerprint of some other data that is required to unlock it and that includes a signature and a script typically. Well, the script is almost always just this person must sign, but it can include any amount of complexity that you Want but because you have to reveal all of the script to unlock those coins because what happens is that like when I send the coins to their new location, they just go in there lock with the hash are locked with the fingerprint of a lot of data and then in order to then unlock that hash. You have to present all of the data that it is the fingerprint of so, it's a cost savings when locking up the coins, but it's not a cost savings at all when you unlock the coins because you then Just changes when you have to broadcast that information to the network on because before it was the person who sent the coins was needed in order to or was needing to put all of the different instructions on chain as to how to unlock them. And now it's the person who unlocks the coins that has to give all that information which actually makes sense when you think about it because the person getting the security of that complex script whose reaping the benefits of it or utilizing whatever service or smart contract inside of it is the person redeeming it not the person that's creating it. So it makes sense that the we would want the cost on that side of the equation the receiver rather than the sender. So just in a normal like sorting out the economics of it that's actually kind of important in my opinion. But again, it doesn't really do anything for privacy or just cost-effectiveness overall. Just kind of putting the cost for the cost should be so So that was that was implemented in 2012 ish? And I can't remember exactly win. But then Mast is a new proposal that it is not implemented yet. This has been in the works for a while. And this is what led to the combination of all the other technologies that are in proposal right now, but Mast is turning that hash into an entire tree of scripts and requiring only your only the path to your script. The one that you are specifically redeeming it with be necessary to unlock it. So a good way to visualize this is to imagine a literally a tree with like two main branches and in each one of them have three branches in each one of those branches have three branches and each one of those have three like you you immediately get to a massive tree of transactions and number of possibilities that you could possibly need. However to like you're one leaf on This tree of possible outcomes for the ownership of these coins. And the only thing that you need to prove to redeem that is to show that you were one of the paths in the tree. So rather than needing the what would it be I said to 3 and 3 and 3. So that's 27 times 254 different leaves essentially on the end of this and you have to present four pieces of information in order to just show that you were involved in In it or in other words, you just need to point to which branch that you were on and trace it all the way back to the root. And that's all you have to do. You don't have to show any of the other branches. Nobody has to know the any of those other branches exist because you can prove that with just, you know, take a right here. Take a left here take a right and right and then you reach the your Leaf of this, you know script tree and that's all you need to do is you just give those instructions and then they can Move the okay. Yeah, you were a final destination you relief on this huge tree of all this stuff that happened and we don't have to know that there's a whole nother half of you know, a whole nother branch that there was any type of path outside of exactly yours yours could have been the entire path in the script. There was no alternative anyway, or it could have been hundreds of paths like 54 in our example or even more than that. You could just continue to stack it indefinitely really and the cool thing about Got it is the data needed to redeem. The script is logarithmic in comparison to the size of the tree. I mean you could literally have a script that was built with 3,000 different outcomes that only required, you know, three different hashes like that your Marco pass to get there only requires three hashes. So that's both a huge huge cost savings on the Redemption of these coins, as you know, obviously you don't have to show the entire tree which currently in the P2 sh setup. You have to show the entire tree or well you have to show the entire set of scripts. But as soon as you do the Merkel eyes apps that abstract syntax tree, you just have to show the One path to the branch to the end of the branch that actually redeems the coins and all the other trees. We held on a whole rest of the tree could be is entirely obscured. It's never visible to anyone other than participants that are involved and that's a huge that's a huge shift in both making incredibly efficient use of the chain because all you need to do is prove that the person who received it received it in a valid way. It's all this is all a game of authentication and verification and the less data. That we need that's the beautiful thing about Merkle trees and why they are so useful. I mean the blockchain or the time chain itself. I prefer the time chain concept now personally, but the Bitcoin blockchain is in fact A variation on the Merkle tree idea. It's a chain of transactions rather than a branching tree of a chain of hashes. Excuse me, rather than a branching tree of hashes, but it serves the same purpose that you can trace it all the way back because The hashes are within the next hash etcetera Etc. So this is a really old concept is one tool that's being used utilize for so many different purposes. And that's just again, that's just Mast and it does uncover the or reveal always reveal the even though it's privacy for everyone else. It isn't any privacy for the person who actually gets the path like a who actually ends up with the redeeming. That person does have to give up the fact give up all the details of at least they're part of the contract and that's what leads us to schnoor signatures in Taproot. So schnoor signature scheme, and it was the reason and actually wasn't used or at least I'm not sure if this was explicitly said, but I know there was some conversation about it at some point with Satoshi. But the patent was not out yet was not run out on Shore signatures. And even though it was a very very popular or I guess maybe not popular is the word very desirable signature scheme and encryption scheme. It was not a free to utilize public Key System public-private key system and it was only a couple years after Bitcoin. I believe that it actually was in the public domain that it's patent ran. Out and but it is a fascinating way to combine data into single into single keys. So rather than using a bunch of separate keys in order to produce a hash like in rp2, sh situation and then having to reveal that data data later it basically creates a way to turn a bunch of public Keys into a new public key like derive Them from each other by combining them in and literally it's not super far off from just adding them together and what it basically means is that every individual can sign with their public keys or excuse me, sign privately with their private keys. And then those signatures can so to speak the added together and they are the corresponding signature threshold signature for the aggregate threshold public key, so, As long as you add the signatures in the exact same way that you add together the public keys. Well, then you've got a valid signature and still nobody in the mix had to give their private key to anyone else and that's a way to so that the the unlocking script is an aggregate just like the Locking script is an aggregate. So you're hiding or combining the information before you even do the Locking so you don't have to you don't. I have to undo it later as long as you recreate the exact same way. The information was added or tweaked later on. You've got its it all it's all valid in. This allows you to tweak. Those things is that you can as long as you're all using the same multiple of the same quote unquote set of instructions of how to manipulate the data to tweak the data, which could be anything multiplied by 2 multiplied it by a thousand multiplied it by A very long ago by a hash multiply it by a new entirely set different set of scripts. Well, it's still just creating a different public key and all that needs is a different signature with all that same stuff applied to it in order to unlock it. So the signature is all that the network ever has to see and it looks indistinguishable from any other signature because all the work that was done to create it. Never had to be broadcast to the chain. It was done before the signature even existed and because of that you can stat you can put Mast underneath that signature and it's a really fascinating way of combining all of this data and not even having to reveal anything about the tree that goes on and and what he means by when he talks about how Since the branches of the tree they are simply proof that the person who is the rightful Redeemer of whatever crazy setup of contracts that are actually involved that the person who is redeeming it has proof has undeniable proof that they are the rightful owner of the coins. They are the rightful recipient of this contract. So if in a Taproot set up there is always a path in the Taproot for everyone who is involved to Simply sign and release it to that person. Well then having that proof going to them with that proof of the the Merkel path to your destination makes it pointless for them to try to cheat. It makes it pointless for them to not simply do a Cooperative close because what Gain, they don't gain anything. They try to do a Cooperative close. They won't get your signature, which means they'll have to do one of the backups and then you broadcast your proof and you get the keys. So it's a it's a way to just slow down the inevitable end of this whole thing and it's a way to force all the participants in this incredibly complex and decentralized agreement or centralized agreement. Whatever it is that everyone is forced to be honest because honesty is Going to be enforced one way or the other. It's just that we can do a whole lot cheaper right now, or you can waste a lot of people's time. And so, duh. We just want to close this thing out and broadcast it. It's very much like lightning except in the sense that the contract is built so that there is a time lock for to dispute. It's essentially the final state of the chain the final state of all the transactions that happened off chain and The rightful owner always has the ability to revoke any previous state which is, you know fraud in that instance. This is very similar to the same thing. Is that except with a you know, a broad scope of what you can do with the smart contract outside of just off chain payments. I mean the Taproot can Encompass a lightning Channel unlike all the scripts and stuff that we're used to seeing like the ability to see how many channels there are on the network. Actually going to disappear because we're not gonna be able to know what to channel and what's not from blockchain analysis. If everybody uses a Taproot a Taproot signature on the only ones that will ever be visible on the Chain are the ones that have uncooperative closes. They're actually disputed which is a tiny tiny fraction of all the channels that are out there. So lightning will go completely dark with Taproot from a sense from a blockchain. Analysis sense of things. However, when you ping the network as a participant of the lightning Network, you will still get updates on channels and stuff. So you'll still be able to have some view of any public channels that are not, you know set up as private on the network, which a lot of them are these days and you can generally get an idea of your neighborhood in the lightning Network and you can map it D probably would be able to map it decently. Well depending on how many nodes I want to be private and how many channels want to be private which I kind of expect to go up with time, but it's going to be kind of crazy like lightning network is going to be very hard to do analysis on because it's analysis is dependent on the ease of distinguishing these things on the blockchain and that is going to get more and more difficult with things like threshold signatures and threshold public keys in which multisig is indistinguishable masked set of contracts is Distinguishable a lightning Network contract is indistinguishable. Everything just looks like a public key. No different from any other public key and all of the complexity is hidden behind a signature. That looks no different than any other signature. This is a really really powerful technology. I've totally outside of the fact that what an incredible efficiency gain to hide so much to hide multiple signatures multiple keys. Well scripts and entire tree of options as to how to unload a contract to the rightful to execute it to the rightful owner behind the exact same amount of data that it takes to send Bitcoin from me to you one addressed to one you txo. I mean, I think if this it really is as secure as it all appears snort doesn't seem to have any problems has been around for a long time. So it's got the Lindy effect for it. I mean there's so much. In this and it doesn't even seem all that controversial. This could be an incredibly important boost to the entire Bitcoin system in so many different ways and the fact that it is privacy through efficiency is one of the one of its most powerful aspects and this is this is one of the many reasons why I think the idea of a you T XO the it night the idea of a current address. I own the Bitcoin Network being solely owned by a single person or entity is going to slowly become a thing of the past because what you need what the core of this system is about making sure that the path to unlock money to unlock value on this chain is provable and is based on the keys of the rightful owner that the keys are the ownership of the value and that does not require. Are one full transaction that can be done through extensions through Merkel paths. Plus hashes plus signatures are so many different ways to combine and expand on that possibility that I think we will essentially figure out how to create tears and branches and layers of networks all on top of this thing where we can move back and forth. We can move throughout these Merkel paths that these Merkle trees that we can move from one leaf to another on a tree that is all hidden behind a single signature and we can exchange value while always knowing that the rightful owner is the only one that could take it to bitcoin and claim the undeniable final settlement over who owns that value and because of that everyone involved has no reason to do anything other than be honest and cooperate with everyone else it is it is an absolutely beautiful. Of incentives and this allows us to scale almost indefinitely. Like we can just will find new ways to extend this in as long as we have a strong base that has no it hardly any attack vector and we can all prove with a full node as to exactly where on that chain of value and ownership only actual Bitcoin time chain that all of that information that proof that we hold unlocks and we can trust that Bitcoin is in fact still solid as a rock. It is undeniable in the scope of you know, jurisdictions and a true ownership Global ownership chain, and then we're looking at the most efficient and capable monetary in value system we've ever seen that this this really will be a whole new internet. Just think about the implications of that something that can scale like for instance like just just recently there was a paper that came out and a bunch of big blockers were boasting and laughing about how this was spelled death for lightning Network. The only ninety percent of transactions went through after, you know, a certain amount of time that they weren't instant like like 30 or 40 percent of more instant or something like that. Ninety percent of them would try multiple paths and then they finally go through but it was like an average of like Whiny seconds or something like that, I can't remember exactly but it was just an assessment of the difficulties and degrees of finding paths. You think about it if we take it at 90% that's a 10x scaling Improvement right there. All you have to do is design a wallet or client that will immediately do an atomic swap or a loop in and loop out in the in the one out of ten cases where it doesn't work and look at the savings that you've got on chain already you've Equivalent of a 10 to 20 Mega byte block just because you're using your utilizing lightning where it works and you can hide the fact that it doesn't work behind Lupin or Loop out behind an alternative a backup past to just send Bitcoin to people and then incremental improvements in the lightning Network add 2 percent to that add 5% of that. They cut it down to one 20th when out every 20 transaction when at every 50 transactions Yes, and think of how fast that compounds on each other that we turn into what is it the equivalent of a hundred megabyte block worth of payments 200 megabyte block worth of payments all within the 1.5 to 2 megabytes that we actually have and that's negating but this totally ignoring any improvement with side chains with the fact that we could have 50 a hundred participants in a single transaction that is unlocked with a single Tap Root. I mean the the possibilities here. It's one of those beautiful things where you just realize that you have a base Foundation of really strong foundation and just like 5 or 10 Lego pieces and what you can build with it is Limitless and I the people who don't see this are missing. Like imagine that every Financial deal business payment system that you ever use no matter how quote unquote centralized. The actual service is no matter how like what jurisdiction you choose from. You always hold a provable path of signatures of hashes that makes you the only sole owner of that value and that you can always always The option to exit in that acts as a barrier to anyone trying to cheat you it's the elephant in the room every time you make an agreement with someone else or someone attempts to corrupt your agreement or someone attempts to take abuse of the trust that you have provided them that they have. There's this elephant in the room that you always have the capability to exit. So it makes no sense for them to do anything but be Ernest is an extension of the beauty of the Bitcoin system in and of itself that you're rewarded for being honest and you're punished. You have a high cost for trying to cheat the system through the proof of work and that is extended into a contract that is backed up by the proof of work incentive and settled to a chain that every single person in the entire world on their mobile phone can validate the undeniable proof of It's just awesome to me. This is such a fascinating way to like the continuous ways to become more efficient to pack pack more information into more densely into this chain of trust in to extend the unbelievable power of Bitcoin into new networks into new agreements into very complex and The faceted sets of ownership and new transaction systems and new liquidity markets. I mean this thing is truly going to be a Financial internet and internet of value in such an incredible way and we're still right at the beginning of this. I mean these were working these people are working on proposals right now to make these things a reality and people are already trying to cause this An open source software people can already play around with it. There are already designing the solutions with this and that's part of what we're going to talk about with Max tomorrow Max hillebrand. We are having him on the show, and I'm so excited to dive more into this. So I hope you guys will listen to tomorrow's episode as well. Don't forget to subscribe to the show. This is the crypto economy where we read all about Bitcoin and the development and the technology everything around the Case of the cryptographic economy. This is that place and I'm the guy who's going to explain and read it all to you. That's what I do. Thank you guys for joining me. Don't forget to check out Bitcoin magazine.com. They are the best resource for this type of stuff in my opinion like hands down Aaron Werdum right at the top of the stuff that I read when something else comes out about like some of these new developments just a huge huge. Thank you to those guys. For the amazing work that they do and if you don't have your physical copies of Bitcoin magazine you were going to fail because they're going to be worth a shit ton later in the future. You got to get him now. They're scarce there Bitcoin magazine only check it out at the shop. I'm the link to it if you want to do that and thank you guys so much for listening. Don't forget to subscribe. Follow me on Twitter at the crypto Kana me. I have the show notes for all this great stuff if you want to dive deeper in the wait, I have the links in the show notes, and we will be back here tomorrow with an interview with Max hillebrand if everything goes well, so don't miss it. I love you all and I will catch you tomorrow until then. Take it easy guys.
One of the many amazing technologies coming to Bitcoin, Taproot is one of the most promising improvements to the privacy, efficiency, & capabilities of the Bitcoin system. Another excellent article breaking it all down by Aaron Van Wirdum, published at BitcoinMagazine.com, today we read & discuss:  "Taproot Is Coming: What It Is, and How It Will Benefit Bitcoin" https://bitcoinmagazine.com/articles/taproot-coming-what-it-and-how-it-will-benefit-bitcoin For a deeper dive into Taproot, check out the links provided at the bottom of the article. For more of Aaron Van Wirdum's excellent work in audio: • Our Chat with Aaron: https://anchor.fm/thecryptoconomy/episodes/CryptoChat_018---Investigating-Bitcoin-with-Aaron-Van-Wirdum-e4rt9e • The "No Input Class" & Eltoo https://anchor.fm/thecryptoconomy/episodes/CryptoQuikRead_297---Simplifying-Lightning--The-Noinput-Class-Aaron-Van-Wirdum-e5fhoa • Statechains: Sending Keys, Not Coins https://anchor.fm/thecryptoconomy/episodes/CryptoQuikRead_272---Statechains--Sending-Keys-Not-Coins-Aaron-Van-Wirdum-e4mue1 • Understanding Lightning Part 1 https://anchor.fm/thecryptoconomy/episodes/CryptoQuikRead_047---Understanding-The-Lightning-Network-Part-1-e2ndtd • Understanding Lightning Part 2 https://anchor.fm/thecryptoconomy/episodes/CryptoQuikRead_048---Understanding-The-Lightning-Network-Part-2-e2ndt4 • Understanding Lightning Part 3 https://anchor.fm/thecryptoconomy/episodes/CryptoQuikRead_049---Understanding-The-Lightning-Network-Part-3-e2ndtc  Grab a hard copy of the latest Bitcoin Magazine edition at their store below: https://store.b.tc/  ---   This episode is sponsored by  · Anchor: The easiest way to make a podcast. 