David A. Harding

Co-author of the Bitcoin Optech weekly newsletter (2018-23) and the third edition of Mastering Bitcoin (2023). Brink.dev grant committee member (2022-24) and former board member (2020-22). Lives in Hilo, Hawaii. All opinions are my own.

Public Key

npub1syluunzwwmc70d85d9alzqc2jrc6pdur7xrax2vqpfxas6tljavsa46ksu

NIP-05 Address

dave@dtrt.org

Profile Code

nprofile1qqsgz07wf388du08kn6xj7l3qv9fpudqk7plrp7n9xqq5nwcd9lewkg532r2n

Author Public Key

npub1syluunzwwmc70d85d9alzqc2jrc6pdur7xrax2vqpfxas6tljavsa46ksu

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Last Notes

2024-10-31 22:18:32

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Yeah, many of my illustrations for the past couple years have been rough drafted by ChatGPT in a diagram language I was familiar with (but no expert), with me then tweaking it manually until I was happy.

2024-10-30 18:31:17

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Obviously, if either the pedestrian or the driver does something stupid, the other party should not be held to blame. However, even in places where jaywalking is illegal, a driver who strikes a pedestrian is at fault if the driver could reasonably have stopped. This is the legal principle of last clear chance: whoever has the last clear chance to avoid harm is ultimately responsible for doing so.

2024-10-30 14:59:35

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I still use Strava. I acknowledge that it reduces my privacy and I hate using a closed platform, but I feel like I personally get a lot of benefit from seeing the activities of other people in my area, both friends and strangers. If I benefit from them, they may benefit from seeing my activity.

2024-10-30 14:51:57

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Seems like a win for freedom, letting people cross the road anywhere when they personally think it's safe.

2024-10-29 08:09:47

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I'm getting married in a few weeks. We met three years ago through a dating app (Bumble). Before we met, I had several other normal dates with normal women I met through apps. I thought the apps were great, but maybe I'm an outlier.

2024-10-28 15:04:02

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Ah, I'll add an alias.

2024-10-28 05:38:04

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https://bitcoinops.org/en/topics/channel-announcements/

2024-10-24 04:39:19

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I think this has been the most influential piece of Szabo's on my thinking about Bitcoin, LN, and related tech.

2024-10-20 16:09:56

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Looks like LMNT is about 1/35th the amount of salt as seawater.
The rule against drinking ocean water is for long-term hydration. If you ingest excess salt, your body purges it by purging water. Seawater is about 3.5% salt. Saline used for human transfusion is about 0.9% salt and that's roughly the max rate at which your body can purge water. So if your drink 1 liter of seawater while your blood sodium is already balanced, you will need to pee or sweat about 3.5 liters of water. Obviously that's going to quickly lead to dehydration. A quick search says LMNT is 1 gram salt, or about 0.1% if added to a liter (kilogram) of water, so even if your blood sodium is fully balanced, your body will only need to purge about 10% of that liter. That allows you to hydrate while replenishing any salt you sweated out during exercise.

2024-09-25 18:56:54

This was my favorite thing to have co-authored this year. The obvious audience for this report is current and prospective donors to Brink, and I think it does a great job of communicating how Brink's engineers help strengthen and enhance the network. But I also wanted to write a report that the engineers could show to their families to help communicate how meaningful the work they do is.
The families of many engineers don't really understand their loved one's work. They can't tell the difference between world-changing development and goofing off at the computer.
What would be great is to give Bitcoin contributors industry-leading salaries, more than megacorps pay for soul-crushing work. If your parents or partner knows you make $500,000/year, they won't think you're goofing off. But every satoshi spent on one contributor is a sat Brink can't spend on another talented contributor who wants to do the work but also needs an income.
Instead, Brink provides more modest grant amounts and focuses on giving engineers the opportunity to work on projects they personally find highly meaningful. For many people, that's a tradeoff they'll happily take. But if your parents or partner or friends have high expectations of you, it can be hard to communicate that you're just as much at the top of your game as a dev at a top-10 tech company even though you make less money.
Where that problem exists, I hope this report will help. Engineers receiving grants from Brink did so many extraordinary things this year. I was overcome with pride of being even a tiny part of the team. I hope both the objective set of accomplishments and the subjective awe will shine through to anyone reading about each engineer's accomplishments, especially their family.
#nevent1q…j53y
#nevent1q…0hcn

2024-09-25 00:14:39

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Thanks! I didn't actually see that in my quick search. That's a decent price.

2024-09-24 21:42:03

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Oh, really? I just quick skimmed Amazon and saw they still want a prescription, but I guess I'll have to dig deeper. https://image.nostr.build/9c5c72e3ff07374bf772b1e9b158943074048f942d1247b4581c8953d5d9843f.jpg

2024-09-24 17:50:17

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It's really annoying to me that you can't buy one without a prescription (or by circumventing normal procurement).

2024-09-18 01:41:08

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For Mastering Bitcoin, the publisher wanted to go with Bitcoin-the-network and bitcoin-the-currency. I was fine with that, as its what I normally used, but I discovered when working with the non-Bitcoiner editor and proofreaders that they had a hard time guessing which was which. I got a lot of queries about whether I really meant to use caps (or vice versa for lowercase), especially since I did occasionally use the wrong case. Next time I work with normies, I'll probably ask to just use common noun casing throughout.

2024-09-13 16:53:42

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♥️

2024-09-12 22:55:34

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@nprofile…sl3l noted in discussion on Delving that you only need a proof of transaction contents (e.g. the coinbase outpoint) if the tx is exactly 64 bytes. Otherwise, a proof of tx size is sufficient, which is compatible with SHA midstate verification (i.e., ~100 bytes max data).

2024-09-04 06:14:59

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Are you sure about this answer? I thought a default node would keep stale blocks it downloaded indefinitely, only deleting them from disk if it was configured to prune.

2024-09-03 18:15:04

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It's very imprecise. Worse, it's only useful for individuals who contribute large amounts of hashrate, i.e. those who could reasonably solo mine. @nprofile…sl3l makes the point that the difficulty of preventing block withholding could be a significant contributor to limiting pool options: https://mailing-list.bitcoindevs.xyz/bitcoindev/Zp%2FGADXa8J146Qqn@erisian.com.au/

2024-09-03 18:05:43

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That seems like it could be compatible with banning withholders. Thanks!

2024-09-03 18:04:39

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You detect it with statistical analysis. If Mallory is excessively unlucky, e.g. she's submitted 3x as many shares as necessary to find a block but none of her shares were blocks, you ban her.

2024-09-03 17:51:28

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What auditability? I thought @nprofile…7cz8 was talking about eliminating miner identity, which prevents eviction of misbehaving miners.
I'm all for anon mining, but pools that allow it now put themselves at risk of block withholding.

2024-09-03 16:11:13

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If there's no traceability, there's no way to ban miners who perform block withholding attacks. @nprofile…sl3l has recently written about this problem and potential solutions (e.g. oblivious shares, which alas requires an invasive hard fork).

2024-09-03 16:05:24

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I ground slept for about 10 years and thought it was great---except when I was sick and wanted some place to lay when feeling miserable. Alas, my fiancee insists on a bed.

2024-08-31 16:32:18

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Ejecting garbage into space during battles and fleet maneuvers could damage their own ships, so they had to be prepared to store it for hours or days. But trash is bulky, so they compacted it. Also, maybe compaction was followed by incineration or some other processes to destroy any potentially classified material that accidentally got thrown away.

2024-08-30 16:48:25

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Amethyst

2024-08-19 19:11:05

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So you save 50 kb on the query but may receive a response that's bloated by potentially more than 50 kb of unwanted data?

2024-08-19 17:28:57

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Isn't that 0.01% error rate over the total number of public keys in the set? E.g. if I follow 1,000 out of the 1 million publeys on nostr, I'll get guaranteed updates from my 1k follows plus updates from about 100 random people (1e6 x 0.0001)?

2024-08-12 16:35:35

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Congratulations!!!

2024-08-06 21:58:16

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We'll be covering Dark Skippy in Friday's Optech Newsletter. I'm guessing @nprofile…f4ja would be happy to have you as a guest on the subsequent Recap podcast next Tuesday.

2024-08-03 21:33:22

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I have an Amazon Basics wireless mouse that's starting to fail, with the scroll wheel having worn down. Looks like I paid $13.99 four years ago, so $3.50/year.

2024-07-08 16:13:18

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I'm unaware of any evidence of long term storage in any prehistoric society of large amounts of honey or fat. The quantities needed to significantly extend human life during famine are huge and preservation using prehistoric methods was difficult and unreliable. It's much easier to keep animals alive than to store their fat. It's much easier to have bees guard their own honey against predation than to have humans guard it.

2024-07-08 16:04:40

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Yeah, 1 kg/day in modern times to maintain weight and full fitness sounds right to me. In prehistoric times, the average human was significantly shorter (so lower BMI) and the body will down regulate calorie burn as it enters starvation, so I guessed the minimum requirement during a prehistoric famine was about half, i e. 0.5 kg.

2024-07-06 17:42:50

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I dunno, you need rather large amounts of them to significantly prolong life during famine, about 0.5 kg/day/person, and you need to protect them from spoilage and insect/animal predation. That only sounds plausible for a static society, but before domestication, only nomadic societies were likely to obtain regular access to honey and non-fish meat.

2024-06-24 01:36:28

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How will vbytes and varops interact? There were a lot of problems when we had both bytes and sigops, e.g. invalid block templates. Now, in taproot, we size transactions as max(vbytes, sigops*50 - 50). Which model will varops use?

2024-06-18 21:07:06

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I use Frigate.

2024-05-18 19:12:01

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No, but it might be useful to track overall address reuse, e.g. what percentage of total BTC supply is in output scripts that have been spent from before.

2024-05-13 20:13:04

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Anything technical?

2024-05-10 21:05:42

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If our civilization is interplanetary, mining will occur when electricity is the cheapest, i.e. near the sun (not the earth).

2024-05-06 15:48:53

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I'm jealous.

2024-05-06 08:34:25

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Yeah, I'll put that on my todo list. Gonna need a bigger home server closet.

2024-05-06 05:29:32

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I don't understand why I've haven't been able to buy a router in the past decade that just works well continuously and supports more than 4 clients.

2024-05-03 17:01:58

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Do you think using a donor directed fund would be easier?

2024-04-30 04:51:16

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Had to send the funds from my Phoenix wallet somewhere and SNI is a resource I frequently use. Can't wait to see the redesign! https://image.nostr.build/3afd2538b3564897fe6bff7136fad114846862ec1930a7949164ae5aa87d45bd.jpg

2024-04-30 04:36:29

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I don't think LN-penalty is the main problem here, as the most powerful form of the attack starts by filling channels with as many expiring HTLCs as possible, which is a problem for any channel design. The only solutions I'm aware of are (1) temporary dynamic block size increases, which only increase the cost of the attack by a small multiple, (2) some form of time stop, although that increases the risk of capital losses from the time value of money, and (3) various bond designs, although they upfront accept losses to the time value of money.
Of those options, I think bonds may be under explored but I also think that the main downsides of time stop may be almost entirely mitigated by John Law's hierarchical channel factories design, which would involve channels being opened by three parties, with two preferred partners being able to continue exchanging funds in the channel even if the third counterparty initiated a force close that was taking forever due to a time stop.

2024-04-30 04:06:14

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The attack you describe was called "forced expiration spam" in the original LN paper. I usually call it an "expiration flood". Other people have other names for it. See https://bitcoinops.org/en/topics/expiration-floods/

2024-04-29 19:37:55

Re: testnet drama.
Last I checked, there was about 1 EH (1,000 PH) of sha256d hashrate for rent through on an easy API. If you really oppose what @npub17u5…t4tp is doing, you can do the following:
- Set up a testnet node.
- On that node, use the invalidateblock RPC to locally reject blocks that you think Lopp created.
- Setup a Stratum v1 server and connect it to your testnet node.
- Rent hashrate and point it at your stratum server.
That should be enough, but if someone tries to exploit the testnet difficulty drop to create long reorgs, set the time on your testnet node to 119 minutes in the future.
But, if you want to be productive, I suggest just switching to signet.

2024-04-25 16:27:47

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BIP63 stealth addresses also has a number but no content. The basic idea is simple but one part was problematic and there was no agreement how to work around it. BIP47 payment codes is one way (that many people don't like); proposed BIP352 silent payments is a modern take on the problem that has broader support (but still comes with tradeoffs).

2024-02-24 23:52:36

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Man, that's not what I associate the abbreviation GCC with. 🤣

2024-02-09 19:54:49

For not the first time, I tried to get Nostr running on my Linux desktop with Firefox and failed. The nos2x-fox extension pegs one of my cores at 100% and the Alby extension wants full access to my LN node to do anything. So, for now, it will continue to be the case that the only time I post or reply on Nostr is when I'm stuck somewhere with only my phone to entertain me.

2024-01-15 05:39:41

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Suggestions:
- Really experiment with public transit in a new place. In places with good taxi service, you can't get stranded, so it's reasonable to just yolo it and not do any route planning when taking the bus/tram/whatever. You'll often discover cool places and nice routes that way.
- Find the parks. People in cities do all sorts of cool things in parks that people with large houses and backyards only rarely do in public. There's something magical about being in a public space with thousands of people all having fun and living the best parts of their lives.
- Look for a public events calendar, check Meetup, and (if you are willing) Facebook. Lots of people means lots of things happening.
- Figure out how to do the things you love even if they seem foreign to the place you are. It's your chance to find amazing people who enjoy those things so much that they're willing to go against the local culture to do them.
- Oh, and if you can, go up the stairs and not an elevator. It's good exercise, gives you a sense of agency, and you'll feel awesome each time you reach your floor.

2024-01-12 18:22:44

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What about swap in potentiam, which can already used with Phoenix today IIUC? https://bitcoinops.org/en/newsletters/2023/12/20/#:~:text=ZmnSCPxj%20and%20Jesse%20Posner%20proposed,transaction%20while%20it%20is%20offline.

2024-01-11 18:16:23

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VanEck also donating: https://www.google.com/amp/s/www.coindesk.com/business/2024/01/05/vaneck-to-donate-5-of-profits-from-btc-etf-to-bitcoin-core-developers/amp/
Disclosure: I'm a member of Brink's grant committee (unpaid).

2024-01-09 20:39:53

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Are you sure that's possible with MIT?

2024-01-02 23:50:18

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There's an archive here based on the public api: https://github.com/jamesob/delving-bitcoin-archive
Code for mirroring yourself: https://github.com/jamesob/discourse-archive
This was discussed on the ML: https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-November/022142.html

2024-01-02 16:47:23

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What's the fundamental difference between the forum and the existing (centralized) dev mailing lists, which have worked reasonably well for over a decade?

2023-12-14 08:46:52

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Using gpt4all with "mistral openorca" which is currently on mistral 7b. I did some quick tests with a hosted version of mistral 8x7b and I was super impressed, so I'm really looking forward to getting that locally when it becomes available.

2023-12-14 03:54:49

Usually I don't find generative AI useful for writing @npub1hku…432p newsletters. I often don't start out fully understanding the ideas we cover and so I can't tell if what the AI writes is accurate or nonsense. Writing it myself forces me to really think about it, and I can just keep iterating on my draft until it feels accurate (and then it gets peer reviewed).
However, this week I'm writing the year in review newsletter and it's fun just pasting in my text from earlier in the year into a LLM running privately on my laptop and asking it to summarize everything into a single paragraph. I can just edit, add links, and I'm done! Whee!

2023-12-14 02:29:09

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https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2022-April/020242.html

2023-12-11 14:05:01

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There's a history of discussion and implementation here: https://bitcoinops.org/en/topics/anchor-outputs/
The summaries aren't detailed, especially not about motivation, but they do point to some conversations that may have been important at the time but would be a bit hard to find now (e.g., they used the old "simplified commitments" name).
See also: https://bitcoinops.org/en/topics/cpfp-carve-out/

2023-12-06 14:32:01

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I've actually bet play money on it having less than 1% at the end of the 2024: https://manifold.markets/harding/will-oceanxyz-find-1-of-the-final-1?r=aGFyZGluZw
(A pretty easy stat to fake, so I wouldn't put too much stock in it)

2023-12-06 06:25:44

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That's what I thought before I moved here, now I eat spam all the time and enjoy it.
I still hate pineapple though.

2023-11-13 00:50:49

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That's not correct. The spenders must send a signed psbt before the receiver gives them a utxo to include. If the spender bails, the receiver can broadcast the signed psbt. Although there's no benefit from the bailing, there's also no loss to either party from it.

2023-11-04 01:33:18

I'm pleased to announce that Mastering Bitcoin (3rd edition), co-authored by @aantonop and myself, has been sent to the printer. Ebooks should be available around Nov 15th. Print books should be available by early December.
https://dtrt.org/posts/mb3e-announcement/
New chapters and sections of the book cover schnorr signatures, scriptless multisignatures, MAST, P2C, taproot, tapscript, bech32(m), fee management, scriptless threshold signatures, compact block filters, compact blocks, and more.
Updates in the third edition include the evolution of Bitcoin scripting, terminology updates, RGB and taproot assets, much more backup and recovery info, and complete witness transaction serialization.
Compared to my initial draft, the book has been much improved thanks to comprehensive technical reviews from npub1j5mp526z5fkz9wkrk6mt5nzu43xndyrwkr8mnqngdqwytgcpc5vqcnsd5c Olaoluwa Osuntokun and René Pickhardt. I can't fully express how much gratitude I have for them.
All of my royalties from Mastering Bitcoin (3rd ed.) will be donated to @bitcoinbrink to support Bitcoin developers. It's impossible to write about Bitcoin technology without wanting to support the people who build it and then give it to the world for free.
This updated book wouldn't have happened without my editors at O'Reilly: Angela Rufino, Michelle Smith, Kristen Brown, and Clare Laylock. Their commitment to giving readers the best possible book shines in every one of the over 500 emails we exchanged during the past 10 months.
I also owe a huge thanks to the inimitable Adam Jonas, who did the scariest thing possible to an educational author: introduced me to teachers such as Femi Longe and Dulce Villarreal who will be depending on the book for their classes. Femi, Dulce: I hope it meets expectations!
Finally, I have to confess that updating the book took more out of me than I expected. I don't think I could've finished if it hadn't been for the unreserved support and encouragement of my incredible partner. Thank you, Amanda. I love you.

2023-05-20 18:18:55

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I hope so.

2023-05-19 18:22:03

Chapter 10 of Mastering Bitcoin (3rd edition) has now been sent to my editor. This chapter is about the P2P network. Major additions include BIP152 compact block relay and BIP157/8 compact block filters.
https://nostr.build/i/df92cd309d31f0dcc1bad6c27c98740c28cef57fbe1ec1e79773653a87e18ea1.jpg

2023-05-13 18:21:43

Just tried Bard and there was misinformation in every answer it gave me. ChatGPT gets lots of stuff wrong too, but I think Bard is about an order of magnitude worse. Unless my anecdotal experience is non-typical, I'm amazed Google is encouraging people to use this thing.---it just makes me think that Google is losing it.

2023-05-13 16:45:14

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Left a reply about what I think might be the issue: https://github.com/JoinMarket-Org/joinmarket-clientserver/issues/1465#issuecomment-1546706665

2023-05-08 16:18:33

Status update #2 on Mastering Bitcoin, 3rd edition: I sent my editor the first draft of Chapter 9 about transaction fees. This chapter consists of 90% new material. It describes the basic principles of Bitcoin's fee (block space) market, fee estimation, fee bumping (both CPFP and RBF, with a infobox about opt-in RBF vs full RBF), transaction pinning, CPFP carve out, and package relay. Sections from the previous edition's Transactions chapter about fees being implicit in a transaction and (anti) fee sniping are moved to this chapter.
This is the last planned major change from the 2nd edition, so I'm hoping to finish the remaining chapters pretty quick.
https://nostr.build/i/c6852d791e2c80b3d1cc31833be2ec878f8736d16a42ae413802b6314d615c1b.jpg

2023-04-21 23:13:22

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What prevents an image server from adding an identical-appearing watermark to an alternative image?

2023-04-19 15:04:06

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I'm not a "screw you" kinda guy, so when I couldn't write short, I usually wrote nothing at all. Sometimes, in retrospect, that was a good call, but it other cases it just meant that misinformation stayed out there or it received a "screw you" or other unhelpful response from someone else.
I think brevity should be encouraged but not required.

2023-04-17 17:26:43

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Unfortunately, with stock BIP158, you can't avoid monitoring for reused addresses until you've spent all the coins you want to spend that you previously received to those addresses. That's because BIP158 "basic" filters use the output scriptPubKey to track both receiving bitcoins and spending them.
For example, Alice receives some bitcoins to bc1pfoo in a transaction in a block. The filter for that block commits to OP_0 foo.
Later, Alice spends that transaction output. The filter for that later block also commits to OP_0 foo.
If, in between those two blocks, someone else sent bitcoins to bc1pfoo, then the filter for that block would also commit to OP_0 foo. It wouldn't be possible for Alice's wallet to determine whether the filter made that commitment because new bitcoins were received to bc1pfoo or because of a spend of the bitcoins she had previously received.

2023-04-17 16:33:47

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It depends a lot on the threat model. Let's consider two scenarios:
1. Mallory is monitoring all traffic to a given IP address (no Tor, or Tor is completely broken) and wants to learn which outputs it controls. Every transaction downloaded by that IP address which doesn't belong to its wallet increases the anonymity set of the transactions which do belong to that IP addresses's wallet. Because BIP157/8 involves downloading whole blocks (typically a few thousand transactions), it would create decent-sized anonymity sets even if there was never a false positive; adding the occasional false positive block just improves that.
By comparison, Bitcoin Core is like having a 100% false positive rate; now the anonymity set is every transaction in the entire best block chain.
2. Mallory knows a Bitcoin address and wants to find the IP address of the wallet controlling that Bitcoin address (again, no Tor). If Mallory has the ability to surveil IP addresses that the wallet might be using, she can spent a tiny bit of money to that address to get the wallet to download that block. Many other wallets will also download that block, either because they had transactions in it or because of the false positive rate, so that's the initial anonymity set. Mallory can then send another tiny bit of money to the address. The wallet she's interested in will download that new block but many of the other wallets which previously downloaded it won't (they didn't have a tx in that block or it wasn't a false positive for them). This shrinks the anonymity set. Each time Mallory sends a bit more money to the address, the anonymity set shrinks further, until she finds the IP address.
By comparison, Bitcoin Core is immune to this attack. It downloads every seemingly-valid block unconditionally.

2023-04-17 15:35:28

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I disagree about there not being any privacy benefit. Every Wasabi instance that's paired with a local node performs exactly the same non-coinjoin/non-broadcasting network operations, making it impossible to use network activity to determine which instance received which transaction outputs. (This is called information theoretic perfect privacy.)
Wasabi instances that use BIP157/8 compact block filters each perform different network operations depending on their transaction history. These operations are performed over Tor, with Wasabi frequently rotating network identities, which defeats simple attacks---but is still far from perfect. If the threat model includes global passive surveillance, record-now-decrypt-when-post-quantum surveillance, crypto or protocol vulnerabilities in Tor or Wasabi, or other threats, then it may be possible to identify the IP address of a wallet controlling a certain address.
More importantly "it only saves a bit of bandwidth and storage" ignores what is, to me, the primary benefit of running a full node: the assurance that the bitcoins you receive have all the characteristics necessary to make them easy to sell in the future, specifically that every previous transfer of those bitcoins was valid according to the consensus rules and that all of those transfers are documented on the block chain currently known to have the most proof of work.

2023-04-17 15:00:41

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What's anti-klepto?

2023-04-16 18:16:25

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Want? Yes. Should? Probably not. Keeping on top of Bitcoin and LN is already more than full time some weeks (including this week, alas).

2023-04-16 17:44:31

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I'd definitely read that.

2023-04-16 16:23:41

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I think that's kind of an interesting dynamic. One one hand, if you have >50% of hash rate in the US, then you have a ~$5 billion/yr industry that at least some politicians are going to want to keep happy. On the other hand, if the censorship is egregious, either the value of BTC is going to drop (contracting the industry) or some users are going to switch to a new PoW function (possibly decimating the industry). It's kind of the same dynamic you get from regulating industry in general, e.g. raising local minimum wage, but the feedback loop in Bitcoin is currently much faster than most industries, so the same politician who's in power when the problem is created is likely to still be in power when the problem manifests.

2023-04-15 00:45:35

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❤❤❤

2023-04-11 20:38:59

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I had the same thought when reading that book, although I rather enjoyed the rest. But during the Money chapter, I was thinking, "nah, I like Szabo's theory way better".

2023-04-09 14:31:27

Status update on Mastering Bitcoin, 3rd edition: yesterday I sent my editor the first draft of Chapter 8 about digital signatures. In addition to small revisions from the second edition about ECDSA and sighashes, the draft now describes schnorr signatures, scriptless multisignatures, and scriptless threshold signatures. Plus there's now a description of the major differences between ECDSA and schnorr signatures. If I finish the remaining 6 chapters early, I hope to come back and add some information about signature adaptors.
https://nostr.build/i/nostr.build_99363bf600b1feb48496720c58d17376ffb68da065170522eee9f1dd74245e48.png