Me when I cannot empty the last 0.0000001 #bitcoin from a wallet: 
Years ago I remember Maxwell being very sniffy about the threshold ECDSA ideas that involved Paillier. There was a swathe of implementations in the last I guess, 6 years or so but, somehow I started reading some papers that were released since 2021 (links below) and realized .. it's kind of a shit show out there. The main protocols are the old Lindell one and GG18/GG20 ; they're using zk proofs and paillier to basically share keys for an ECDSA calculation. It is complex, and it doesn't "flow" as nicely as using one prime order group. An example: in one of the ZK proofs in GG18, you need to calculate a value t_1 = e * beta + gamma, where e is a typical fiat shamir hash, beta is the secret and gamma is a blinding factor. this looks very familiar right? (s = k + ex), but there's a vital detail: t_1 is *just an integer*, not an element of a finite field. Hence, even though e and beta might be values in a field of order N, let's say, then if you choose gamma to also be in that same 0..N-1 set, you've suddenly leaked the secret!
Why? Because e*beta is in the range 0..N^2, not 0..N. The way to exploit that is to just divide by e: t1/e = beta + gamma/e. And since gamma/e is less than 1 with probability 0.5, the right hand side is basically just beta!
This is one example, but others included improperly formed paillier public keys and absence of range proof checks, seen in implementations in the wild. Both Binance and Bitgo had the dubious privilege of being mentioned as having implementations that could leak the entire set of private keys in *one* signature - even covertly (i.e. the signing goes through). Not saying everything hasn't been fixed from these reports, but, sheesh.
https://eprint.iacr.org/2021/1621
https://eprint.iacr.org/2023/1234
https://eprint.iacr.org/2019/114
#cryptography
Thank you for sharing!
#bitcoin is code (among other definitions), and the code makes the purest form of money
Everything else can try to be anything else—have fun with that
I would add find challenges often
When I was given/inherited a box of #legos—not a set but just a cardboard box full of lego bricks—but they we’re like six or eight different shapes
Rectangle of 8 bumps🧱
Square of 4
Long stick
Long flat stick
Big pad
…plus some broken pieces and some knock-off brand pieces that didn’t connect well
It was the most perfect toy that could be anything I wanted—imagination made it work. Sometimes the resulting shape had to be imagined, too
I sometimes wish modern legos didn’t come with instruction manuals
#Bitcoin 🧡💜 #nostr
I’ve made a #privatekey just for that paradigm…
Unless one forsakes all of cyberspace, analog can only get you so far in the digital realm
All that matters is hashrate and merchant adoption rate.
nostr:nprofile1qqsdhcrqt2w8x9et446j8ge8kgmd2h4ykc6wsrnc4yqnmdu3lr74ktqpz3mhxue69uhhyetvv9ujuerpd46hxtnfduq3vamnwvaz7tmjv4kxz7fwwpexjmtpdshxuet5qyxhwumn8ghj7mn0wvhxcmmvslrw4j and nostr:nprofile1qqszq5u5k7esc9stdjv2se9k2fmcjg5x8g6jz4wjzh7ytxwr7yvwhvcpr3mhxue69uhkummnw3ez6vp39eukz6mfdphkumn99e3k7mgpr3mhxue69uhkummnw3ez6vpj9eukz6mfdphkumn99e3k7mgpremhxue69uhkummnw3ez6vpn9ejx7unpveskxar0wfujummjvu0a59dr putting in the hard yards.
Amen! Now moar search tools!!
Another thing that bothered me about #fiat and #banks—you are allowed to withdraw cash from “any ATM in the worldwide network”, but the moment you want to deposit cash into an ATM that isn’t your bank’s ATM…❌
Stick with #bitcoin 
#bitcoin operates in a modular finite field. What does that mean, and can you think of any other examples in the world or nature where the same thing exists?
I can’t get over the two-tone colouring of stainless steel and brass of the #bitcoin private key
#striking #bitcoin #nostr #privatekey #offline #airgapped #$5wrenchattackcountermeasurers https://video.nostr.build/dc288b83b38d713fa1f44286c5b4ce8f91c09e01bca1945b7f1715c913a41529.mp4
It’s a long list….Might be a shorter list of what I am not into—that’s my typical problem
All things #bitcoin, including making #bitcoin accessible, too
What about you?
I will set out and notify #nostr someday. A little trip would restore the soul