Posts tagged #Cryptography
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Bitcoin and quantum computing: counting for yourself with a node
The third piece of the «Bitcoin and quantum computing» family: not the numbers, but how to redo them. Every command needed to count for yourself, with your own node, how many coins already have their public key in view: the census of the UTXO set by lock type and by age, the pass that counts reuse, the outpoint index, the check of your own addresses without handing them to anyone. Three levels, from minutes to days, that can be left half done while still giving a verifiable result. Every step carries the real output of our own run at block 957,301 and the fingerprints anyone must land on by redoing it. Public code, MIT licence.
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Bitcoin's locks
Every coin on Bitcoin sits behind a lock: the scriptPubKey, the program that states under which conditions it can be spent. A reference piece on the lock types, from the first outputs of 2009 to Taproot and the quantum-resistant proposals: P2PK, P2PKH, bare multisig, P2SH, SegWit (P2WPKH and P2WSH), P2TR, each shown byte by byte on a real transaction verifiable with a node. What each type exposes of the public key, why a lock and an address are not the same thing, and how to read the language of scripts: pushes, ops and the stack.
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The number used only once
Every digital signature consumes, besides the key, a second secret number generated for the occasion and good only once: the nonce. If it repeats, two signatures give back the private key with a subtraction: it happened to the PlayStation 3 and to Bitcoin wallets on Android in 2013. How the recovery works in ECDSA and in Schnorr, shown on the bytes of real signatures; why a nonce that is merely predictable betrays as well; and the point that concerns Bitcoin: a node validates a signature born from a disastrous nonce like any other, consensus cannot notice.
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How big is «practically impossible»?
«It is practically impossible for someone else to generate your own seed» sounds like a way out, and anyone who does not buy it deserves an answer rather than reassurance. How big the space a Bitcoin wallet's seed comes from really is, why the right question is not whether someone guesses yours but whether two identical seeds will ever turn up among all the seeds ever generated, what it would cost a perfect machine just to count them, what difference twelve words instead of twenty-four actually makes, and what a passphrase adds. The fragile point is not the coincidence but the birth, which is to say the generator: the Android episode of 2013 and the Coldcard defect of July 2026.
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Bitcoin and quantum computing: the data (July 2026)
How much of all bitcoin already has its public key in view, since when, and at what pace it keeps exposing itself: 7.02 million BTC, about 35% of the circulating supply, of which 5.08 million exposed by address reuse and 1.93 million by construction (the original P2PK and Taproot). A census of the UTXO set at block 957,301, carried out with an ordinary node and reproducible down to the fingerprint, read table by table and figure by figure: concentration per lock, the curve by epoch of revelation, the pace of reuse year by year. This text is a deep dive off the path that starts from the post on the quantum computing threat: there the reasoning and the wider considerations, here the numbers and the method to check them with.
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Bitcoin and quantum computing
A quantum computer will not be able to rewrite Bitcoin's ledger: it will probably be able, one day, to open some of its locks. What Shor's and Grover's algorithms actually do, why elliptic curve signatures are the target and hashes are not, which coins already have their public key in view (about 35% of the circulating supply, recounted on our own node) and which do not, where the machines stand with dates attached, where the post-quantum migrations under discussion stand (BIP-360, BIP-361), and why the hard part is not technical but a matter of governance: what to do with the coins of those who can no longer move them. A snapshot declared as of July 2026.