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[109.224.244.24]) by gmr-mx.google.com with ESMTPS id 006d021491bc7-69d77385303si58872eaf.3.2026.05.21.12.40.06 for (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Thu, 21 May 2026 12:40:07 -0700 (PDT) Received-SPF: pass (google.com: domain of conduition@proton.me designates 109.224.244.24 as permitted sender) client-ip=109.224.244.24; Date: Thu, 21 May 2026 19:39:57 +0000 To: Alex From: "'conduition' via Bitcoin Development Mailing List" Cc: Bitcoin Development Mailing List Subject: Re: [bitcoindev] Post-Quantum BIP-86 Recovery via zk-STARK Proof of BIP-32 Seed Knowledge Message-ID: In-Reply-To: <49236a10-94ea-440a-9b53-63ae2c7ac964n@googlegroups.com> References: <02378fd1-17a4-47aa-89fa-ee87626def65n@googlegroups.com> <49236a10-94ea-440a-9b53-63ae2c7ac964n@googlegroups.com> Feedback-ID: 72003692:user:proton X-Pm-Message-ID: 45c4e9cb3f79895a099af8df7fdeb7a46bfe04c3 MIME-Version: 1.0 Content-Type: multipart/signed; protocol="application/pgp-signature"; micalg=pgp-sha512; boundary="------b35a7d3a1ef1d5fcdd994bf2a603211804b35c60393776f00bead442dc5831e6"; charset=utf-8 X-Original-Sender: conduition@proton.me X-Original-Authentication-Results: gmr-mx.google.com; dkim=pass header.i=@proton.me header.s=protonmail header.b=AR8iWzFB; spf=pass (google.com: domain of conduition@proton.me designates 109.224.244.24 as permitted sender) smtp.mailfrom=conduition@proton.me; dmarc=pass (p=QUARANTINE sp=QUARANTINE dis=NONE) header.from=proton.me X-Original-From: conduition Reply-To: conduition Precedence: list Mailing-list: list bitcoindev@googlegroups.com; contact bitcoindev+owners@googlegroups.com List-ID: X-Google-Group-Id: 786775582512 List-Post: , List-Help: , List-Archive: , List-Unsubscribe: , X-Spam-Score: -1.0 (-) This is an OpenPGP/MIME signed message (RFC 4880 and 3156) --------b35a7d3a1ef1d5fcdd994bf2a603211804b35c60393776f00bead442dc5831e6 Content-Type: multipart/mixed;boundary=---------------------7f0ca486501dda1c228d5df509aeef16 -----------------------7f0ca486501dda1c228d5df509aeef16 Content-Type: multipart/alternative;boundary=---------------------ed62dac9fcdf5626346066b3bbe62018 -----------------------ed62dac9fcdf5626346066b3bbe62018 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="UTF-8" Laolu's OP benchmarks which you cite used a design which was hard to arithm= etize, so the proofs took ~2s to verify and almost a minute to prove. After= some suggestions from Luke and myself, he brought the benchmark verify tim= e down to the millisecond range, and the proving time down to just a few se= conds. https://groups.google.com/g/bitcoindev/c/Q06piCEJhkI/m/5QOIiIozAgAJ Also these benchmarks would improve even further if we use a custom circuit= instead of an arithmetizing VM. regards, conduition On Thursday, April 30th, 2026 at 5:52 PM, Alex wrot= e: > > STARKs don't take multiple seconds to verify. You can run the code in m= y repo > > to see, it verifies in tens of milliseconds [1]. > And >=20 > > Verification takes ~1.8 seconds >=20 > are not logically consistent. Your original statement was 1.8 seconds and= I referred to it as such, but now you say it's tens of milliseconds. Techn= ically 1.8 seconds is some multiple of tens of milliseconds, true, but I wa= s referring to your original statement of 1.8 seconds. > The core point is that; exposing the complexity that is STARK verificatio= n in Bitcoin nodes, where 1.8 seconds of CPU-time is expected (as per your = original statement), this is a gaping flesh wound in terms of DOS attack su= rface. >=20 > Further on, the same argument regarding standardization of zkVMs or Circu= its is highly problematic and complex, a bug in such a Circuit cannot be fi= xed without scrambling the verification and there is no way so standardize = it other than through arbitrary code versioning. >=20 > Whether you recursively prove a proof and so on is irrelevant to the comp= lexity and DOS question. You could make a STARK that certified the entire B= itcoin chain in a few KB of data, but the complexity and DOS attack surface= for such a recursive proof is just as galactic as 1 single proof. >=20 > The point is that, if you expose STARK verifications anyone can send high= ly costly STARKs that take multiple seconds of CPU time (a DOS attack). >=20 > onsdag 29 april 2026 kl. 03:21:51 UTC+2 skrev Olaoluwa Osuntokun: >=20 > > Hi Sadiq, > >=20 > >=20 > > > The scheme extends to BIP-352 (Silent Payments) > > Yup, as shown in my latest post, we can batch aggregate multiple claims= into a > > single proof. If this were to be deployed at some point in the future, = devs > > would be able to scower wallets/protocol/codebases for other recovery > > proofs/claims that could be added. > >=20 > >=20 > > > The zk-STARK proof? or this mechanism should definitely be bound to t= he > > > spending transaction and the input being spent. > > Def, this would be it would be straight forward to bind the proof to a = given > > wtxid/sighash. > >=20 > >=20 > > > Curious why not generalise beyond BIP-32? P2PKH and P2WPKH without BI= P-32 > > > still commit to an unrevealed secret =E2=80=94 HASH160(k=C2=B7G) =E2= =80=94 as long as the pubkey > > > has never previously appeared on-chain. A zk-STARK proof should apply= here > > > too? > > No fundamental reason, just I decided to focus the initial demo on P2TR= . One > > could easily swap in this section where the Taproot Output key is deriv= ed with > > another script type instead [1]. > >=20 > > [1]: https://github.com/Roasbeef/bip32-pq-zkp/blob/main/bip32/taproot.g= o#L91-L94 > >=20 > > -- Laolu > >=20 > >=20 > > On Mon, Apr 13, 2026 at 12:21=E2=80=AFPM sadiq Ismail wrote: > >=20 > > > Hi Laolu, list, > > >=20 > > > Nice work. > > >=20 > > > The scheme extends to BIP-352 (Silent Payments). The BIP-352 receiver= reconstructs the output P using their private scan key, public spend key, = and public information from the spending transaction A. > > > See BIP-352 Scanning. BIP-352 recommends but does not mandate BIP-32 = for deriving the scan and spend keys, but specifies the following derivatio= n paths when BIP-32 is used: > > >=20 > > > b_scan =3D BIP32Derive(s, m/352'/coin_type'/account'/1'/0) > > > b_spend =3D BIP32Derive(s, m/352'/coin_type'/account'/0'/0) > > >=20 > > > For all silent payment addresses generated using BIP-32, your techniq= ue applies. The prover produces a zk-STARK proof that the program BIP32Deri= ve(s, p_scan) and BIP32Derive(s, p_spend) were run correctly, > > > and that the resulting keys reconstruct the on-chain output P using a= long with A. > > >=20 > > > As you highlighted txid is not committed in the proof currently, the = argument is replayable. The current POC does not bind to where the coins go= . Anyone who observes the chain could copy it and attach it to a different = transaction, spending the same UTXO to a different address. Worse for silen= t payment, because all user UTXO have the same secret BIP32Derive(s, p_scan= ) and BIP32Derive(s, p_spend) except for A. > > > The zk-STARK proof? or this mechanism should definitely be bound to t= he spending transaction and the input being spent. > > >=20 > > > Curious why not generalise beyond BIP-32? P2PKH and P2WPKH without BI= P-32 still commit to an unrevealed secret =E2=80=94 HASH160(k=C2=B7G) =E2= =80=94 as long as the pubkey has never previously appeared on-chain. A zk-S= TARK proof should apply here too? The prover argues for the correctness of = HASH160(k=C2=B7G) =3D h, where k is the private key scalar and k=C2=B7G is = the elliptic-curve point, without ever revealing k or the pubkey. This woul= d allow recovery of a broader set of funds. If it were decided that classic= al signatures for these output types are invalidated and only a valid zk-ST= ARK proof is required to spend, anyone who holds the original secret can un= lock their funds. > > >=20 > > > P.S. I am not for or against disabling valid spend paths post-quantum= , just discussing the technical possibilities. > > >=20 > > > Best, > > > Abubakar Sadiq > > > On Friday, April 10, 2026 at 7:47:09=E2=80=AFPM UTC+2 conduition wrot= e: > > >=20 > > > > Ah! Amazing work! 2 seconds to prove is really crazy. Proving a sin= gle SHA256 and one modular addition on my CPU back in the day took like 20 = seconds. Your GPU is coming in clutch for this. I best RISC0 has also impro= ved quite a bit since then. > > > > I think the next optimization step would be pre-seeding the two SHA= 512 midstates from the host, so you only need to prove two SHA512 compressi= on calls instead of four. Intuitively I expect this would at best halve you= r prover time from 2sec, to probably a little over 1sec, and your verifier = time will probably drop as well since that also seems to scale with circuit= complexity. > > > >=20 > > > > I think I have two half-decent arguments now as to why this won't a= ffect security: > > > >=20 > > > > First, even if a fraudulent prover is handed the correct midstates = to use, the prover would still have to do the hard work of finding the pare= nt secret key needed as a witness. This is at least the same difficulty as = finding the parent `sk` if we just hashed it without a chaincode at all, us= ing two bare SHA512 calls - the only thing that changes is the midstate, an= d the SHA512 input length suffix. Starting from a different midstate doesn'= t magically give the attacker a head-start in a 256-bit search space lookin= g for `sk`. A frauduent prover would know the child secret key `k =3D sk + = int(I[32:]) % n`, but they don't know `int(I[32:])` or `sk` so they cannot = solve for either. > > > >=20 > > > >=20 > > > > Nominally, the fraudulent prover wouldn't even know the correct mid= states, so their task is strictly harder. > > > >=20 > > > > Secondly, here's another argument as to why finding the midstates i= n the first place should also be hard. > > > >=20 > > > >=20 > > > > Any adversary who could solve this problem by finding the right mid= states could be used as an oracle to prove the existence of partial 2-cycle= s in SHA512. > > > >=20 > > > >=20 > > > > - Given a SHA512 hash `I`, set `sk =3D int(I[32:])` > > > > - Compute `k =3D sk + sk % n` > > > > - Use the black-box fraudulent prover on the child key `k` to fin= d correct midstates such that > > > > =20 > > > >=20 > > > > ` ` > > > > `` `I =3D=3D SHA512( || SHA512( || 0x00 || sk= || i))` `` > > > > `k =3D=3D int(I[32:]) + sk % n` > > > > `=3D=3D sk + sk % n` > > > >=20 > > > >=20 > > > > Remember that `sk =3D int(I[32:])`. Thus for these conditions to ho= ld, the proof forger must be able to find not just the correct midstates, b= ut also midstates which give a 2-stage partial hash cycle so that: > > > >=20 > > > >=20 > > > > `I =3D=3D SHA512( || SHA512( || 0x00 || I[32:= ] || i))` > > > >=20 > > > >=20 > > > > This seems unlikely or at least very difficult. > > > >=20 > > > >=20 > > > > regards, > > > > conduition > > > >=20 > > > > On Thursday, April 9th, 2026 at 5:56 PM, Olaoluwa Osuntokun wrote: > > > >=20 > > > > > Hi Condution, > > > > >=20 > > > > > So I implemented both variants of your idea. My intuition was rig= ht in that it > > > > > doesn't do much to reduce the size of the final succinct size, bu= t the final > > > > > xpriv variant resulted in a significant reduction in both proving= time, and > > > > > also memory usage. I also re-ran the original succint proof for t= he original > > > > > Taproot claim and got a better value for the final proof time (de= f need a > > > > > better benchmark env+set up!). > > > > >=20 > > > > > Here's a breakdown of the resource requirements for the various p= roofs: > > > > > * Full Taproot > > > > > image ID: > > > > > 8a6a2c27dd54d8fa0f99a332b57cb105f88472d977c84bfac077cbe70907a690 > > > > > composite: > > > > > seal 1797880 > > > > > prove 49.32s > > > > > verify 0.10s > > > > > peak RSS 11907399680 > > > > > succinct: > > > > > seal 222668 > > > > > prove 64.30s > > > > > verify 0.03s > > > > > peak RSS 11927207936 > > > > >=20 > > > > > * Hardened xpub > > > > > image ID: > > > > > ad4ebc0ef6ce51e0f581cc8d14742a5b97738e9decd3fe2b0f1746de5bad9617 > > > > > composite: > > > > > seal 513680 > > > > > prove 14.63s > > > > > verify 0.04s > > > > > peak RSS 11783503872 > > > > > succinct: > > > > > seal 222668 > > > > > prove 17.29s > > > > > verify 0.02s > > > > > peak RSS 11782307840 > > > > >=20 > > > > > * Hardened xpriv > > > > > image ID: > > > > > 8401a36e4f54cb2beaf9ac7677603806cf9d775e90ef5a70168045a3c0df0849 > > > > > composite: > > > > > seal 234568 > > > > > prove 1.98s > > > > > verify 0.02s > > > > > peak RSS 3144171520 > > > > > succinct: > > > > > seal 222668 > > > > > prove 2.84s > > > > > verify 0.02s > > > > > peak RSS 3145990144 > > > > >=20 > > > > > So we can see that the succinct proof sizes are all about the sam= e. However the > > > > > xpriv variant can be proved directly in just 2 seconds on my mach= ine! It also > > > > > requires just 3 GB of memory for the proof as well. > > > > >=20 > > > > > I've created some additional supporting documentation to detail e= xactly what > > > > > the new proofs do and their results: > > > > >=20 > > > > > * https://github.com/Roasbeef/bip32-pq-zkp/blob/main/docs/reduced= -variants.md > > > > >=20 > > > > > * https://github.com/Roasbeef/bip32-pq-zkp/blob/1c89fdb398180a2b3= eff7761b7f4b233d455c6c9/README.md#reduced-proof-variants > > > > >=20 > > > > > * https://github.com/Roasbeef/bip32-pq-zkp/blob/438c548ca9b49d83e= f4019974a5171f5e06fa840/docs/claim.md#reduced-variant-claims > > > > >=20 > > > > >=20 > > > > > Once again, thanks for the great ideas! I wonder if we can improv= e on this > > > > > round of proof golf further before reaching down a lower level wi= th some sort > > > > > of AIR compiler =F0=9F=A4=94. > > > > >=20 > > > > > -- Laolu > > > > >=20 > > > > > On Thu, Apr 9, 2026 at 1:53=E2=80=AFPM Olaoluwa Osuntokun wrote: > > > > >=20 > > > > > > Hi Conduition, > > > > > >=20 > > > > > > > You need only prove this much more general statement (2): "I = know a BIP32 > > > > > > > xpriv which derives this xpub via one or more hardened steps"= . > > > > > >=20 > > > > > > > I'm amending my prior suggestion slightly: The circuit (guest= program) > > > > > > > could take in an xpriv (e.g. at m/86'/0') and output a child = xpriv > > > > > > > (e.g. at m/86'/0'/0') to the journal (instead of outputting a= child > > > > > > > xpub). > > > > > >=20 > > > > > > That's an excellent insight! > > > > > >=20 > > > > > > As mentioned in my recent reply, with risc0's "succinct" receip= t type, I was > > > > > > able to get the proof size down to 220 KB, at the cost of 3.5x = longer total > > > > > > proving time. > > > > > >=20 > > > > > > Your proposal definitely reduces the complexity of the core sta= tement to be > > > > > > proved, which would speed up the proving time for the normal > > > > > > default/composite receipt type. > > > > > >=20 > > > > > > I'll try to hack this up, and then run a head to head compariso= n to see this > > > > > > simpler statement actually results in a smaller proof then the = final > > > > > > succinct receipt of either of the proof variants. Based on my c= urrent > > > > > > intuition w.r.t the lower level details, I think the final succ= inct proof > > > > > > size would be on the same order of magnitude re size. > > > > > >=20 > > > > > > However, this can still be a win as then this would provide pot= ential future > > > > > > users with a less resource intensive proof, which can then be > > > > > > aggregated/rolled up into a final succinct proof in a batched m= anner. > > > > > >=20 > > > > > > This line of optimization is also more interesting if one were = to look at > > > > > > hand rolling a custom AIR to avoid the overhead that the RISC-V= emulation > > > > > > adds to the rirsc0 proof chain, given that it entirely skips do= ing any EC > > > > > > operations at all for the final statement. > > > > > >=20 > > > > > > ---- > > > > > >=20 > > > > > > Re the commit/reveal approach, to be honest I'm not fully caugh= t up on that > > > > > > proposal. That original thread got pretty long, so I dropped of= after a > > > > > > point =F0=9F=98=85. I'll revisit that specific branch of the th= read so I can digest it > > > > > > and develop a proper opinion, then get back to you re compariso= ns! > > > > > >=20 > > > > > > -- Laolu > > > > > >=20 > > > > > > On Wed, Apr 8, 2026 at 1:23=E2=80=AFPM conduition wrote: > > > > > >=20 > > > > > > > Oh, I've been a fool, a foolish fool. > > > > > > >=20 > > > > > > > We don't even need to do point multiplication in the circuit = at all. > > > > > > >=20 > > > > > > > I'm amending my prior suggestion slightly: The circuit (guest= program) could take in an xpriv (e.g. at `m/86'/0'`) and output a child xp= riv (e.g. at `m/86'/0'/0'`) to the journal (instead of outputting a child x= pub). > > > > > > >=20 > > > > > > > This is safe because remember, EC spending has been disabled = in this context, and to a quantum attacker, an xpub is computationally equi= valent to its xpriv. So why bother hiding it? The child xpriv doesn't give = an observer anything they can't already do with the equivalent xpub. > > > > > > >=20 > > > > > > > The guest program then is basically the BIP32 CKDpriv algorit= hm, restricted to a single hardened derivation step. The verifier gets the = child xpriv, but can't use it to forge new proofs. Honest verifiers use the= xpriv to derive the child address(es) as suggested in my last message, to = authenticate spending. > > > > > > >=20 > > > > > > > Designing the guest program like this will massively reduce y= our circuit complexity, because EC point multiplication is wayyyyy harder f= or the RISC0 compiler to arithmetize than a simple hash function. In my pri= or work with RISC0, I made a guest program which ran a SHA256 hash and an E= C point multiplication. I found that pruning EC point arithmetic from my gu= est program improved prover runtime by a factor of over 100x. > > > > > > >=20 > > > > > > > If I am not fever-dreaming and this is indeed possible, then = the new circuit's complexity will be dominated not by point multiplication,= but by the HMAC-SHA512 call. Our new task is then to figure out how much w= e can internally optimize the HMAC-SHA512 call for STARK proving. Here's a = few ideas. > > > > > > >=20 > > > > > > > If you bust open HMAC-SHA512, it looks like this: > > > > > > >=20 > > > > > > > `HMAC_SHA512 =3D SHA512((K=E2=8A=950x5c) || SHA512((K=E2=8A= =950x36) || msg))` > > > > > > >=20 > > > > > > > ...where in the context of BIP32 hardened CKD, the HMAC key `= K` is the chaincode (padded with zeros to 128 bytes) and `msg =3D (0x00 || = sk || i)` is the parent secret key and child index. > > > > > > >=20 > > > > > > > Since `len(K) =3D 128` is the SHA512 block size, we need a to= tal of 4 SHA512 compression calls: > > > > > > >=20 > > > > > > > 1. to compress `(K=E2=8A=950x36)` > > > > > > > 2. to compress the `msg` (and SHA512 padding/length) > > > > > > > 3. to compress (K=E2=8A=950x5c), and > > > > > > > 4. a final compression call to tie it all together. > > > > > > >=20 > > > > > > >=20 > > > > > > > The output of that last compression call is partitioned into = the child chaincode, and a key delta which is added to the parent secret ke= y (modulo the curve order), producing the child EC secret key. This last st= ep is arithmetically simple; the SHA512 calls are where most of the arithme= tic complexity lies. > > > > > > >=20 > > > > > > > The question then becomes, which of these compression calls c= an be done outside the circuit, and which are truly essential for security? > > > > > > >=20 > > > > > > > Note how the parent secret key is the most important piece fo= r soundness. The circuit needs to prove the parent secret key existed in th= e hash function preimage, and is correctly related to the child secret key = via modular addition. So compression call (2) seems unavoidable. The others= are less rigid. > > > > > > >=20 > > > > > > > I'd argue that if we really dig into the hard relation we're = trying to prove here, we can reduce it to this statement: > > > > > > >=20 > > > > > > > Given a child xpriv with secret key `k`, chaincode `c` and in= dex `i`, I know a preimage `x` and secret key `sk` such that: > > > > > > > ` ` > > > > > > > `I <- SHA512( || SHA512( || 0x00 || sk = || i)`) > > > > > > > `c =3D=3D I[:32]` > > > > > > > `k =3D=3D int(I[32:]) + sk % n` > > > > > > >=20 > > > > > > > Seeing as the `` slots are arbitrary, and we know = in BIP32 they are always exactly one-block long, it seems easy to throw out= the compression calls (1) and (3). The host can precompute the relevant SH= A512 midstates outside the circuit, and pass the midstates into the guest p= rogram as secret inputs. The tradeoff is that this permits malicious prover= s the flexibility of choosing their starting midstates (though hash input l= ength can be fixed at 192 bytes). I'm not entirely sure if this meaningfull= y weakens the verifier's soundness. Ethan Heilman might have opinions on th= is, he knows a lot more about attacking hash functions than I do. Intuitive= ly, I doubt sampling random SHA512 midstates is that much better than sampl= ing a random HMAC key (chaincode) `K` and computing the resulting midstates= . > > > > > > >=20 > > > > > > >=20 > > > > > > > This reduces our circuit to, i think, the minimum acceptable = security floor for provers: two SHA512 compression calls, which commit to a= parent secret key. > > > > > > >=20 > > > > > > >=20 > > > > > > >=20 > > > > > > >=20 > > > > > > > regards, > > > > > > > conduition > > > > > > > On Wednesday, April 8th, 2026 at 12:09 PM, 'conduition' via B= itcoin Development Mailing List wrote: > > > > > > >=20 > > > > > > > > Hi Laolu, > > > > > > > > Great work getting this working in the real world. I've hea= rd many people on delving and the mailing list conjecture based on this ide= a, but you're the first person i've seen who's willing to put their money w= here their mouth is, and actually build a prototype. Bravo! > > > > > > > >=20 > > > > > > > > It seems to me the circuit (guest program) could be simplif= ied. Notice how the guest code computes the entire HD wallet key path, incl= uding hardened and non-hardened derivation steps, and also computes the tap= root output key with key-tweaking. I'd argue these steps are extraneous to = the core hard relation you want the STARK to prove, and could be safely rem= oved to reduce proof size and improve performance. > > > > > > > >=20 > > > > > > > > In reality, you needn't go so far as to prove (1) "I know a= BIP39 seed which derives this taproot output key". You need only prove thi= s much more general statement (2): "I know a BIP32 xpriv which derives this= xpub via one or more hardened steps". The latter statement (2) still canno= t be forged by a quantum adversary even if they know your account-level xpu= b, but it entails far less computation to prove and verify. The rest of the= original statement (1) can be done externally outside the circuit. > > > > > > > >=20 > > > > > > > > Example. If i have a wallet with a taproot address at `m/86= '/0'/0'/1/2`, I could prove I know the xpriv at `m/86'/0'` which derives th= e xpub at `m/86'/0'/0'`. Then I provide the remaining key path elements /`1= /2` in the witness. Note, i do not mean we derive the xpriv at `m/86'/0'` i= nside the guest program. I mean the prover derives `m/86'/0'` first (in the= host), and then writes that xpriv into the guest program's inputs. The gue= st program derives and outputs the xpub at `m/86'/0'/0'`. The verifier may = check the STARK output (xpub) is correctly computed, then use the given key= -path to manually derive the taproot address from the xpub themselves, outs= ide the circuit, and validate that address against the UTXO i'm spending. T= he verifier thus has confirmed the prover knew an xpriv which (through a ha= rdened derivation step) derives the correct taproot output key. > > > > > > > >=20 > > > > > > > > This change significantly reduces the size of the circuit. = >From a glance, I see the original guest program performs 6 HMAC-SHA512 call= s (1 for the master key, 5 for the BIP32 derivation steps), two SHA256 comp= ression calls (for the taptweak hash), and two point multiplications. With = this simplified variant, we are invoking only a single HMAC-SHA512 call and= a single point multiplication. I can't say for sure, but I expect this wil= l improve your proof size and runtime significantly. > > > > > > > >=20 > > > > > > > > This change also makes the circuit more generally applicabl= e to other rescue contexts. For instance, it could be applied to BIP340 xon= ly keys inside a taproot script tree, or in a P2(W)SH address to an ECDSA p= ublic key, or to P2(W)PKH addresses. > > > > > > > >=20 > > > > > > > > Concerned about publishing xpubs? Remember that we are assu= ming regular EC spending is locked in this context, so it is safe-ish to sh= are account xpubs with quantum attackers. At best the xpub can be used for = surveillance but not forgery. If one would prefer not to share the account-= level xpub on-chain for privacy reasons, the proof could be extended to als= o derive the unhardened child xpub at `/1/2` inside the guest program (but = we still do not need to do the taproot key tweaking in the guest program). > > > > > > > >=20 > > > > > > > > We should also talk scaling efficiency. Given the cost of S= TARKs, this style of proof should be able to authorize spends for more than= one UTXO. Say you have a wallet with 10 different UTXOs held by distinct a= ddresses in the same BIP44 account. One single STARK proof could authorize = spending all 10 of them, by simply committing all 10 input signature hashes= into the journal, and labeling the inputs with the corresponding 10 BIP32 = key paths somehow. The verifier would need to check the proof only once and= not 10 times. The 10 UTXO spends could be validated using the common xpub = from the STARK proof's journal. > > > > > > > >=20 > > > > > > > > For a slightly related work proving a similar relation for = hashed addresses, using different STARK technology stacks, see this delving= post. > > > > > > > >=20 > > > > > > > > However, all this said, my personal preference for long-ter= m procrastinator rescue is still for commit/reveal strategies which prove e= ssentially the same statement about BIP32 in a two-step procedure. They get= the job done with much lighter cryptographic machinery and much smaller wi= tnesses: a few hundred bytes over two transactions, compared to a few milli= on bytes in one transaction with STARKs. Boris Nagaev and I discussed this = on the list a while back. That said, commit/reveal requires more careful de= sign and seems to demand the use of external quantum-safe coins to make the= commitment in the first place, so perhaps the cost would be worth it to so= me people? IDK. What do you think of commit/reveal compared to STARKs for t= his purpose? > > > > > > > >=20 > > > > > > > > regards, > > > > > > > > conduition > > > > > > > > On Wednesday, April 8th, 2026 at 12:18 AM, Olaoluwa Osuntok= un wrote: > > > > > > > >=20 > > > > > > > > > Hi y'all, > > > > > > > > >=20 > > > > > > > > > I found some spare time this last weekend to dust off a l= ittle side project > > > > > > > > > I started last August: extend TinyGo [1] to be able to pr= oduce RISC-V ELF > > > > > > > > > binaries capable of being run as a guest on the risc0 pla= tform to generate > > > > > > > > > zk-STARK proofs of arbitrary programs. Initially, I didn'= t really have a > > > > > > > > > clear end target application, it was mainly a technical c= hallenge to force > > > > > > > > > me to learn a bit more about the RISC-V platform, and als= o the host/guest > > > > > > > > > architecture of risc0. Fast forward ~9 months later, and = an initial killer > > > > > > > > > use case popped into my mind: a zk-STARK proof that a Tap= root output public > > > > > > > > > key was generated using BIP-32, via a given BIP-86 deriva= tion path. > > > > > > > > >=20 > > > > > > > > > More formally: > > > > > > > > > ```math > > > > > > > > > \mathcal{R} =3D \left\lbrace\; > > > > > > > > > (\overbrace{K,\, C}^{\textsf{public}} ;\; \underbrace{s,\= , \mathbf{p}}_{\textsf{witness}}) > > > > > > > > > \;\middle|\; > > > > > > > > > \begin{aligned} > > > > > > > > > K &=3D \textsf{BIP86Taproot}\bigl(\textsf{BIP32Derive}(s,= \, \mathbf{p})\bigr) \\ > > > > > > > > > C &=3D \textsf{SHA256}\bigl(\texttt{"bip32-pq-zkp:path:v1= "} \;\|\; \mathbf{p}\bigr) > > > > > > > > > \end{aligned} > > > > > > > > > \;\right\rbrace > > > > > > > > > ``` > > > > > > > > >=20 > > > > > > > > > where $K$ is the Taproot output key, $C$ is the path comm= itment, $s$ is the > > > > > > > > > BIP-32 seed, and $\mathbf{p}$ is the derivation path. > > > > > > > > >=20 > > > > > > > > >=20 > > > > > > > > > I was able to get everything working e2e over the weekend= , after making > > > > > > > > > some tweaks to my initial architectural game plan! > > > > > > > > >=20 > > > > > > > > > The TL;DR is that: > > > > > > > > >=20 > > > > > > > > > * Given that the Taproot commitment scheme is post-quantu= m secure [3], in > > > > > > > > > the future we can deploy a soft fork to _disable_ the key= spend path, > > > > > > > > > and force all Taproot spends to instead flow through the = script path > > > > > > > > > (not my idea, commonly discussed amongst developers, not = sure who > > > > > > > > > proposed it first). At that point, Taproot starts to rese= mble BIP-360. > > > > > > > > >=20 > > > > > > > > > * That works for script path spends, but then leaves all = the BIP-86 > > > > > > > > > wallets in a bad position, as they generated outputs that= provably > > > > > > > > > don't commit to a script path at all. > > > > > > > > >=20 > > > > > > > > > * A 2023 paper (Protecting Quantum Procrastinators with S= ignature > > > > > > > > > Lifting: A Case Study in Cryptocurrencies [4]) proposed a= solution to this, > > > > > > > > > namely _seed lifting_ (use BIP-32 as the one-way function= to the > > > > > > > > > Picnic PQ Signature scheme) to provide a post-quantum pro= of of secret > > > > > > > > > information a quantum attacker wouldn't be able to easily= obtain. > > > > > > > > >=20 > > > > > > > > > * The downside of that is that it reveals the secret BIP = 32 seed, > > > > > > > > > exposing other non migrated UTXOs of a user. > > > > > > > > >=20 > > > > > > > > > * With this project I've cobbled together a series of pro= jects to be able > > > > > > > > > to generate a zk-STARK proof that a Taproot output public= key was > > > > > > > > > generated via BIP-32 invocation of a BIP-86 derivation pa= th. > > > > > > > > >=20 > > > > > > > > > * In the future a variant of this scheme can be used to e= nable wallets > > > > > > > > > that generated the private keys via BIP-86, to have a pos= t quantum safe > > > > > > > > > exit path in case they don't bother moving their coins in= time to the > > > > > > > > > yet-to-be-decided post quantum signature scheme. > > > > > > > > >=20 > > > > > > > > > To achieve this end, I needed to create/fork a series of = repos: > > > > > > > > >=20 > > > > > > > > > * tinygo-zkvm: https://github.com/Roasbeef/tinygo-zkvm > > > > > > > > > * A fork of TinyGo that supports the flavor of RISC-V (rv= 32im) that > > > > > > > > > risc0 requires to generate/execute a guest program to lat= er be proved > > > > > > > > > by the host. > > > > > > > > >=20 > > > > > > > > > * risc0: https://github.com/Roasbeef/risc0 > > > > > > > > > * Mostly a bug fix to their c-guest example, along with s= ome > > > > > > > > > additional documentation on how to get things running. Th= e repo is > > > > > > > > > unmodified other than that. Recent updates to the repo ma= de the > > > > > > > > > entire process much easier (Go guest+host), more on that = later. > > > > > > > > >=20 > > > > > > > > > * go-zkvm: https://github.com/Roasbeef/go-zkvm > > > > > > > > > * Go utilities to take a RISC-V ELf binary produced by ti= nygo-zkvm, and > > > > > > > > > package it in the expected R0BF format, which combines th= e user > > > > > > > > > generated RISC-V ELF (the thing that is executed to gener= ate the > > > > > > > > > proof) along with the v1compat ELF kernel, which is risc0= 's execution > > > > > > > > > environment. > > > > > > > > >=20 > > > > > > > > > * This also includes a Go host package, which loads the g= uest program, > > > > > > > > > executes it, and generates a trace to later be proved. Th= is is > > > > > > > > > achieved via a C FFI compat layer between Go and the orig= inal Rust > > > > > > > > > host/proving/verification code. > > > > > > > > >=20 > > > > > > > > > * bip-32-pq-zkp: https://github.com/Roasbeef/bip32-pq-zkp > > > > > > > > > * The project that packages everything together, this con= tains the: > > > > > > > > > * Guest Go program that defines the secret witness and > > > > > > > > > claim/constraints of the proof. > > > > > > > > >=20 > > > > > > > > > * The C FFI wrapper around the OG Rust host, which is use= d to load > > > > > > > > > the guest program, execute it, generate a trace, then fin= ally > > > > > > > > > generate a proof. > > > > > > > > >=20 > > > > > > > > > Details of the final proof as generated on my Mac Book (A= pple Silicon M4 > > > > > > > > > Max, 128 GB of RAM): > > > > > > > > > * Takes ~55 seconds or so to generate+proof, including ex= ecution. This > > > > > > > > > uses Metal for GPU acceleration on the platform. > > > > > > > > > * Uses ~12 GB of ram. > > > > > > > > > * Final proof size is ~1.7 MB. > > > > > > > > > * Verification takes ~1.8 seconds, and uses ~32 MB of mem= ory. > > > > > > > > >=20 > > > > > > > > > On several layers, this demo is far from optimized (more = on that later), > > > > > > > > > this is meant to serve as a PoC to demonstrate that with = the latest > > > > > > > > > software+hardware, a proof of this complexity is well wit= hin reach. > > > > > > > > >=20 > > > > > > > > > For those curious re the e2e details I've generated this = tutorial that > > > > > > > > > explains the entire system top to bottom: > > > > > > > > > https://github.com/Roasbeef/go-zkvm/blob/main/docs/tutori= al.md. > > > > > > > > >=20 > > > > > > > > > If you got to this point in this mail, and don't care abo= ut the lower level > > > > > > > > > details, thanks for reading up until now, and feel free t= o return back to > > > > > > > > > the _The Net of a Million Lies_, or as better known in ou= r Universe: > > > > > > > > > Monitoring the Situation and/or slopfotainment! =F0=9F=AB= =A1 > > > > > > > > >=20 > > > > > > > > > ## Motivation + Background > > > > > > > > >=20 > > > > > > > > > As commonly known, in the case of an adversary that posse= sses a quantum > > > > > > > > > computer capable of breaking classical asymmetric cryptog= raphy, any coins > > > > > > > > > stored in UTXOs with a known public key are vulnerable. T= his is the case > > > > > > > > > for any P2PK outputs from waaaay back, and also any other= outputs that have > > > > > > > > > revealed their public key. Pubkey reveal might happen due= to address re-use > > > > > > > > > (spending from the same script twice), or Taproot outputs= , which publish > > > > > > > > > the public key plainly in the pkScript. > > > > > > > > >=20 > > > > > > > > > As detailed in [3], for Taproot outputs, a widely circula= ted plan is > > > > > > > > > roughly to: disable the _keyspend_ path (requires a simpl= e signature), > > > > > > > > > enforcing a new rule that all Taproot spends must then fl= ow through the > > > > > > > > > script path. Spending via the script path requires an ope= ning of the > > > > > > > > > Taproot commitment (C =3D I + H(I || H(M))), which was sh= own to be binding even > > > > > > > > > under classic assumptions, as H(M) (tapscript merkle root= ) is still a > > > > > > > > > collision-resistant function. > > > > > > > > >=20 > > > > > > > > > That means any UTXO that _does_ commit to a script path h= as a future escape > > > > > > > > > hatch _if_ such a softfork would need to be deployed in t= he future. > > > > > > > > > However, what about all the other wallets that use BIP 86= , and don't commit > > > > > > > > > to a script path at all? Under a strict version of this e= xisting > > > > > > > > > proposal, those wallets would basically be locked forever= . > > > > > > > > >=20 > > > > > > > > > The goal of this work is to demonstrate a practical solut= ion (discussed > > > > > > > > > against devs, but never implemented AFAICT): generate a z= k proof that an > > > > > > > > > output was generated using BIP-86. For the zk-Proof, we s= elect zk-STARKs, > > > > > > > > > as they're plausibly post quantum since they rely only on= symmetric > > > > > > > > > cryptography: layers of merkle trees over an execution tr= ace, along with > > > > > > > > > some novel sampling/error-correction algorithms. > > > > > > > > >=20 > > > > > > > > > At this point, you may be asking: "if the quantum adversa= ry can derive the > > > > > > > > > private key to a random taproot public key, then how exac= tly does this > > > > > > > > > help?". The answer lies in the structure of BIP-32! BIP-3= 2 takes an initial > > > > > > > > > 128-512-bit seed (with BIP-39, either 12 or 24 words), th= en runs it through > > > > > > > > > HMAC-SHA512 keyed by "Bitcoin seed" to produce the master= extended private > > > > > > > > > key. An adversary who wants to forge this proof needs to = find a _colliding_ > > > > > > > > > seed: a different seed s' such that HMAC-SHA512("Bitcoin = seed", s') produces > > > > > > > > > the same master key. The BHT algorithm (Brassard-Hoyer-Ta= pp [6]) is the > > > > > > > > > best known quantum collision finder, and it runs in time = proportional to the > > > > > > > > > cube root of the output space: 2^(n/3). For HMAC-SHA512's= 512-bit output, > > > > > > > > > that's ~2^171 quantum operations, well above even NIST's = highest > > > > > > > > > post-quantum security category. Therefore, if you generat= ed a wallet using > > > > > > > > > BIP-32, you possess _another_ secret that a quantum adver= sary can't > > > > > > > > > efficiently reconstruct! > > > > > > > > >=20 > > > > > > > > > This demo focuses on the Taproot case, but the rough appr= oach also applies > > > > > > > > > to any other output generated via BIP-32. BIP 32 was orig= inally published in > > > > > > > > > 2012, over 14 years ago. So safe to say that _most_ walle= ts were generated > > > > > > > > > under this scheme. However, Bitcoin Core only officially = adopted BIP-32 in > > > > > > > > > 2016/2018, moving away from their existing key pool struc= ture. I can't say > > > > > > > > > how much BTC is held today in outputs generated with Bitc= oin Core's original > > > > > > > > > key pool, but if you have coins generated via that mechan= ism, you may want > > > > > > > > > to consider migrating them to a BIP-32 wallet. > > > > > > > > >=20 > > > > > > > > > ## TinyGo + RISC-V + risc0 > > > > > > > > >=20 > > > > > > > > > Now for some of the lower level details. risc0 is a STARK= based proving > > > > > > > > > system that takes a RISC-V ELF binary generated by a gues= t program (any > > > > > > > > > program generating using their flavor of rv32im can be pr= oved), executes > > > > > > > > > that in a host environment, generates a trace, then produ= ces a STARK proof > > > > > > > > > from that. > > > > > > > > >=20 > > > > > > > > > Today you can take some subset of Rust, compile it to an = ELF using their > > > > > > > > > toolchain, then execute it, generate a trace, to finally = prove+verify it > > > > > > > > > using their system. > > > > > > > > >=20 > > > > > > > > > This demo took a bit of a round about journey to achieve = this, as after > > > > > > > > > all, the journey is most of the fun, ain't it! > > > > > > > > >=20 > > > > > > > > > For the past 10 years or so, my Bitcoin stack of choice (= lnd/btcsuite) uses > > > > > > > > > a series of Go libraries, so I wanted to be able to re-us= e them, first for > > > > > > > > > this demo, then also in the future for other projects. > > > > > > > > >=20 > > > > > > > > > TinyGo is a special Go compiler based on LLVM, that targe= ts mostly embedded > > > > > > > > > environments. You can use it to generate go programs that= can run on > > > > > > > > > micro controllers, or on web assembly (producing a smalle= r binary than if > > > > > > > > > you used the normal stdlib path). > > > > > > > > >=20 > > > > > > > > > TinyGo supports RISC-V, but _not_ the 32-bit variant of R= ISC-V that risc0 > > > > > > > > > relies on. So the first step here was to create a new tar= get definition for > > > > > > > > > TinyGo: riscv32-unknown-none, which uses base integer + m= ultiply/divide > > > > > > > > > instructions with no compressed instructions, which uses = 4 KB stacks for > > > > > > > > > each task. From there, I created a new linker script > > > > > > > > > (`targets/riscv32im-risc0-zkvm-elf.ld`) which created a m= emory layer > > > > > > > > > identical to what risc0 expects. The final component was = a new runtime > > > > > > > > > (`src/runtime/runtime_zkvm.go`), which implemented a few = platform specific > > > > > > > > > syscalls for risc0 (putchar(), exit(), ticks(), and growH= eap()). > > > > > > > > >=20 > > > > > > > > > When I tried to get this working last year, I had to also= implement a number > > > > > > > > > of kernel syscalls (called ecalls in the platform [7]) to= handle: read+write > > > > > > > > > to stdin/stdout, halting, and the journaling mechanism (t= he transcript of > > > > > > > > > execution committed to), which basically implement the ke= rnel that the guest > > > > > > > > > executes in. Fast forward to 2026, and after pulling the = latest version of > > > > > > > > > the repo, I realized that they now make a libzkvm_platfor= m.a, which packages > > > > > > > > > up the kernel nicely to be linked against. So I threw out= my custom kernel > > > > > > > > > code, and slotted that in instead. > > > > > > > > >=20 > > > > > > > > > The final component is a C FFI layer that enables me to u= se _both_ a Go > > > > > > > > > guest (the program to be proved) and a Go host (the thing= that executes the > > > > > > > > > program and generates the final proof). > > > > > > > > >=20 > > > > > > > > > ## BIP-32+Taproot zk-STARK Proof > > > > > > > > >=20 > > > > > > > > > With basic proofs working (like the classic: I know the f= actorization of a > > > > > > > > > number `n`), I was unblocked to generate the actual proof= . The claim/proof > > > > > > > > > is represented with the following JSON artifact: > > > > > > > > > ``` > > > > > > > > > { > > > > > > > > > "schema_version": 1, > > > > > > > > > "image_id": "8a6a2c27dd54d8fa0f99a332b57cb105f88472d977c8= 4bfac077cbe70907a690", > > > > > > > > > "claim_version": 1, > > > > > > > > > "claim_flags": 1, > > > > > > > > > "require_bip86": true, > > > > > > > > > "taproot_output_key": "00324bf6fa47a8d70cb5519957dd54a02b= 385c0ead8e4f92f9f07f992b288ee6", > > > > > > > > > "path_commitment": "4c7de33d397de2c231e7c2a7f53e5b581ee3c= 20073ea79ee4afaab56de11f74b", > > > > > > > > > "journal_hex": "010000000100000000324bf6fa47a8d70cb551995= 7dd54a02b385c0ead8e4f92f9f07f992b288ee64c7de33d397de2c231e7c2a7f53e5b581ee3= c20073ea79ee4afaab56de11f74b", > > > > > > > > > "journal_size_bytes": 72, > > > > > > > > > "proof_seal_bytes": 1797880, > > > > > > > > > "receipt_encoding": "borsh" > > > > > > > > > } > > > > > > > > > ```` > > > > > > > > >=20 > > > > > > > > > The `image_id` is basically a hash of the ELF, so you kno= w what the prover > > > > > > > > > executed. There are then a few flags that control the cla= im version and > > > > > > > > > whether BIP-86 derivation is a part of the proof. BIP-86 = was only adopted > > > > > > > > > post-Taproot, so if you have an existing BIP-44 path, you= can instead opt to > > > > > > > > > claim that instead. The Taproot key we're generating the = proof against is > > > > > > > > > also part of the _public data_, as it sits plainly on the= chain for all to > > > > > > > > > see. We then also include a `path_commitment`, which is a= commitment to the > > > > > > > > > exact BIP 86 path that the prover used. Finally, we also = commit to the > > > > > > > > > journal hex, which is basically a commitment to the publi= c claim. > > > > > > > > >=20 > > > > > > > > > Assuming you've built the project, then you can generate = the proof (even > > > > > > > > > passing in an arbitrary BIP-32 seed and derivation path w= ith) > > > > > > > > > ``` > > > > > > > > > make prove GO_GOROOT=3D/path/to/go1.24.4 > > > > > > > > > ``` > > > > > > > > >=20 > > > > > > > > > Then verify it with: > > > > > > > > > ``` > > > > > > > > > make verify GO_GOROOT=3D/path/to/go1.24.4 > > > > > > > > > ``` > > > > > > > > >=20 > > > > > > > > > The default prove target writes: > > > > > > > > > * ./artifacts/bip32-test-vector.receipt > > > > > > > > > * ./artifacts/bip32-test-vector.claim.json > > > > > > > > >=20 > > > > > > > > > The receipt is the STARK proof artifact. claim.json is th= e stable, > > > > > > > > > human-readable description of the public statement being = proved. > > > > > > > > >=20 > > > > > > > > > ## Application to a Future Keyspend Disabling Soft fork > > > > > > > > >=20 > > > > > > > > > As mentioned above, assuming the community is forced to d= eploy a keyspend > > > > > > > > > disabling soft fork in the future, we can also deploy som= e variant of > > > > > > > > > this proof to enable both BIP-86 wallets, and also any BI= P-32 wallet, to > > > > > > > > > sweep their funds into a new PQ output. > > > > > > > > >=20 > > > > > > > > > In 2026, we've shown that this is achievable using 2 year= old consumer > > > > > > > > > hardware. I don't doubt that the upcoming advancements (e= g: photonics, new > > > > > > > > > flavor of high bandwidth memory, etc) in hardware (driven= by the fierce AI > > > > > > > > > race) will make such a proof even more feasible. > > > > > > > > >=20 > > > > > > > > > One thing to note is that this proof has a few layers of = indirection, > > > > > > > > > mainly the RISC-V layer that adds overhead which increase= the total amount > > > > > > > > > of steps, and therefore the size of the proof. A producti= on grade > > > > > > > > > deployment would likely instead hand roll a custom STARK = proof for this > > > > > > > > > exact statement, to achieve a faster and smaller proof). > > > > > > > > >=20 > > > > > > > > > # Future Work > > > > > > > > >=20 > > > > > > > > > In terms of future work, there're a number of interesting= following up > > > > > > > > > projects that can be pursued from here. > > > > > > > > >=20 > > > > > > > > > One basic one is that the current proof doesn't actually = commit to a > > > > > > > > > spending txid and/or sighash. That can be trivially incor= porated into the > > > > > > > > > proof. Going a step further, the execution of the guest p= rogram can even > > > > > > > > > _generate_ a valid schnorr signature to permit spending. > > > > > > > > >=20 > > > > > > > > > Looking to the memory+computational requirements necessar= y to generate the > > > > > > > > > proof, I've left two low hanging fruits: > > > > > > > > >=20 > > > > > > > > > 1. First, we can speed up the Elliptic Curve operations t= he proof requires > > > > > > > > > (scalar base mult, then addition, or more performantly Do= uble Scalar > > > > > > > > > Multiplication via the Strauss-Shamir trick). For this we= can use the > > > > > > > > > syscalls/precompile in the risc0 env for big integer arit= hmetic: > > > > > > > > > sys_bigint and sys_bigint2. With this, the guest calls in= to the kernel > > > > > > > > > to use an optimized/accelerated circuit for the modular a= rithmetic, > > > > > > > > > reducing cycles, steps, and thus proof size. > > > > > > > > >=20 > > > > > > > > > 2. Second right now, the entire claim is a single proof. = Instead, we can > > > > > > > > > first break that up using their recursive proof/compositi= on syscalls: > > > > > > > > > sys_verify_integrity+sys_verify_integrity2. We can then a= ssembled a > > > > > > > > > series of these proofs into a _single_ statement, which c= an save block > > > > > > > > > space by aggregating N proofs into a single proof. > > > > > > > > >=20 > > > > > > > > > -- Laolu > > > > > > > > >=20 > > > > > > > > > [1]: https://tinygo.org/ > > > > > > > > >=20 > > > > > > > > > [2]: https://risczero.com/ > > > > > > > > >=20 > > > > > > > > > [3]: https://eprint.iacr.org/2025/1307 > > > > > > > > >=20 > > > > > > > > > [4]: https://eprint.iacr.org/2023/362 > > > > > > > > >=20 > > > > > > > > > [5]: https://microsoft.github.io/Picnic/ > > > > > > > > >=20 > > > > > > > > > [6]: https://en.wikipedia.org/wiki/BHT_algorithm > > > > > > > > >=20 > > > > > > > > > [7]: https://github.com/Roasbeef/go-zkvm/blob/main/docs/e= call-reference.md > > > > > > > > >=20 > > > > > > > > > -- > > > > > > > > > You received this message because you are subscribed to t= he Google Groups "Bitcoin Development Mailing List" group. > > > > > > > > > To unsubscribe from this group and stop receiving emails = from it, send an email to bitcoindev+...@googlegroups.com. > > > > > > > > > To view this discussion visit https://groups.google.com/d= /msgid/bitcoindev/CAO3Pvs_PciUi%2BzBrCps3acO14sgeHVUANx9w6TVwUf_AYcd_qQ%40m= ail.gmail.com. > > > > > > > >=20 > > > > > > > > -- > > > > > > > > You received this message because you are subscribed to the= Google Groups "Bitcoin Development Mailing List" group. > > > > > > > > To unsubscribe from this group and stop receiving emails fr= om it, send an email to bitcoindev+...@googlegroups.com. > > > > > > > > To view this discussion visit https://groups.google.com/d/m= sgid/bitcoindev/ciibnh-b0x-rLwA8pY5NURBfPvG58gLcS7yPLIIkFV5IzA1k-PTsPZqYU8u= UyQRxLCnEFhGcrRCTM39N2AYEy0Db2H_UwIse3Hg9XEXNEYg%3D%40proton.me. > > > > >=20 > > > > > -- > > > > > You received this message because you are subscribed to the Googl= e Groups "Bitcoin Development Mailing List" group. > > > > > To unsubscribe from this group and stop receiving emails from it,= send an email to bitcoindev+...@googlegroups.com. > > > >=20 > > > > > To view this discussion visit https://groups.google.com/d/msgid/b= itcoindev/CAO3Pvs9tps%3DbsMQyA%2BHvhK-u%2BXqRwWtjTq8WXZi%2BcveAVwPi9A%40mai= l.gmail.com. > > >=20 > > > -- > > > You received this message because you are subscribed to the Google Gr= oups "Bitcoin Development Mailing List" group. > > > To unsubscribe from this group and stop receiving emails from it, sen= d an email to bitcoindev+...@googlegroups.com. > >=20 > > > To view this discussion visit https://groups.google.com/d/msgid/bitco= indev/02378fd1-17a4-47aa-89fa-ee87626def65n%40googlegroups.com. >=20 > -- > You received this message because you are subscribed to the Google Groups= "Bitcoin Development Mailing List" group. > To unsubscribe from this group and stop receiving emails from it, send an= email to bitcoindev+unsubscribe@googlegroups.com. > To view this discussion visit https://groups.google.com/d/msgid/bitcoinde= v/49236a10-94ea-440a-9b53-63ae2c7ac964n%40googlegroups.com. --=20 You received this message because you are subscribed to the Google Groups "= Bitcoin Development Mailing List" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to bitcoindev+unsubscribe@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/= RFikSfAeyAprXI7h03OdRBA1f9DlXYHZZjGM_3KMKeYMDv9cIsnRkq2Evwrs0uXBMTefRzb8Hv2= p04Y9iOLHK9Ru3MBvmofkLxoNBsZuo9I%3D%40proton.me. -----------------------ed62dac9fcdf5626346066b3bbe62018 Content-Type: multipart/related;boundary=---------------------b289a574442af66fd44ba7bf7236af48 -----------------------b289a574442af66fd44ba7bf7236af48 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Laolu's OP = benchmarks which you cite used a design which was hard to arithmetize, so t= he proofs took ~2s to verify and almost a minute to prove. After some sugge= stions from Luke and myself, he brought the benchmark verify time down to t= he millisecond range, and the proving time down to just a few seconds.

=

Also these benchmar= ks would improve even further if we use a custom circuit instead of an arit= hmetizing VM.

regards,
conduition
On Thursday, April 30th, 2026 at 5:52 PM, Alex <alexhultman@gmai= l.com> wrote:
> STARKs don't take multiple secon= ds to verify. You can run the code in my repo
> to see, it verifies i= n tens of milliseconds [1].

And


are not logically consistent. = Your original statement was 1.8 seconds and I referred to it as such, but n= ow you say it's tens of milliseconds. Technically 1.8 seconds is some multi= ple of tens of milliseconds, true, but I was referring to your original sta= tement of 1.8 seconds.

The core point is that; exposing the complexity that is STAR= K verification in Bitcoin nodes, where 1.8 seconds of CPU-time is expected = (as per your original statement), this is a gaping flesh wound in terms of = DOS attack surface.

Further on, the same argument regarding standard= ization of zkVMs or Circuits is highly problematic and complex, a bug in su= ch a Circuit cannot be fixed without scrambling the verification and there = is no way so standardize it other than through arbitrary code versioning.
Whether you recursively prove a proof and so on is irrelevant to the = complexity and DOS question. You could make a STARK that certified the enti= re Bitcoin chain in a few KB of data, but the complexity and DOS attack sur= face for such a recursive proof is just as galactic as 1 single proof.
<= br>The point is that, if you expose STARK verifications anyone can send hig= hly costly STARKs that take multiple seconds of CPU time (a DOS attack).
on= sdag 29 april 2026 kl. 03:21:51 UTC+2 skrev Olaoluwa Osuntokun:
Hi = Sadiq,


> The scheme extends to = BIP-352 (Silent Payments)

Yup, as = shown in my latest post, we can batch aggregate multiple claims into a
s= ingle proof. If this were to be deployed at some point in the future, devs<= br>would be able to scower wallets/protocol/codebases for other recoveryproofs/claims that could be added.

> The zk-STARK proof? or this mechanism should definitely be bound to = the
> spending transaction and the input being spent.

<= /div>
Def, this would be it would be straight forward = to bind the proof to a given
wtxid/sighash.
=


> Curious why not generalise beyond BIP-32? P2PKH and P2WPK= H without BIP-32
> still commit to an unrevealed secret =E2=80=94 HAS= H160(k=C2=B7G) =E2=80=94 as long as the pubkey
> has never previously= appeared on-chain. A zk-STARK proof should apply here
> too?
No fundamental reason, just I decided to= focus the initial demo on P2TR. One
could easily swap in this section w= here the Taproot Output key is derived with
another script type instead = [1].

[1]: https://github.com/Roasb= eef/bip32-pq-zkp/blob/main/bip32/taproot.go#L91-L94

-- Laolu
=


On Mon, Apr 13, 2026 at 12:21=E2= =80=AFPM sadiq Ismail <ask4ism...@gmail.co= m> wrote:
Hi Laolu, list,

Nice work.

= The scheme extends to BIP-352 (Silent Payments). The BIP-352 receiver recon= structs the output P using their private scan key, public spend key, and pu= blic information from the spending transaction A.
See BIP-352 Scanning. = BIP-352 recommends but does not mandate BIP-32 for deriving the scan and sp= end keys, but specifies the following derivation paths when BIP-32 is used:=

b_scan =3D BIP32Derive(s, m/352'/coin_type'/account'/1'/0)
= b_spend =3D BIP32Derive(s, m/352'/coin_type'/account'/0'/0)

For = all silent payment addresses generated using BIP-32, your technique applies= . The prover produces a zk-STARK proof that the program BIP32Derive(s, p_sc= an) and BIP32Derive(s, p_spend) were run correctly,
and that the result= ing keys reconstruct the on-chain output P using along with A.

As you highlighted txid is not committed in the proof currently, the argum= ent is replayable. The current POC does not bind to where the coins go. Any= one who observes the chain could copy it and attach it to a different trans= action, spending the same UTXO to a different address. Worse for silent pay= ment, because all user UTXO have the same secret BIP32Derive(s, p_scan) and= BIP32Derive(s, p_spend) except for A.
The zk-STARK proof? or thi= s mechanism should definitely be bound to the spending transaction and the = input being spent.

Curious why not generalise beyond BIP-32? P2PKH = and P2WPKH without BIP-32 still commit to an unrevealed secret =E2=80=94 HA= SH160(k=C2=B7G) =E2=80=94 as long as the pubkey has never previously appear= ed on-chain. A zk-STARK proof should apply here too? The prover argues for = the correctness of HASH160(k=C2=B7G) =3D h, where k is the private key scal= ar and k=C2=B7G is the elliptic-curve point, without ever revealing k or th= e pubkey. This would allow recovery of a broader set of funds. If it were d= ecided that classical signatures for these output types are invalidated and= only a valid zk-STARK proof is required to spend, anyone who holds the ori= ginal secret can unlock their funds.

P.S. I am no= t for or against disabling valid spend paths post-quantum, just discussing = the technical possibilities.

Best,
Abubakar Sadiq
On Friday, April 10= , 2026 at 7:47:09=E2=80=AFPM UTC+2 conduition wrote:
Ah!= Amazing work! 2 seconds to prove is really crazy. Proving a single SHA256 = and one modular addition on my CPU back in the day took like 20 seconds. Yo= ur GPU is coming in clutch for this. I best= RISC0 has also improved quite a bit since then.

I think the next optimi= zation step would be pre-seeding the two SHA512 midstates from the host, so= you only need to prove two SHA512 compression calls instead of four. Intui= tively I expect this would at best halve your prover time from 2sec, to pro= bably a little over 1sec, and your verifier time will probably drop as well= since that also seems to scale with circuit complexity.
=
I think I have = two half-decent arguments now as to why this won't affect security: =

Firs= t, even if a fraudulent prover is handed th= e correct midstates to use, the prover would still have to do the hard work of finding the par= ent secret key needed as a witness. This is at least the same difficulty as= finding the parent sk=E2=80=8B=E2=80=8B if we just hashed it without a chaincode at all, using= two bare SHA512 calls - the only thing that changes is the midstate, and t= he SHA512 input length suffix. Starting from a different midstate doesn't m= agically give the attacker a head-start in a 256-bit search space looking f= or sk=E2=80=8B. A frauduent prover would know the child secret key k =3D sk + int(I[32:]) % = n=E2=80=8B= =E2=80=8B, = but they don't know int(I[32:]) or sk=E2=80=8B so they cannot = solve for either.

Nominally, the fraudulent prover wouldn't even know the correct midstat= es, so their task is strictly harder.

Secondly, here's another argument = as to why finding the midstates in the first place should also be hard.

Any adversary who could= solve this problem by finding the right midstates could be used as an orac= le to prove the existence of partial 2-cycles in SHA512.
=
  • Given a SHA512 hash I=E2=80=8B=E2=80=8B, set sk =3D int(I[= 32:])=E2=80=8B=E2=80= =8B=E2=80=8B
  • Compute= k = =3D sk + sk % n=E2=80=8B
  • Use the black-box fraudulent prover on the child key k=E2=80=8B<= span style=3D"font-family:Arial,sans-serif">=E2=80=8B to find correct midstates such= that

<= div>I =3D=3D SHA51= 2(<something> || SHA512(<something> || 0x00 || sk || i))= =E2=80=8B=E2=80= =8B=E2=80=8B
k =3D=3D int(I[32:]) + sk % n=E2=80=8B
= =3D=3D sk + sk % n=E2=80=8B=E2=80=8B

Remember that sk =3D int(I[= 32:])=E2=80=8B= =E2=80=8B. Thus for these conditions to hold, the proof forger must be able= to find not just the correct midstates, but also midstates which give a 2-= stage partial hash cycle so that:

I =3D=3D SHA512(&= lt;something> || SHA512(<something> || 0x00 || I[32:] || i))=E2=80=8B

This seems unlikely or at least very difficult.

regards,
conduition
On Thursday, April 9th, 2026 at 5:56 PM, Olaoluwa Osuntokun <lao...@gmail.com> wrote:
Hi Condution,

So I implemented both va= riants of your idea. My intuition was right in that it
doesn't do much t= o reduce the size of the final succinct size, but the final
xpriv varian= t resulted in a significant reduction in both proving time, and
also mem= ory usage. I also re-ran the original succint proof for the original
Tap= root claim and got a better value for the final proof time (def need a
b= etter benchmark env+set up!).

Here's a breakdown of the resource req= uirements for the various proofs:
* Full Taproot
image ID:
= 8a6a2c27dd54d8fa0f99a332b57cb105f88472d977c84bfac077cbe70907a690
= composite:
seal 1797880
prove 49.32s
verify 0.= 10s
peak RSS 11907399680
succinct:
seal 222668
= prove 64.30s
verify 0.03s
peak RSS 11927207936
<= br> * Hardened xpub
image ID:
ad4ebc0ef6ce51e0f581cc8d14742a= 5b97738e9decd3fe2b0f1746de5bad9617
composite:
seal 513680 prove 14.63s
verify 0.04s
peak RSS 11783503872 succinct:
seal 222668
prove 17.29s
verify 0= .02s
peak RSS 11782307840

* Hardened xpriv
image I= D:
8401a36e4f54cb2beaf9ac7677603806cf9d775e90ef5a70168045a3c0df084= 9
composite:
seal 234568
prove 1.98s
veri= fy 0.02s
peak RSS 3144171520
succinct:
seal 222668
prove 2.84s
veri= fy 0.02s
peak RSS 3145990144

So we can see that the succinct proof sizes are all about the sam= e. However the
xpriv variant can be proved directly in just 2 seconds on= my machine! It also
requires just 3 GB of memory for the proof as well.=

I've created some additional supporting documentation to detail exa= ctly what
the new proofs do and their results:

* https://github.com/Roasbeef/bip32-pq-zkp/blob/main/docs/= reduced-variants.md

* https://github.com/Roasbeef/bip32-pq-zkp/blob/1c89fdb398180a2b3eff776= 1b7f4b233d455c6c9/README.md#reduced-proof-variants

* https://github.com/Roasbeef/= bip32-pq-zkp/blob/438c548ca9b49d83ef4019974a5171f5e06fa840/docs/claim.md#re= duced-variant-claims


Once again, thanks for the great ideas!= I wonder if we can improve on this
round of proof golf further before r= eaching down a lower level with some sort
of AIR compiler =F0=9F=A4=94.<= br>

-- Laolu

<= div dir=3D"ltr" class=3D"gmail_attr">On Thu, Apr 9, 2026 at 1:53=E2=80=AFPM= Olaoluwa Osuntokun <lao...@gmai= l.com> wrote:
Hi Conduition,

> You need only prove t= his much more general statement (2): "I know a BIP32
> xpriv which de= rives this xpub via one or more hardened steps".

> I'm amending m= y prior suggestion slightly: The circuit (guest program)
> could take= in an xpriv (e.g. at m/86'/0') and output a child xpriv
> (e.g. at m= /86'/0'/0') to the journal (instead of outputting a child
> xpub).
That's an excellent insight!

As mentioned in my recent reply,= with risc0's "succinct" receipt type, I was
able to get the proof size = down to 220 KB, at the cost of 3.5x longer total
proving time.

Yo= ur proposal definitely reduces the complexity of the core statement to beproved, which would speed up the proving time for the normal
default/c= omposite receipt type.

I'll try to hack this up, and then run a hea= d to head comparison to see this
simpler statement actually results in a= smaller proof then the final
succinct receipt of either of the proof va= riants. Based on my current
intuition w.r.t the lower level details, I t= hink the final succinct proof
size would be on the same order of magnitu= de re size.

However, this can still be a win as then this would prov= ide potential future
users with a less resource intensive proof, which c= an then be
aggregated/rolled up into a final succinct proof in a batched= manner.

This line of optimization is also more interesting if one w= ere to look at
hand rolling a custom AIR to avoid the overhead that the = RISC-V emulation
adds to the rirsc0 proof chain, given that it entirely = skips doing any EC
operations at all for the final statement.

---= -

Re the commit/reveal approach, to be honest I'm not fully caught u= p on that
proposal. That original thread got pretty long, so I dropped o= f after a
point =F0=9F=98=85. I'll revisit that specific branch of the t= hread so I can digest it
and develop a proper opinion, then get back to = you re comparisons!

-- Laolu


On Wed, Apr 8, 2026 at 1:2= 3=E2=80=AFPM conduition <condu..= .@proton.me> wrote:
Oh, I= 've been a fool, a foolish fool.

We don't even need to do point multiplication in the circui= t at all.
<= br>
I'm ame= nding my prior suggestion slightly: The circuit (guest program) could take = in an xpriv (e.g. at m/86'/0'=E2=80=8B) and output a child = xpriv (e.g. at m/86'/0'/0'=E2=80=8B) to the journal (inste= ad of outputting a child xpub).

This is safe because remember, EC spending has been = disabled in this context, and to a quantum attacker, an xpub is computation= ally equivalent to its xpriv. So why bother hiding it? The child xpriv does= n't give an observer anything they can't already do with the equivalent xpu= b.

The guest pro= gram then is basically the BIP32 CKDpriv algorithm, restricted to a single = hardened derivation step. The verifier gets the child xpriv, but can't use = it to forge new proofs. Honest verifiers use the xpriv to derive the child = address(es) as suggested in my last message, to authenticate spending.

Designing the guest p= rogram like this will massively reduce your circuit complexity, because EC = point multiplication is wayyyyy harder for the RISC0 compiler to ari= thmetize than a simple hash function. In my prior work with RISC0, I made a guest program which ran a SHA25= 6 hash and an EC point multiplication. I found that pruning EC point arithm= etic from my guest program improved prover runtime by a factor of over 100x= .

If I am not fev= er-dreaming and this is indeed possible, then the new circuit's complexity = will be dominated not by point multiplication, but by the HMAC-SHA512 call.= Our new task is then to figure out how much we can internally optimize the= HMAC-SHA512 call for STARK proving. Here's a few ideas.

If you bust open HMAC-SHA512, it lo= oks like this:

HMAC_SHA512 =3D SHA512((K=E2=8A=950x5c) || SHA512((K= =E2=8A=950x36) || msg))=E2=80=8B

...where in the context of BIP32 hardened CK= D, the HMAC key K=E2=80=8B is the chaincode (padded with zeros= to 128 bytes) and msg =3D (0x00 || sk || i) is the parent sec= ret key and child index.

Since len(K) =3D 128=E2=80=8B is the SHA512=E2=80=8B = block size, we need a total of 4 SHA512 compression calls:
  1. to= compress (K=E2=8A=950x36)=E2=80=8B
  2. to compress the msg=E2=80= =8B (and SHA512 padding/length)
  3. to compress (K=E2=8A=950x5c), and
  4. a final compression call to tie it all together.

The output of that last c= ompression call is partitioned into the child chaincode, and a key delta wh= ich is added to the parent secret key (modulo the curve order), producing the child= EC secret key. This last step is arithmetically simple; the SHA512 calls a= re where most of the arithmetic complexity lies.

The question then becomes, which= of these compression calls can be done outside the circuit, and which are = truly essential for security?

Note how the parent secret key is the most important piece fo= r soundness. The circuit needs to prove the parent secret key existed in th= e hash function preimage, and is correctly related to the child secret key = via modular addition. So compression call (2) seems unavoidable. The others= are less rigid.

= I'd argue that if we really dig into the hard relation we're trying to prov= e here, we can reduce it to this statement:

Given a child xp= riv with secret key k=E2=80=8B, chaincode c=E2=80=8B and index i=E2=80=8B, I know a preimage x=E2=80=8B and secret key sk=E2=80=8B<= /font> such th= at:
=
I <- SHA512(<something> || SHA512(<something> |= | 0x00 || sk || i)=E2=80=8B)
c =3D=3D I[:32]=E2=80=8B
k =3D=3D int(I[32= :]) + sk % n=E2=80=8B

Seeing as the <something>=E2=80=8B slots= are arbitrary, and we know in BIP32 they are always exactly one-block long= , it seems easy to throw out the compression calls (1) and (3). The host ca= n precompute the relevant SHA512 midstates outside the circuit, and pass th= e midstates into the guest program as secret inputs. The tradeoff is that this permit= s malicious provers the flexibility of choosing their starting midstates (t= hough hash input length can be fixed at 192 bytes). I'm not entirely sure i= f this meaningfully weakens the verifier's soundness. Ethan Heilman might h= ave opinions on this, he knows a lot more about attacking hash functions th= an I do. Intuitively, I doubt sampling random SHA512 midstates is that much= better than sampling a random HMAC key (chaincode) K=E2=80=8B= and computing the resulting midstates.

This reduces o= ur circuit to, i think, the minimum acceptable security floor for provers: = two SHA512 compression calls, which commit to a parent secret key.


regards,=
conduition=
On Wednesday, April 8th, 2026 at 12:09 PM, 'conduition' via Bitcoin= Development Mailing List <bitco= ...@googlegroups.com> wrote:
Hi Laolu,

Great work getting this working= in the real world. I've heard many people on delving and the mailing list = conjecture based on this idea, but you're the first person i've seen who's = willing to put their money where their mouth is, and actually build a proto= type. Bravo!

It seems to me the circuit (guest pro= gram) could be simplified. Notice how the guest code compute= s the entire HD wallet key path, including hardened and= non-hardened derivation steps, and also computes the tapr= oot output key with key-tweaking. I'd argue these steps are extraneous to t= he core hard relation you want the STARK to prove, and could be safely remo= ved to reduce proof size and improve performance.

= In reality, you needn't go so far as to prove (1) "I know a BIP39 seed w= hich derives this taproot output key". You need only prove this much mo= re general statement (2): "I know a BIP32 xpriv which derives this xpub = via one or more hardened steps". The latter statement (2) still cannot = be forged by a quantum adversary even if they know your account-level xpub,= but it entails far less computation to prove and verify. The rest of the o= riginal statement (1) can be done externally outside the circuit.

Example. If i have a wallet with a taproot address at= m/86'/0'/0'/1/2=E2=80=8B, I could prove I know the xpr= iv at m/86'/0'=E2=80=8B which derives the xpub at= m/86'/0'/0'=E2=80=8B. Then I provide the remaini= ng key path elements /1/2=E2=80=8B in the witness. Note, i = do not mean we derive the xpriv at m/86'/0'=E2=80=8B inside the guest program. I mean the prover der= ives m/86'/0'=E2=80=8B first (in the host), and then writes that xpriv into the guest program's inputs. = The guest program derives and outputs the xpub at m/86'/= 0'/0'=E2=80=8B. The verifier may check the STARK output (xpub) is co= rrectly computed, then use the given key-path to manually derive the taproo= t address from the xpub themselves, outside the circuit, and validate= that address against the UTXO i'm spending. The verifier thu= s has confirmed the prover knew an xpriv which (through a hardened derivati= on step) derives the correct taproot output key.

T= his change significantly reduces the size of the circuit. From a glance, I = see the original guest program performs 6 HMAC-SHA512 calls (1 for the mast= er key, 5 for the BIP32 derivation steps), two SHA256 compression calls (fo= r the taptweak hash), and two point multiplications. With this simplified v= ariant, we are invoking only a single HMAC-SHA512 call and a single point m= ultiplication. I can't say for sure, but I expect this will improve your pr= oof size and runtime significantly.

This change al= so makes the circuit more generally applicable to other rescue contexts. Fo= r instance, it could be applied to BIP340 xonly keys inside a taproot scrip= t tree, or in a P2(W)SH address to an ECDSA public key, or to P2(W)PKH addr= esses.

Concerned about publishing xpubs? Remember that we are assuming= regular EC spending is locked in this context, so it is safe-ish to share = account xpubs with quantum attackers. At best the xpub can be used for surv= eillance but not forgery. If one would prefer not to share the accou= nt-level xpub on-chain for privacy reasons, the proof could be extended to = also derive the unhardened child xpub at /1/2=E2=80=8B inside the guest program (but we still do= not need to do the taproot key tweaking in the guest program).
<= /div>

We should also talk scaling efficiency. Given the = cost of STARKs, this style of proof should be able to authorize spends for = more than one UTXO. Say you have a wallet with 10 different UTXOs held by d= istinct addresses in the same BIP44 account. One single STARK proof could a= uthorize spending all 10 of them, by simply committing all 10 input signatu= re hashes into the journal, and labeling the inputs with the corresponding 10 BIP32 key paths some= how. The verifier would need to check the proof only once and= not 10 times. The 10 UTXO spends could be validated using the common xpub = from the STARK proof's journal.

For a slightly rel= ated work proving a similar relation for hashed addresses, using different = STARK technology stacks, see this delving post.=

However, all this said, my personal preference fo= r long-term procrastinator rescue is still for commit/reveal strategies whi= ch prove essentially the same statement about BIP32 in a two-step procedure= . They get the job done with much lighter cryptographic machinery and much = smaller witnesses: a few hundred bytes over two transactions, compared to a= few million bytes in one transaction with STARKs. Boris N= agaev and I discussed this on the list a while back. That said, commit/= reveal requires more careful design and seems to demand the use of external= quantum-safe coins to make the commitment in the first place, so perhaps t= he cost would be worth it to some people? IDK. What do you think of commit/= reveal compared to STARKs for this purpose?

regards,
condui= tion

<= /div>
On Wednesday, April 8th, 2026 at 12:18 AM, Olaoluwa Osuntokun <<= a rel=3D"noreferrer nofollow noopener">lao...@gmail.com> wrote:
Hi y'all,
I found some spare time this last weekend to dust off a little side pr= oject
I started last August: extend TinyGo [1] to be able to produce RIS= C-V ELF
binaries capable of being run as a guest on the risc0 platform t= o generate
zk-STARK proofs of arbitrary programs. Initially, I didn't re= ally have a
clear end target application, it was mainly a technical chal= lenge to force
me to learn a bit more about the RISC-V platform, and als= o the host/guest
architecture of risc0. Fast forward ~9 months later, an= d an initial killer
use case popped into my mind: a zk-STARK proof that = a Taproot output public
key was generated using BIP-32, via a given BIP-= 86 derivation path.

More formally:
```math
\mathcal{R} =3D \le= ft\lbrace\;
(\overbrace{K,\, C}^{\textsf{public}} ;\; \underbrace{s,\, \= mathbf{p}}_{\textsf{witness}})
\;\middle|\;
\begin{aligned}
K &a= mp;=3D \textsf{BIP86Taproot}\bigl(\textsf{BIP32Derive}(s,\, \mathbf{p})\big= r) \\
C &=3D \textsf{SHA256}\bigl(\texttt{"bip32-pq-zkp:path:v1"} = \;\|\; \mathbf{p}\bigr)
\end{aligned}
\;\right\rbrace
```

w= here $K$ is the Taproot output key, $C$ is the path commitment, $s$ is the<= br>BIP-32 seed, and $\mathbf{p}$ is the derivation path.


I was a= ble to get everything working e2e over the weekend, after making
some tw= eaks to my initial architectural game plan!

The TL;DR is that:
* Given that the Taproot commitment scheme is post-quantum secure [3], = in
the future we can deploy a soft fork to _disable_ the keyspend pa= th,
and force all Taproot spends to instead flow through the script = path
(not my idea, commonly discussed amongst developers, not sure w= ho
proposed it first). At that point, Taproot starts to resemble BIP= -360.

* That works for script path spends, but then leaves all the= BIP-86
wallets in a bad position, as they generated outputs that pr= ovably
don't commit to a script path at all.

* A 2023 paper= (Protecting Quantum Procrastinators with Signature
Lifting: A Case = Study in Cryptocurrencies [4]) proposed a solution to this,
namely _= seed lifting_ (use BIP-32 as the one-way function to the
Picnic PQ S= ignature scheme) to provide a post-quantum proof of secret
informati= on a quantum attacker wouldn't be able to easily obtain.

* The dow= nside of that is that it reveals the secret BIP 32 seed,
exposing ot= her non migrated UTXOs of a user.

* With this project I've cobbled= together a series of projects to be able
to generate a zk-STARK pro= of that a Taproot output public key was
generated via BIP-32 invocat= ion of a BIP-86 derivation path.

* In the future a variant of this= scheme can be used to enable wallets
that generated the private key= s via BIP-86, to have a post quantum safe
exit path in case they don= 't bother moving their coins in time to the
yet-to-be-decided post q= uantum signature scheme.

To achieve this end, I needed to create/for= k a series of repos:

* tinygo-zkvm: https://github.com/Roasbeef/tinygo-zkvm
* A fork of TinyGo t= hat supports the flavor of RISC-V (rv32im) that
risc0 requires to = generate/execute a guest program to later be proved
by the host.
* risc0: https://github.com/Roasbeef/risc0
* Mostly a bug fix to their c-guest example, along with some
= additional documentation on how to get things running. The repo is
= unmodified other than that. Recent updates to the repo made the
= entire process much easier (Go guest+host), more on that later.

= * go-zkvm: https://github.com/Roasbeef/go-zkvm
* Go utilities to take a RISC-V ELf binary produced by tinygo-zkv= m, and
package it in the expected R0BF format, which combines the = user
generated RISC-V ELF (the thing that is executed to generate = the
proof) along with the v1compat ELF kernel, which is risc0's ex= ecution
environment.

* This also includes a Go host pac= kage, which loads the guest program,
executes it, and generates a = trace to later be proved. This is
achieved via a C FFI compat laye= r between Go and the original Rust
host/proving/verification code.=

* bip-32-pq-zkp: https://gith= ub.com/Roasbeef/bip32-pq-zkp
* The project that packages everyth= ing together, this contains the:
* Guest Go program that defines t= he secret witness and
claim/constraints of the proof.

= * The C FFI wrapper around the OG Rust host, which is used to load
= the guest program, execute it, generate a trace, then finally
= generate a proof.

Details of the final proof as generated on my = Mac Book (Apple Silicon M4
Max, 128 GB of RAM):
* Takes ~55 seconds= or so to generate+proof, including execution. This
uses Metal for G= PU acceleration on the platform.
* Uses ~12 GB of ram.
* Final pr= oof size is ~1.7 MB.
* Verification takes ~1.8 seconds, and uses ~32 M= B of memory.

On several layers, this demo is far from optimized (mor= e on that later),
this is meant to serve as a PoC to demonstrate that wi= th the latest
software+hardware, a proof of this complexity is well with= in reach.

For those curious re the e2e details I've generated this t= utorial that
explains the entire system top to bottom:
https://= github.com/Roasbeef/go-zkvm/blob/main/docs/tutorial.md.

If you g= ot to this point in this mail, and don't care about the lower level
deta= ils, thanks for reading up until now, and feel free to return back to
th= e _The Net of a Million Lies_, or as better known in our Universe:
Monit= oring the Situation and/or slopfotainment! =F0=9F=AB=A1

## Motivatio= n + Background

As commonly known, in the case of an adversary that p= ossesses a quantum
computer capable of breaking classical asymmetric cry= ptography, any coins
stored in UTXOs with a known public key are vulnera= ble. This is the case
for any P2PK outputs from waaaay back, and also an= y other outputs that have
revealed their public key. Pubkey reveal might= happen due to address re-use
(spending from the same script twice), or = Taproot outputs, which publish
the public key plainly in the pkScript.
As detailed in [3], for Taproot outputs, a widely circulated plan is<= br>roughly to: disable the _keyspend_ path (requires a simple signature),enforcing a new rule that all Taproot spends must then flow through thescript path. Spending via the script path requires an opening of the
T= aproot commitment (C =3D I + H(I || H(M))), which was shown to be binding e= ven
under classic assumptions, as H(M) (tapscript merkle root) is still = a
collision-resistant function.

That means any UTXO that _does_ c= ommit to a script path has a future escape
hatch _if_ such a softfork wo= uld need to be deployed in the future.
However, what about all the other= wallets that use BIP 86, and don't commit
to a script path at all? Unde= r a strict version of this existing
proposal, those wallets would basica= lly be locked forever.

The goal of this work is to demonstrate a pra= ctical solution (discussed
against devs, but never implemented AFAICT): = generate a zk proof that an
output was generated using BIP-86. For the z= k-Proof, we select zk-STARKs,
as they're plausibly post quantum since th= ey rely only on symmetric
cryptography: layers of merkle trees over an e= xecution trace, along with
some novel sampling/error-correction algorith= ms.

At this point, you may be asking: "if the quantum adversary can = derive the
private key to a random taproot public key, then how exactly = does this
help?". The answer lies in the structure of BIP-32! BIP-32 tak= es an initial
128-512-bit seed (with BIP-39, either 12 or 24 words), the= n runs it through
HMAC-SHA512 keyed by "Bitcoin seed" to produce the mas= ter extended private
key. An adversary who wants to forge this proof nee= ds to find a _colliding_
seed: a different seed s' such that HMAC-SHA512= ("Bitcoin seed", s') produces
the same master key. The BHT algorithm (Br= assard-Hoyer-Tapp [6]) is the
best known quantum collision finder, and i= t runs in time proportional to the
cube root of the output space: 2^(n/3= ). For HMAC-SHA512's 512-bit output,
that's ~2^171 quantum operations, w= ell above even NIST's highest
post-quantum security category. Therefore,= if you generated a wallet using
BIP-32, you possess _another_ secret th= at a quantum adversary can't
efficiently reconstruct!

This demo f= ocuses on the Taproot case, but the rough approach also applies
to any o= ther output generated via BIP-32. BIP 32 was originally published in
201= 2, over 14 years ago. So safe to say that _most_ wallets were generated
= under this scheme. However, Bitcoin Core only officially adopted BIP-32 in<= br>2016/2018, moving away from their existing key pool structure. I can't s= ay
how much BTC is held today in outputs generated with Bitcoin Core's o= riginal
key pool, but if you have coins generated via that mechanism, yo= u may want
to consider migrating them to a BIP-32 wallet.

## Tiny= Go + RISC-V + risc0

Now for some of the lower level details. risc0 i= s a STARK based proving
system that takes a RISC-V ELF binary generated = by a guest program (any
program generating using their flavor of rv32im = can be proved), executes
that in a host environment, generates a trace, = then produces a STARK proof
from that.

Today you can take some su= bset of Rust, compile it to an ELF using their
toolchain, then execute i= t, generate a trace, to finally prove+verify it
using their system.
<= br>This demo took a bit of a round about journey to achieve this, as after<= br>all, the journey is most of the fun, ain't it!

For the past 10 ye= ars or so, my Bitcoin stack of choice (lnd/btcsuite) uses
a series of Go= libraries, so I wanted to be able to re-use them, first for
this demo, = then also in the future for other projects.

TinyGo is a special Go c= ompiler based on LLVM, that targets mostly embedded
environments. You ca= n use it to generate go programs that can run on
micro controllers, or o= n web assembly (producing a smaller binary than if
you used the normal s= tdlib path).

TinyGo supports RISC-V, but _not_ the 32-bit variant of= RISC-V that risc0
relies on. So the first step here was to create a new= target definition for
TinyGo: riscv32-unknown-none, which uses base int= eger + multiply/divide
instructions with no compressed instructions, whi= ch uses 4 KB stacks for
each task. From there, I created a new linker sc= ript
(`targets/riscv32im-risc0-zkvm-elf.ld`) which created a memory laye= r
identical to what risc0 expects. The final component was a new runtime=
(`src/runtime/runtime_zkvm.go`), which implemented a few platform speci= fic
syscalls for risc0 (putchar(), exit(), ticks(), and growHeap()).
=
When I tried to get this working last year, I had to also implement a n= umber
of kernel syscalls (called ecalls in the platform [7]) to handle: = read+write
to stdin/stdout, halting, and the journaling mechanism (the t= ranscript of
execution committed to), which basically implement the kern= el that the guest
executes in. Fast forward to 2026, and after pulling t= he latest version of
the repo, I realized that they now make a libzkvm_p= latform.a, which packages
up the kernel nicely to be linked against. So = I threw out my custom kernel
code, and slotted that in instead.

T= he final component is a C FFI layer that enables me to use _both_ a Go
g= uest (the program to be proved) and a Go host (the thing that executes the<= br>program and generates the final proof).

## BIP-32+Taproot zk-STAR= K Proof

With basic proofs working (like the classic: I know the fact= orization of a
number `n`), I was unblocked to generate the actual proof= . The claim/proof
is represented with the following JSON artifact:
``= `
{
"schema_version": 1,
"image_id": "8a6a2c27dd54d8fa0f99a332= b57cb105f88472d977c84bfac077cbe70907a690",
"claim_version": 1,
"c= laim_flags": 1,
"require_bip86": true,
"taproot_output_key": "003= 24bf6fa47a8d70cb5519957dd54a02b385c0ead8e4f92f9f07f992b288ee6",
"path_= commitment": "4c7de33d397de2c231e7c2a7f53e5b581ee3c20073ea79ee4afaab56de11f= 74b",
"journal_hex": "010000000100000000324bf6fa47a8d70cb5519957dd54a0= 2b385c0ead8e4f92f9f07f992b288ee64c7de33d397de2c231e7c2a7f53e5b581ee3c20073e= a79ee4afaab56de11f74b",
"journal_size_bytes": 72,
"proof_seal_byt= es": 1797880,
"receipt_encoding": "borsh"
}
````

The `ima= ge_id` is basically a hash of the ELF, so you know what the prover
execu= ted. There are then a few flags that control the claim version and
wheth= er BIP-86 derivation is a part of the proof. BIP-86 was only adopted
pos= t-Taproot, so if you have an existing BIP-44 path, you can instead opt toclaim that instead. The Taproot key we're generating the proof against is=
also part of the _public data_, as it sits plainly on the chain for all= to
see. We then also include a `path_commitment`, which is a commitment= to the
exact BIP 86 path that the prover used. Finally, we also commit = to the
journal hex, which is basically a commitment to the public claim.=

Assuming you've built the project, then you can generate the proof = (even
passing in an arbitrary BIP-32 seed and derivation path with)
`= ``
make prove GO_GOROOT=3D/path/to/go1.24.4
```

Then verify it= with:
```
make verify GO_GOROOT=3D/path/to/go1.24.4
```

Th= e default prove target writes:
* ./artifacts/bip32-test-vector.receipt=
* ./artifacts/bip32-test-vector.claim.json

The receipt is the = STARK proof artifact. claim.json is the stable,
human-readable descripti= on of the public statement being proved.

## Application to a Future = Keyspend Disabling Soft fork

As mentioned above, assuming the commun= ity is forced to deploy a keyspend
disabling soft fork in the future, we= can also deploy some variant of
this proof to enable both BIP-86 wallet= s, and also any BIP-32 wallet, to
sweep their funds into a new PQ output= .

In 2026, we've shown that this is achievable using 2 year old cons= umer
hardware. I don't doubt that the upcoming advancements (eg: photoni= cs, new
flavor of high bandwidth memory, etc) in hardware (driven by the= fierce AI
race) will make such a proof even more feasible.

One t= hing to note is that this proof has a few layers of indirection,
mainly = the RISC-V layer that adds overhead which increase the total amount
of s= teps, and therefore the size of the proof. A production grade
deployment= would likely instead hand roll a custom STARK proof for this
exact stat= ement, to achieve a faster and smaller proof).

# Future Work

= In terms of future work, there're a number of interesting following up
p= rojects that can be pursued from here.

One basic one is that the cur= rent proof doesn't actually commit to a
spending txid and/or sighash. Th= at can be trivially incorporated into the
proof. Going a step further, t= he execution of the guest program can even
_generate_ a valid schnorr si= gnature to permit spending.

Looking to the memory+computational requ= irements necessary to generate the
proof, I've left two low hanging frui= ts:

1. First, we can speed up the Elliptic Curve operations the pro= of requires
(scalar base mult, then addition, or more performantly D= ouble Scalar
Multiplication via the Strauss-Shamir trick). For this = we can use the
syscalls/precompile in the risc0 env for big integer = arithmetic:
sys_bigint and sys_bigint2. With this, the guest calls i= nto the kernel
to use an optimized/accelerated circuit for the modul= ar arithmetic,
reducing cycles, steps, and thus proof size.

= 2. Second right now, the entire claim is a single proof. Instead, we can first break that up using their recursive proof/composition syscalls:<= br> sys_verify_integrity+sys_verify_integrity2. We can then assembled a<= br> series of these proofs into a _single_ statement, which can save blo= ck
space by aggregating N proofs into a single proof.

-- Laol= u

[1]: https://tinygo.org/
[2]: https://risczero.com/<= br>
[3]: https://eprint.iacr.org/2025/1307
[4]: https://eprint.iacr.org/2023/362

[= 5]: https://microsoft.github.io/Picnic/
[6]: https://en.wikipedia.org/w= iki/BHT_algorithm

[7]: https://github.com/Ro= asbeef/go-zkvm/blob/main/docs/ecall-reference.md

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