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[109.224.244.29]) by gmr-mx.google.com with ESMTPS id 46e09a7af769-7dbf3f31361si241681a34.4.2026.04.08.08.53.49 for (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Wed, 08 Apr 2026 08:53:50 -0700 (PDT) Received-SPF: pass (google.com: domain of conduition@proton.me designates 109.224.244.29 as permitted sender) client-ip=109.224.244.29; Date: Wed, 08 Apr 2026 15:53:42 +0000 To: Olaoluwa Osuntokun 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: References: Feedback-ID: 72003692:user:proton X-Pm-Message-ID: 64e26b9ef36baa4f41ccd1edbdf45c6b21ae144a MIME-Version: 1.0 Content-Type: multipart/signed; protocol="application/pgp-signature"; micalg=pgp-sha512; boundary="------d200152275f4ada5e0724f42d66dd61f3fb3608cf2df76581cf0063913787078"; 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=DQIZonko; spf=pass (google.com: domain of conduition@proton.me designates 109.224.244.29 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) --------d200152275f4ada5e0724f42d66dd61f3fb3608cf2df76581cf0063913787078 Content-Type: multipart/mixed;boundary=---------------------2290f4c07bb2b1fba693c138fa150ae9 -----------------------2290f4c07bb2b1fba693c138fa150ae9 Content-Type: multipart/alternative;boundary=---------------------7a8e2d97c4d0a87d757cd378d8080766 -----------------------7a8e2d97c4d0a87d757cd378d8080766 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="UTF-8" Hi=C2=A0Laolu, Great work getting this working in the real world. I've heard many people o= n delving and the mailing list conjecture based on this idea, but you're th= e first person i've seen who's willing to put their money where their mouth= is, and actually build a prototype. Bravo! It seems to me the circuit (guest program) could be simplified. Notice how= =C2=A0the guest code computes the entire HD wallet key path, including hard= ened=C2=A0and=C2=A0non-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. In reality, you needn't go so far as to prove (1)=C2=A0"I know a BIP39 seed= which derives this taproot output key". You need only prove this much more= general statement (2):=C2=A0"I know a BIP32 xpriv which derives this xpub = via one or more hardened steps". The latter statement (2) still cannot be f= orged 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 origi= nal statement (1) can be done externally outside the circuit. Example. If i have a wallet with a taproot address at=C2=A0`m/86'/0'/0'/1/2= `, I could prove I know the xpriv at=C2=A0`m/86'/0'` which derives the xpub= at=C2=A0`m/86'/0'/0'`. Then I provide the remaining key path elements /`1/= 2` in the witness. Note, i=C2=A0do not=C2=A0mean we=C2=A0derive=C2=A0the xp= riv at=C2=A0`m/86'/0'` inside the guest program. I mean the prover derives= =C2=A0`m/86'/0'` first (in the host), and=C2=A0then writes that xpriv into = the guest program's inputs.=C2=A0The guest program derives and outputs the = xpub at=C2=A0`m/86'/0'/0'`.=C2=A0The verifier may check the STARK output (x= pub) is correctly computed, then use the given key-path to manually derive = the taproot address from the xpub themselves, outside the circuit, and vali= date=C2=A0that address=C2=A0against 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. This 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 mas= ter key, 5 for the BIP32 derivation steps), two SHA256 compression calls (f= or 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 will improve your p= roof size and runtime significantly. This change also makes the circuit more generally applicable to other rescu= e contexts. For instance, it could be applied to BIP340 xonly keys inside a= taproot script tree, or in a P2(W)SH address to an ECDSA public key, or to= P2(W)PKH addresses. 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 xpub= s 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-ch= ain for privacy reasons, the proof could be extended to also derive the unh= ardened child xpub at=C2=A0`/1/2` inside the guest program (but we still do= not need to do the taproot key tweaking in the guest program). We should also talk scaling efficiency. Given the cost of STARKs, this styl= e of proof should be able to authorize spends for more than one UTXO. Say y= ou have a wallet with 10 different UTXOs held by distinct addresses 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 journa= l, and labeling the inputs with=C2=A0the=C2=A0corresponding 10 BIP32 key pa= ths somehow. The verifier would need to check the proof only once and not 1= 0 times. The 10 UTXO spends could be validated using the common xpub from t= he STARK proof's journal. For a slightly related work proving a similar relation for hashed addresses= , using different STARK technology stacks,=C2=A0see this delving post. However, all this said, my personal preference for long-term procrastinator= rescue is still for commit/reveal strategies which prove essentially the s= ame statement about BIP32 in a two-step procedure. They get the job done wi= th much lighter cryptographic machinery and much smaller witnesses: a few h= undred bytes over two transactions, compared to a few million bytes in one = transaction with STARKs.=C2=A0Boris Nagaev and I discussed this on the list= a while back. That said, commit/reveal requires more careful design and se= ems 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 some people? = IDK. What do you think of commit/reveal compared to STARKs for this purpose= ? regards, conduition On Wednesday, April 8th, 2026 at 12:18 AM, Olaoluwa Osuntokun wrote: > Hi y'all, >=20 > I found some spare time this last weekend to dust off a little side proje= ct > I started last August: extend TinyGo [1] to be able to produce RISC-V ELF > binaries capable of being run as a guest on the risc0 platform to generat= e > zk-STARK proofs of arbitrary programs. Initially, I didn't really have a > clear end target application, it was mainly a technical challenge to forc= e > me to learn a bit more about the RISC-V platform, and also the host/guest > architecture of risc0. Fast forward ~9 months later, and an initial kille= r > use case popped into my mind: a zk-STARK proof that a Taproot output publ= ic > key was generated using BIP-32, via a given BIP-86 derivation 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})\b= igr) \\ > C &=3D \textsf{SHA256}\bigl(\texttt{"bip32-pq-zkp:path:v1"} \;\|\; \mathb= f{p}\bigr) > \end{aligned} > \;\right\rbrace > ``` >=20 > where $K$ is the Taproot output key, $C$ is the path commitment, $s$ is t= he > 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-quantum secure [3], in > the future we can deploy a soft fork to _disable_ the keyspend 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 resemble 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 Signature > Lifting: A Case Study in Cryptocurrencies [4]) proposed a solution to thi= s, > namely _seed lifting_ (use BIP-32 as the one-way function to the > Picnic PQ Signature scheme) to provide a post-quantum proof 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 projects 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 path. >=20 > * In the future a variant of this scheme can be used to enable wallets > that generated the private keys 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 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 (rv32im) that > risc0 requires to generate/execute a guest program to later be proved > by the host. >=20 > * 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. >=20 > * go-zkvm: https://github.com/Roasbeef/go-zkvm > * Go utilities to take a RISC-V ELf binary produced by tinygo-zkvm, 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 execution > environment. >=20 > * This also includes a Go host package, which loads the guest program, > executes it, and generates a trace to later be proved. This is > achieved via a C FFI compat layer between Go and the original Rust > host/proving/verification code. >=20 > * bip-32-pq-zkp: https://github.com/Roasbeef/bip32-pq-zkp > * The project that packages everything together, this contains 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 used to load > the guest program, execute it, generate a trace, then finally > generate a proof. >=20 > 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 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 memory. >=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 within 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/tutorial.md. >=20 > If you got to this point in this mail, and don't care about the lower lev= el > details, thanks for reading up until now, and feel free to return back to > the _The Net of a Million Lies_, or as better known in our 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 possesses a quantum > computer capable of breaking classical asymmetric cryptography, any coins > stored in UTXOs with a known public key are vulnerable. This is the case > for any P2PK outputs from waaaay back, and also any other outputs that ha= ve > revealed their public key. Pubkey reveal might happen due to address re-u= se > (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 circulated plan is > roughly to: disable the _keyspend_ path (requires a simple signature), > enforcing a new rule that all Taproot spends must then flow through the > script path. Spending via the script path requires an opening of the > Taproot commitment (C =3D I + H(I || H(M))), which was shown to be bindin= g 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 has a future esca= pe > hatch _if_ such a softfork would need to be deployed in the future. > However, what about all the other wallets that use BIP 86, and don't comm= it > to a script path at all? Under a strict version of this existing > proposal, those wallets would basically be locked forever. >=20 > The goal of this work is to demonstrate a practical solution (discussed > against devs, but never implemented AFAICT): generate a zk proof that an > output was generated using BIP-86. For the zk-Proof, we select zk-STARKs, > as they're plausibly post quantum since they rely only on symmetric > cryptography: layers of merkle trees over an execution trace, along with > some novel sampling/error-correction algorithms. >=20 > At this point, you may be asking: "if the quantum adversary can derive th= e > 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 takes an initi= al > 128-512-bit seed (with BIP-39, either 12 or 24 words), then runs it throu= gh > HMAC-SHA512 keyed by "Bitcoin seed" to produce the master extended privat= e > key. An adversary who wants to forge this proof needs to find a _collidin= g_ > seed: a different seed s' such that HMAC-SHA512("Bitcoin seed", s') produ= ces > the same master key. The BHT algorithm (Brassard-Hoyer-Tapp [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 generated a wallet usin= g > BIP-32, you possess _another_ secret that a quantum adversary can't > efficiently reconstruct! >=20 > This demo focuses on the Taproot case, but the rough approach also applie= s > to any other output generated via BIP-32. BIP 32 was originally published= in > 2012, over 14 years ago. So safe to say that _most_ wallets were generate= d > under this scheme. However, Bitcoin Core only officially adopted BIP-32 i= n > 2016/2018, moving away from their existing key pool structure. I can't sa= y > how much BTC is held today in outputs generated with Bitcoin Core's origi= nal > key pool, but if you have coins generated via that mechanism, you may wan= t > 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 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 proo= f > 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) us= es > a series of Go libraries, so I wanted to be able to re-use them, first fo= r > this demo, then also in the future for other projects. >=20 > TinyGo is a special Go compiler based on LLVM, that targets mostly embedd= ed > environments. You can use it to generate go programs that can run on > micro controllers, or on web assembly (producing a smaller binary than if > you used the normal stdlib path). >=20 > 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 f= or > TinyGo: riscv32-unknown-none, which uses base integer + multiply/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 memory layer > identical to what risc0 expects. The final component was a new runtime > (`src/runtime/runtime_zkvm.go`), which implemented a few platform specifi= c > syscalls for risc0 (putchar(), exit(), ticks(), and growHeap()). >=20 > When I tried to get this working last year, I had to also implement a num= ber > of kernel syscalls (called ecalls in the platform [7]) to handle: read+wr= ite > to stdin/stdout, halting, and the journaling mechanism (the transcript of > execution committed to), which basically implement the kernel that the gu= est > executes in. Fast forward to 2026, and after pulling the latest version o= f > the repo, I realized that they now make a libzkvm_platform.a, which packa= ges > up the kernel nicely to be linked against. So I threw out my custom kerne= l > code, and slotted that in instead. >=20 > The final component is a C FFI layer that enables me to use _both_ a Go > guest (the program to be proved) and a Go host (the thing that executes t= he > program and generates the final proof). >=20 > ## BIP-32+Taproot zk-STARK Proof >=20 > With basic proofs working (like the classic: I know the factorization of = a > number `n`), I was unblocked to generate the actual proof. The claim/proo= f > is represented with the following JSON artifact: > ``` > { > "schema_version": 1, > "image_id": "8a6a2c27dd54d8fa0f99a332b57cb105f88472d977c84bfac077cbe70907= a690", > "claim_version": 1, > "claim_flags": 1, > "require_bip86": true, > "taproot_output_key": "00324bf6fa47a8d70cb5519957dd54a02b385c0ead8e4f92f9= f07f992b288ee6", > "path_commitment": "4c7de33d397de2c231e7c2a7f53e5b581ee3c20073ea79ee4afaa= b56de11f74b", > "journal_hex": "010000000100000000324bf6fa47a8d70cb5519957dd54a02b385c0ea= d8e4f92f9f07f992b288ee64c7de33d397de2c231e7c2a7f53e5b581ee3c20073ea79ee4afa= ab56de11f74b", > "journal_size_bytes": 72, > "proof_seal_bytes": 1797880, > "receipt_encoding": "borsh" > } > ```` >=20 > The `image_id` is basically a hash of the ELF, so you know what the prove= r > executed. There are then a few flags that control the claim 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 t= o > see. We then also include a `path_commitment`, which is a commitment to t= he > 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. >=20 > 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 > ``` >=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 the 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 deploy a keyspend > disabling soft fork in the future, we can also deploy some variant of > this proof to enable both BIP-86 wallets, and also any BIP-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 (eg: photonics, ne= w > flavor of high bandwidth memory, etc) in hardware (driven by the fierce A= I > 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 amoun= t > of steps, and therefore the size of the proof. A production 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 incorporated into the > proof. Going a step further, the execution of the guest program can even > _generate_ a valid schnorr signature to permit spending. >=20 > Looking to the memory+computational requirements necessary to generate th= e > proof, I've left two low hanging fruits: >=20 > 1. First, we can speed up the Elliptic Curve operations the proof require= s > (scalar base mult, then addition, or more performantly Double 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 into the kernel > to use an optimized/accelerated circuit for the modular arithmetic, > 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/composition syscalls: > sys_verify_integrity+sys_verify_integrity2. We can then assembled a > series of these proofs into a _single_ statement, which can 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/ecall-reference.m= d >=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/CAO3Pvs_PciUi%2BzBrCps3acO14sgeHVUANx9w6TVwUf_AYcd_qQ%40mail.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 from it, send an e= mail to bitcoindev+unsubscribe@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/= ciibnh-b0x-rLwA8pY5NURBfPvG58gLcS7yPLIIkFV5IzA1k-PTsPZqYU8uUyQRxLCnEFhGcrRC= TM39N2AYEy0Db2H_UwIse3Hg9XEXNEYg%3D%40proton.me. -----------------------7a8e2d97c4d0a87d757cd378d8080766 Content-Type: multipart/related;boundary=---------------------89276fe28041354938924028a675019a -----------------------89276fe28041354938924028a675019a Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hi Laolu,

Great work getting this working in the real world. I've heard many peop= le on delving and the mailing list conjecture based on this idea, but you'r= e the first person i've seen who's willing to put their money where their m= outh is, and actually build a prototype. Bravo!

It seems to me the circuit (guest program) could b= e simplified. Notice how the guest code computes the entire HD wallet key path, including = hardened and non-harden= ed derivation steps, and also computes the taproot output key with key-twea= king. I'd argue these steps are extraneous to the core hard relation you wa= nt the STARK to prove, and could be safely removed to reduce proof size and= improve performance.

I= n 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= this much more general statement (2): "I know a BIP32 xpr= iv 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 kn= ow your account-level xpub, but it entails far less computation to prove an= d verify. The rest of the original statement (1) can be done externally out= side the circuit.

Examp= le. 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 xpriv at m/86'/0'=E2=80=8B which derives the = xpub at m/86'/0'/0'=E2=80=8B. Then = I provide the remaining key path elements /1/2=E2=80= =8B in the witness. Note, i do not m= ean we derive the xpriv at m/86'/0'=E2=80=8B inside the guest program. I mean the pr= over derives m/86'/0'=E2=80=8B firs= t (in the host), and then writes that xpriv i= nto the guest program's inputs. The guest program derives and outp= uts the xpub at m/86'/0'/0'=E2=80= =8B. The verifier may check the STARK output (xpub) is correctly compu= ted, then use the given key-path to manually derive the taproot address fro= m the xpub themselves, outside the circuit, and validate = that address against the UTXO i'm spending. The verifi= er thus has confirmed the prover knew an xpriv which (through a hardened de= rivation step) derives the correct taproot output key.
<= br style=3D"scrollbar-width:thin;scrollbar-color:rgba(0, 0, 0, 0.35) rgba(0= , 0, 0, 0)">
This 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 master key, 5 for the BIP32 derivation steps),= two SHA256 compression calls (for the taptweak hash), and two point multip= lications. 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 will improve your proof size and runtime significantly.
<= div style=3D"scrollbar-width:thin;scrollbar-color:rgba(0, 0, 0, 0.35) rgba(= 0, 0, 0, 0)">
This change also makes the ci= rcuit more generally applicable to other rescue contexts. For instance, it = could be applied to BIP340 xonly keys inside a taproot script tree, or in a= P2(W)SH address to an ECDSA public key, or to P2(W)PKH addresses.

Concerned a= bout 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 quan= tum attackers. At best the xpub can be used for surveillance but not forger= y. If one would prefer not to share the account-level xpub on-chain = for privacy reasons, the proof could be extended to also derive the unharde= ned 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).

We should also= talk scaling efficiency. Given the cost of STARKs, this style of proof sho= uld be able to authorize spends for more than one UTXO. Say you have a wall= et with 10 different UTXOs held by distinct addresses in the same BIP44 acc= ount. One single STARK proof could authorize spending all 10 of them, by si= mply committing all 10 input signature hashes into the journal, and labelin= g the inputs with the correspon= ding 10 BIP32 key paths somehow. The verifier would need to c= heck the proof only once and not 10 times. The 10 UTXO spends could be vali= dated using the common xpub from the STARK proof's journal.

For a slightly related work proving a = similar relation for hashed addresses, using different STARK technology sta= cks, see this delving post.<= /div>

However, all this said,= my personal preference for long-term procrastinator rescue is still for co= mmit/reveal strategies which prove essentially the same statement about BIP= 32 in a two-step procedure. They get the job done with much lighter cryptog= raphic machinery and much smaller witnesses: a few hundred bytes over two t= ransactions, compared to a few million bytes in one transaction with STARKs= . Boris Nagaev and I discuss= ed this on the list a while back. That said, commit/reveal requires mor= e careful design 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 wo= rth it to some people? IDK. What do you think of commit/reveal compared to = STARKs for this purpose?

regards,
conduition

On Wednesday, April 8th, 2026 at 12:18 AM, Olaoluwa Osuntokun <l= aolu32@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/risc0<= /a>
* 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-zk= vm
* Go utilities to take a RISC-V ELf binary produced by tinygo= -zkvm, and
package it in the expected R0BF format, which combines = the 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.

* This also includes a Go host= package, which loads the guest program,
executes it, and generate= s a trace to later be proved. This is
achieved via a C FFI compat = layer between Go and the original Rust
host/proving/verification c= ode.

* bip-32-pq-zkp: https://git= hub.com/Roasbeef/bip32-pq-zkp
* The project that packages everyt= hing together, this contains the:
* Guest Go program that defines = the 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 second= s or so to generate+proof, including execution. This
uses Metal for = GPU acceleration on the platform.
* Uses ~12 GB of ram.
* Final p= roof size is ~1.7 MB.
* Verification takes ~1.8 seconds, and uses ~32 = MB of memory.

On several layers, this demo is far from optimized (mo= re on that later),
this is meant to serve as a PoC to demonstrate that w= ith the latest
software+hardware, a proof of this complexity is well wit= hin reach.

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-zk= vm/blob/main/docs/tutorial.md.

If you got to this point in this = mail, and don't care about the lower level
details, thanks for reading u= p until now, and feel free to return back to
the _The Net of a Million L= ies_, or as better known in our Universe:
Monitoring the Situation and/o= r slopfotainment! =F0=9F=AB=A1

## Motivation + Background

As = commonly known, in the case of an adversary that possesses a quantum
com= puter capable of breaking classical asymmetric cryptography, any coins
s= tored in UTXOs with a known public key are vulnerable. This 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 pu= blish
the public key plainly in the pkScript.

As detailed in [3],= for Taproot outputs, a widely circulated plan is
roughly to: disable th= e _keyspend_ path (requires a simple signature),
enforcing a new rule th= at all Taproot spends must then flow through the
script path. Spending v= ia the script path requires an opening of the
Taproot commitment (C =3D = I + H(I || H(M))), which was shown to be binding even
under classic assu= mptions, as H(M) (tapscript merkle root) is still a
collision-resistant = function.

That means any UTXO that _does_ commit to a script path ha= s a future escape
hatch _if_ such a softfork would need to be deployed i= n the 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 thi= s existing
proposal, those wallets would basically be locked forever.
The goal of this work is to demonstrate a practical solution (discusse= d
against devs, but never implemented AFAICT): generate a zk proof that = an
output was generated using BIP-86. For the zk-Proof, we select zk-STA= RKs,
as they're plausibly post quantum since they rely only on symmetric=
cryptography: layers of merkle trees over an execution trace, along wit= h
some novel sampling/error-correction algorithms.

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 takes an initial
128-512-= bit seed (with BIP-39, either 12 or 24 words), then runs it through
HMAC= -SHA512 keyed by "Bitcoin seed" to produce the master extended private
k= ey. An adversary who wants to forge this proof needs to find a _colliding_<= br>seed: a different seed s' such that HMAC-SHA512("Bitcoin seed", s') prod= uces
the same master key. The BHT algorithm (Brassard-Hoyer-Tapp [6]) is= the
best known quantum collision finder, and it runs in time proportion= al 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 hig= hest
post-quantum security category. Therefore, if you generated a walle= t using
BIP-32, you possess _another_ secret that a quantum adversary ca= n't
efficiently reconstruct!

This demo focuses on the Taproot cas= e, but the rough approach also applies
to any other output generated via= BIP-32. BIP 32 was originally published in
2012, over 14 years ago. So = safe to say that _most_ wallets were generated
under this scheme. Howeve= r, Bitcoin Core only officially adopted BIP-32 in
2016/2018, moving away= from their existing key pool structure. I can't say
how much BTC is hel= d today in outputs generated with Bitcoin Core's original
key pool, but = if you have coins generated via that mechanism, you may want
to consider= migrating them to a BIP-32 wallet.

## TinyGo + RISC-V + risc0
Now for some of the lower level details. risc0 is a STARK based provingsystem that takes a RISC-V ELF binary generated by a guest program (anyprogram generating using their flavor of rv32im can be proved), executes<= br>that in a host environment, generates a trace, then produces a STARK pro= of
from that.

Today you can take some subset of Rust, compile it = to an ELF using their
toolchain, then execute it, generate a trace, to f= inally prove+verify it
using their system.

This demo took a bit o= f a round about journey to achieve this, as after
all, the journey is mo= st of the fun, ain't it!

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

TinyGo is a special Go compiler based on LLVM, th= at targets mostly embedded
environments. You can use it to generate go p= rograms that can run on
micro controllers, or on web assembly (producing= a smaller binary than if
you used the normal stdlib path).

TinyG= o supports RISC-V, but _not_ the 32-bit variant of RISC-V that risc0
rel= ies on. So the first step here was to create a new target definition forTinyGo: riscv32-unknown-none, which uses base integer + multiply/divideinstructions with no compressed instructions, which uses 4 KB stacks foreach task. From there, I created a new linker script
(`targets/riscv32= im-risc0-zkvm-elf.ld`) which created a memory layer
identical to what ri= sc0 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 growHeap()).

When I tried to get t= his working last year, I had to also implement a number
of kernel syscal= ls (called ecalls in the platform [7]) to handle: read+write
to stdin/st= dout, halting, and the journaling mechanism (the transcript of
execution= committed to), which basically implement the kernel that the guest
exec= utes in. Fast forward to 2026, and after pulling the latest version of
t= he repo, I realized that they now make a libzkvm_platform.a, which packages=
up the kernel nicely to be linked against. So I threw out my custom ker= nel
code, and slotted that in instead.

The final component is a C= FFI layer that enables me to use _both_ a Go
guest (the program to be p= roved) and a Go host (the thing that executes the
program and generates = the final proof).

## BIP-32+Taproot zk-STARK Proof

With basic= proofs working (like the classic: I know the factorization of a
number = `n`), I was unblocked to generate the actual proof. The claim/proof
is r= epresented with the following JSON artifact:
```
{
"schema_versi= on": 1,
"image_id": "8a6a2c27dd54d8fa0f99a332b57cb105f88472d977c84bfac= 077cbe70907a690",
"claim_version": 1,
"claim_flags": 1,
"req= uire_bip86": true,
"taproot_output_key": "00324bf6fa47a8d70cb5519957dd= 54a02b385c0ead8e4f92f9f07f992b288ee6",
"path_commitment": "4c7de33d397= de2c231e7c2a7f53e5b581ee3c20073ea79ee4afaab56de11f74b",
"journal_hex":= "010000000100000000324bf6fa47a8d70cb5519957dd54a02b385c0ead8e4f92f9f07f992= b288ee64c7de33d397de2c231e7c2a7f53e5b581ee3c20073ea79ee4afaab56de11f74b", "journal_size_bytes": 72,
"proof_seal_bytes": 1797880,
"recei= pt_encoding": "borsh"
}
````

The `image_id` is basically a has= h of the ELF, so you know what the prover
executed. There are then a few= flags that control the claim 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 _pub= lic 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 p= ath that the prover used. Finally, we also commit to the
journal hex, wh= ich is basically a commitment to the public claim.

Assuming you've b= uilt the project, then you can generate the proof (even
passing in an ar= bitrary BIP-32 seed and derivation path with)
```
make prove GO_GOROO= T=3D/path/to/go1.24.4
```

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

The default prove target wr= ites:
* ./artifacts/bip32-test-vector.receipt
* ./artifacts/bip32= -test-vector.claim.json

The receipt is the STARK proof artifact. cla= im.json is the stable,
human-readable description of the public statemen= t being proved.

## Application to a Future Keyspend Disabling Soft f= ork

As mentioned above, assuming the community is forced to deploy a= keyspend
disabling soft fork in the future, we can also deploy some var= iant of
this proof to enable both BIP-86 wallets, and also any BIP-32 wa= llet, to
sweep their funds into a new PQ output.

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

One thing to note is that this= proof has a few layers of indirection,
mainly the RISC-V layer that add= s overhead which increase the total amount
of steps, and therefore the s= ize of the proof. A production grade
deployment would likely instead han= d roll a custom STARK proof for this
exact statement, to achieve a faste= r and smaller proof).

# Future Work

In terms of future work, = there're a number of interesting following up
projects that can be pursu= ed from here.

One basic one is that the current proof doesn't actual= ly 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= program can even
_generate_ a valid schnorr signature to permit spendin= g.

Looking to the memory+computational requirements necessary to gen= erate the
proof, I've left two low hanging fruits:

1. First, we = can speed up the Elliptic Curve operations the proof requires
(scala= r base mult, then addition, or more performantly Double Scalar
Multi= plication via the Strauss-Shamir trick). For this we can use the
sys= calls/precompile in the risc0 env for big integer arithmetic:
sys_bi= gint and sys_bigint2. With this, the guest calls into the kernel
to = use an optimized/accelerated circuit for the modular arithmetic,
red= ucing 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:
sys_verify_integri= ty+sys_verify_integrity2. We can then assembled a
series of these pr= oofs into a _single_ statement, which can save block
space by aggreg= ating N proofs into a single proof.

-- Laolu

[1]: https://tinygo.org/

[2]: https://risczero.com/

[3]: https://eprint.iacr.org/2025/1307

[4]: https://eprint.iacr.org/2023/362

[5]: https://microsoft.github.io/Picni= c/

[6]: https://en.wikipedia= .org/wiki/BHT_algorithm

[7]: https://github.com/Roasbeef/go-zkvm/blob/main/do= cs/ecall-reference.md

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