gnark unsoundness in variable comparison / non-unique binary decomposition

Impact

For some in-circuit values, it is possible to construct two valid decomposition to bits. In addition to the canonical decomposition of a, for small values there exists a second decomposition for a+r (where r is the modulus the values are being reduced by). The second decomposition was possible due to overflowing the field where the values are defined.

Internally, the comparison methods frontend.API.Cmp and frontend.API.IsLess used binary decomposition and checked the bitwise differences. This allows a malicious prover to construct a valid proof for a statement a < b even if a > b.

The issue impacts all users using API.Cmp or API.IsLess methods. Additionally, it impacts the users using bits.ToBinary or API.ToBinary methods if full-width decomposition is requested (the default behaviour if no options are given).

The issues does not impact comparison methods in field emulation (package std/math/emulated) and dedicated comparison package (std/math/cmp).

Patches

Fix has been implemented in pull request #835 and merged in commit 59a4087261a6c73f13e80d695c17b398c3d0934f to master branch. The release v0.9.0 and onwards include the fix.

The fix added additional comparison of the decomposed bit-vector to the modulus of the in-circuit values.

Workarounds

Upgrading to version v0.9.0 should fix the issue without needing to change the calls to value comparison methods.

Alternatively, users can use the std/math/cmp gadget, which additionally allows to bound the number of bits being compared, making the comparisons more efficient if the bound on the absolute difference of the values is known.

References

• https://github.com/Consensys/gnark/pull/835
• https://github.com/zkopru-network/zkopru/issues/116
• https://github.com/iden3/circomlib/pull/48

Acknowledgement

The vulnerability was reported by Marcin Kostrzewa @ Reilabs.