The summary is that the proof of knowledge associated to a commitment is crucial to bind the commitment to the actual circuit variables that were supposed to be committed. However, the same σ is used for all proofs of knowledge for the commitments, which allows mixing between them, making it possible to fix the value of all but one commitment before choosing the circuit variable assignments. In more detail: To …
This report concerns the Groth16 prover when used with commitments (as in frontend.Committer). To simplify exposition of the issue, I will focus on the case of a single commitment, to only private witnesses. But the issue should be present whenever commitments are used that include private witnesses. The commitment to private witnesses w_i is computed as c = sum_i w_i * b_i where b_i would be ProvingKey.CommitmentKeys[0].Basis[i] in the code. …
Impact gnark provides a gadget in the standard library to allow optimized checking of the bitwidth of the inputs. The gadget works by constructing a fixed lookup table containing all valid entries, partitioning the input and checking that all parts are inside the lookup table. The range checker gadget does not take into account that the highest partition may be less than the width limit, allowing the inputs to be …
Impact The vulnerability allows a third party to derive a valid proof from a valid initial tuple {proof, public_inputs}, corresponding to the same public inputs as the initial proof. It is due to a randomness being generated using a small part of the scratch memory describing the state, allowing for degrees of freedom in the transcript. Note that the impact is limited to the PlonK verifier smart contract. Patches We …
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 …