In systems where computations are performed in remote or potentially untrusted environments(e.g. Ethereum NaaS providers such as Infura), how can we gain confidence in the accuracy of the results? Zero-knowledge proofs (ZKPs) provide an intriguing solution for verifying specific aspects of computation.

My focus:

  • Proofs for Function Outputs: Can we generate a ZKP that directly verifies the output (return value) of a function call, given its inputs and any relevant contextual state?
  • Beyond State Transitions: While ZKPs in blockchains often prove state transitions, I'm interested in the specifics of attesting to a singular function result.
  • Challenges and Approaches: What are the cryptographic considerations, potential circuit design patterns, and trade-offs in constructing proofs for function call outputs?


  1. Are there theoretical limitations to proving arbitrary function results, or are there classes of functions that are well-suited?
  2. How would the process of generating and verifying such a proof look in practice?
  3. What are the potential efficiency bottlenecks (proof size, computation time) to consider?
  • $\begingroup$ For additional context I asked a more tailored question here $\endgroup$
    – MShakeG
    Commented Mar 20 at 10:57

1 Answer 1

  1. No, there are no theoretical limitations to proving the correctness of the result of some function $f$ as long as this function is computable by a polynomial-size boolean circuit. I'm not sure why zero-knowledge is relevant here; if you have access to both the output and input of the function, you can verify the computation by running it. If instead you want a succinct way of verifying computation (i.e. that takes strictly less time than computing $f$), there are also results for that. The theory behind succinct proofs is based on the PCP Theorem. If you only know the output $y$ and some part $x$ of the input and want to check that there is $w$ such that $f(x,w)=y$, then this is indeed possible to verify this in zero-knowledge (hiding $w$) since the question is framed as an NP statement.
  2. The most generic way of proving NP statements about boolean circuits that I am aware of is the MPC-in-the-Head framework. The proofs can be made non-interactive through the Fiat-Shamir transform.
  3. There is a lot of research activity around making the MPC-in-the-Head technique more efficient since it is used for many candidate post-quantum signature schemes. You can check out the candidates in NIST's most recent call to have an idea of the efficiency.

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