# what is the difference between proofs and arguments of knowledge?

What is the difference between proofs and arguments of knowledge in the context of zero-knowledge?

I have read this sentence in this ePrint:

It is useful to distinguish between zero-knowledge proofs, with statistical soundness, and zero-knowledge arguments with computational soundness. In general proofs can only have computational zero-knowledge, while arguments may have perfect zero-knowledge.

It is also indicated in this article that:

Zero-knowledge protocols come in several flavors, depending on how one formulates the two security conditions: (1) the zero-knowledge condition, which says that the verifier “learns nothing” other than the fact the assertion being proven is true, and (2) the soundness conditions, which says that the prover cannot convince the verifier of a false assertion. In statistical zero knowledge, the zero-knowledge condition holds regardless of the computational resources the verifier invests into trying to learn something from the inter-action. In computational zero knowledge, we only require that a probabilistic polynomial-time verifier learn nothing from the interaction.1 Similarly, for soundness, we have statistical soundness, a.k.a. proof systems, where even a computationally unbounded prover cannot convince the verifier of a false statement (except with negligible probability), and computational soundness, a.k.a. argument systems [BCC], where we only require that a polynomial-time prover cannot convince the verifier of a false statement.

Which I assume that a zero knowledge argument is just a zero knowledge proof that has computational soundness rather than statistical soundness.

Am I right?

## 1 Answer

Yes, you are right. In a proof, the soundness holds against a computationally unbounded prover and in an argument, the soundness only holds against a polynomially bounded prover. Arguments are thus often called "computationally sound proofs".

• It's worth noting that the terms are often used interchangeably in recent literature. Take Pinocchio's abstract for example: "The proof is only 288 bytes". The linked Bootle et al paper observes this distinction for the most part, but still uses "proof" to mean "argument" in a couple places, like "Our proofs are considerably larger as well, especially for the square root version." – Daniel Lubarov Aug 16 '20 at 12:48
• Yes, it should usually be clear from the context if one is dealing with proofs or arguments and also often in not so recent literature arguments are simply referred to as proofs. – DrLecter Aug 16 '20 at 14:43