Any bleeding-edge field has trouble agreeing on terms, and only with time some terms end up stabilizing and standardizing themselves. Some of these terms are a bit weird in the zero-knowledge proof field: we talk about SNARKs and SNARGs and zk-SNARKs and STARKs and so on.

It all started from a clever pun “succinct non-interactive argument of knowledge” and ended up with weird consequences as not every new scheme was deemed “succinct”. So much so that naming branched (STARKs are “scalable” and not “succinct”) or some schemes can’t even be called anything. This is mostly because succinct not only means really small proofs, but also really small verifier running time.

If we were to classify verifier running time between the different schemes it usually goes like this:

• KZG (used in Groth16 and Plonk): super fast
• FRI (used in STARKs): fast
• Bulletproof (used in kimchi): somewhat fast

Using the almost-standardized categorization, only the first one can be called a SNARK, the second one is usually called a STARK, and I’m not even sure how we call the third one, a NARK?

But does it really make sense to reserve SNARK to the first scheme? It turns out people are using all three schemes because they are all dope and fast(er) than running the program by yourself. Since SNARK has become the main term for general-purpose zero-knowledge proofs, then let’s just use that!

I’m not the only one that wants to call STARKs and bulletproofs SNARKs, Justin Thaler also makes that point here:

the “right” definition of succinct should capture any protocol with qualitatively interesting verification costs – and by “interesting,” I mean anything with proof size and verifier time that is smaller than the associated costs of the trivial proof system. By “trivial proof system,” I mean the one in which the prover sends the whole witness to the verifier, who checks it directly for correctness