There are a lot of constructions of succinct non-interactive arguments of knowledge out there, even after filtering out those which are publicly verifiable and support proving unstructured languages such as Boolean or arithmetic circuit satisfiability (circuit-SAT) or rank-1 constraint satisfiability (R1CS). The table below is a quick, not necessarily accurate, summary of what is available at the moment.

Year	Scheme	Size	Trans	Preproc	Algebraic	PQ	Published	Reference	Note
2018	Bulletproof (Group)	polylog	Yes	No	No	No	SP18	link
2020	Lakonia	polylog	Yes	No	No	No	–	link
2019	Sonic	1	No	Yes	No	No	CCS19	link	Universal updatable CRS
2020	Marlin	1	No	Yes	No	No	EC20	link	Universal updatable CRS
2020	Spartan	sqrt	Yes	Yes	No	No	C20	link
2020	SuperSonic	polylog	Yes	Yes	No	No	EC20	link
2020	Kopis	polylog	Yes	Yes	No	No	–	link
2020	Xiphos	polylog	Yes	Yes	No	No	–	link
2016	Groth16	1	No	Yes	Yes	No	EC16	link
2018	GKMMM18	1	No	Yes	Yes	No	C18	link	Universal updatable CRS
2020	Bulletproof (Lattice)	polylog	Yes	No	No	Yes	C20,C21	BLNS20,AL21,ACK21
2017	Ligero	sqrt	Yes	No	No	Yes	CCS17	link
2019	Aurora	polylog	Yes	No	No	Yes	EC19	link
2021	Brakedown	sqrt	Yes	Yes	No	Yes	–	link
2021	Shockwave	sqrt	Yes	Yes	No	Yes	–	link
2020	Fractal	polylog	Yes	Yes	No	Yes	EC20	link

Size: Proof size as a function of statement size, fixed multiplicative factor polynomial in security parameter omitted
Trans: Transparent setup, i.e. lack of a trusted setup
Preproc: Verifier can preprocess the statement to make verification time sublinear in statement size
Algebraic: Only uses low-degree algebraic operations over the underlying group/ring/field, does not use random oracles or hash functions (which could be seen as high-degree operations)
PQ: Post-quantum in the most liberal sense, i.e. as long as it is not based on groups

Last Updated on 11/07/2022.