2018, Dan Boneh, Yuval Ishai, Amit Sahai, David J. Wu, Quasi-Optimal SNARGs via Linear Multi-Prover Interactive Proofs, Jesper Buus Nielsen, Vincent Rijmen (editors), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on Cryptographic Techniques, Proceedings, Part III, Springer, LNCS 10822, page 224,
A SNARG is publicly verifiable if anyone can verify the proofs, and it is designated-verifier if only the holder of a secret verification state (generated along with the CRS) can verify proofs.
Source: wiktionary
However, SNARGs and SNARKs (blockchain implementations of SNARGs) rely on pre-quantum assumptions and are not post-quantum secure. Hence, lattice-based SNARGs are proposed (Boneh et al., 2017).
Source: wiktionary
2021, Yael Taumann Kalai, Vinod Vaikuntanathan, Rachel Yun Zhang, Somewhere Statistical Soundness, Post-Quantum Security, and SNARGs, Kobbi Nissim, Brent Waters (editors), Theory of Cryptography: 19th International Conference, TCC 2021, Proceedings, Part I, Springer, LNCS 13042, page 355,
In this section, we construct SNARGs for languages with a (computational) non-signaling mathsf PCP, assuming the existence of a SNARG for mathsf BatchNP.
Source: wiktionary