So arithmetization-oriented ciphers are used e.g. used in ZK-SNARKs? How long have these ciphers existed?
The first cipher to have this property was, I think, LowMC (2015). There have been a bunch more proposals since -- MiMC (2016), GMiMC (2019), Starkad and Poseidon (2019), Vision and Rescue (2019), and Rescue-Prime [1] (2020). I may be missing some; there was a rapid development in this field in the last years.