Vitalik Buterin Publishes "Exploring Circle STARKs"

PANews reported on July 23 that Ethereum co-founder Vitalik Buterin published an article titled "Exploring Circle STARKs", discussing a construct known as Circle STARKs. It has some unique properties and is designed to be compatible with the efficient Mersenne31 field. Vitalik believes that compared to regular STARK, Circle STARKs do not bring much additional complexity for developers. In the implementation process, compared to the regular FRI, there are essentially only three differences I observed. The mathematical principle behind the "polynomial" operated by Circle FRI is quite counter-intuitive and takes time to understand and appreciate. However, this complexity is hidden in such a way that it's not easily noticeable by developers. The complexity of Circle mathematics is encapsulated rather than systemic. Understanding Circle FRI and Circle FFT can also be a good knowledge portal towards understanding other "exotic FFTs": most notably binary domain FFT used previously in Binius and LibSTARK, as well as more exotic constructs like elliptic curve FFT which use one-to-one mappings well-coordinated with elliptic curve point operations. Combined with Mersenne31, BabyBear, and binary domain technologies (like Binius), we indeed feel we are approaching the efficiency limit of the STARK "base layer". At this point, it's expected that the frontier of STARK optimization will shift towards creating highly efficient arithmetic versions of primitives like hash functions and signatures (and optimizing these primitives themselves for this purpose), creating recursive constructions for greater parallelization, arithmetizing virtual machines to improve developer experience along with other advanced tasks.