Overview of Circle STARKs
Circle STARKs are a variant of Scalable and Transparent Arguments of Knowledge (STARK) designed to work efficiently with the Mersenne31 prime field ($2^{31}-1$). Standard STARKs require large multiplicative subgroups of size $2^n$ for Fast Fourier Transform (FFT) and Fast Reed-Solomon IOP (FRI), which Mersenne31 does not naturally provide. Circle STARKs solve this by operating over 2D points on a 'Circle Curve' rather than 1D field elements, enabling the construction of the necessary multiplicative subgroups for efficient FFT and FRI operations.