Explore Circle STARKs

In recent years, the trend in the design of STARKs protocols has shifted towards using smaller fields. The earliest implementations of STARKs used 256-bit fields, but this design is less efficient. To address this issue, STARKs have begun to use smaller fields such as Goldilocks, Mersenne31, and BabyBear.

Using small fields improves proof speed, but also brings new challenges. For example, when selecting random points in small fields, the selectable range becomes smaller, making it easier for attackers to crack. Therefore, additional measures are needed to enhance security.

Circle STARKs is a new solution. It employs a special group structure that enables the efficient implementation of the FRI protocol on small fields such as Mersenne31. The core of Circle STARKs is to leverage the geometric properties of circular groups to map operations in two-dimensional space to one-dimensional space, thereby enhancing computational efficiency.

Circle STARKs also supports Circle FFT, which is a special FFT algorithm. Unlike conventional FFT, Circle FFT operates on functions in the Riemann-Roch space rather than strictly defined polynomials. While this difference is mathematically complex, it is virtually negligible for developers.

In terms of implementation details, Circle STARKs have some differences from conventional STARKs, such as the arithmetic operations, disappearing polynomials, and reverse bit ordering. However, overall, Circle STARKs are not much more complex for developers than conventional STARKs.

Circle STARKs combined with Mersenne31 fields can achieve very efficient proofs. It makes full use of space in computational tracking, reducing waste. Although solutions like Binius are superior in some aspects, the concept of Circle STARKs is simple, easy to understand and implement.

As the efficiency of the STARKs base layer approaches its limits, future optimization directions may include: optimizing the arithmetic of cryptographic primitives, using recursive constructions to improve parallelism, and improving the arithmetic of the virtual machine to enhance the developer experience, among others.