Fox is an Ethereum zkRollup using ZK-EVM and its original ZK-FOAKS technology. ZK-STARKS comes from Zero Knowledge - Fast Objective Argument of Knowledges that is faster than Stark with linear proof time, sublinear verification time, transparent, and proof recursion inside.

Fox uses some algorithms to accelerate cryptography in its Folder & ZK-FOAKS.

One of the first places to look when accelerating cryptography is to evaluate various algorithmic approaches to the problem. Our protocol is a family of algorithms driven by low-level primitives such as modular multiplication. To begin it is best to understand what group operations are consuming the most compute resources/time, and then investigate the low-level algorithms that are used to implement the primitives of higher-level cryptographic protocols.

It is important to understand that every algorithm represents a unique set of tradeoffs between latency, throughput, power, and area. When selecting an algorithm it is imperative that you understand both the desired goal as well as the underlying hardware that is available for you to use. Algorithmic decisions can not be made in isolation and need to consider the target implementation.

While investigating the operations, we discovered that modular multiplication and modular squaring were consuming the vast majority of the compute cycles. In order to accelerate the above-mentioned cryptographic constructions, we began to evaluate various algorithms and representations that could be used to accelerate these operations. Some such algorithms include schoolbook multiplication, Montgomery multiplication, and Barrett reduction, while representations include polynomial form and residue numeral system.