Learning new things!
A polynomial field, also called a finite field or Galois field, is a field constructed by taking polynomials over a smaller field and reducing them modulo an irreducible polynomial. It is used to create fields with more elements than the base field.
A …
An extension field \( \mathbb{F}_{q^m} \) is constructed by extending a smaller field \( \mathbb{F}_q \) (the base field) with additional elements, typically through the introduction of a root of an irreducible polynomial over \( \mathbb{F}_q \).
this statemachine example has component with different degrees:
StateTRansitionEval is the evaluation function, coordinate mark the number of the Eval
statemachine 0 has just two numbers, the mix_into put these numbers in to channel
statemachine 1 aslo implement the mix_into function, and mix all …
Related type:
TraitsResolver helps to find the implementation for a given trait function and concrete type arguments.
TraitsResolver has a function resolve_trait_function_reference (see below) for a given polynomial reference, it resolves its trait
one of the input to this polynomialReference,
using fibo_no_public example, PolynomialReference looks like:
remove_trait_implsFollowing the first post: Circle STARK: Understanding Circle Group’s Operation as Rotation
The goal of this post is to explain 2-adic FFT on circle domain.
In STARK, there are two cases where FFT is used:
A Rust program is compiled to ELF, using traditional compiler (as ELF is not only used for ZKVM, but also for embedded system as well, this step is pretty much standard)
instruction explanation:
ADD, value1 stored in address xD, added this value by 5 and store the value in x29…
Runtime refers to the period when a program is actively running or executing on a …
The goal of this blog is to explain circle group without complex mathematical definitions. However, this approach is not rigorous, it serves more like a intuition of understanding the geometry of a circle group. Before diving into the blog, may you need some pre-readings like Exploring circle STARKs or Yet …
Using multiplicative group of size 16 to demonstrate the concept of coset.
suppose we have a trace \([1,2,3,4]\) , and we want to prove \(f(x)+1=f(gx)\)
\(g\) is the group generator for cyclic group of size 4, the same size of the trace.
Canonical coset:
odd coset setup
CirclePointIndex is just a wrapper of usize, which represent actually the order of the coset generator.
when creating a new coset, we need a generator and shiftoffset, the shiftoffset mostly be the generator of the subgroup of one log size bigger
so here, CirclePointIndex::subgroup_gen is …