# Binius notes
## Modern SNARK landscape
![image](https://hackmd.io/_uploads/BJxxHr7s6.png)
- STARKS are bandwidth boud meaning that they become more computationally heavy when moving data into FPGA is heavy.
![image](https://hackmd.io/_uploads/rJL_BS7ia.png)
![image](https://hackmd.io/_uploads/ByLFHBQjp.png)
![image](https://hackmd.io/_uploads/r1iovBQip.png)
![image](https://hackmd.io/_uploads/SyL-dBmop.png)
![image](https://hackmd.io/_uploads/B1Js_Smop.png)
- d is the degree of the field extension.
- add = xor
- in the classical case for multiply
- we have univariate quotient ring, we start with polynomials of F_2, quotient this by something irreducible like of d.
- so the lements of ring are polynomials of degree 127 or less. And these bits are the coeff of polynomials.
- TO multiply two, we multiplication inside this ring, as binary polynomials and then reduce modulo $X^{128}+{----}$
- New way for multiply
![image](https://hackmd.io/_uploads/SkO_sBXsa.png)
![image](https://hackmd.io/_uploads/HyiZ2Smip.png)
- these X are rings
![image](https://hackmd.io/_uploads/SkcaJIXjT.png)
![image](https://hackmd.io/_uploads/Bkar-U7sp.png)
![image](https://hackmd.io/_uploads/BJxPM8Xj6.png)
![image](https://hackmd.io/_uploads/SkqaSeuiT.png)
- start profgressing to further layers
- gng to multilinear poly, which are in a giant single column of bits lets say and eval that poly at diff points
![image](https://hackmd.io/_uploads/Bysc8gusp.png)