# Implement Montgomery reduction, use it to optimize FFT - Implement partial Montgomery reduction subroutines for [ff crate](https://github.com/matter-labs/ff) as a trait. - Use the outcome of this task along with additional research to improve FFT operation in [`plonk` branch of `bellman` crate](https://github.com/matter-labs/bellman/tree/plonk). Example of one of FFT approaches can be found [here](https://github.com/matter-labs/bellman/blob/plonk/src/plonk/fft/cooley_tukey_ntt/mod.rs). Unsafe code is allowed. FFT implementation may be not "in-place" - Use outcomes of the previous work to also speed-up LDE operation - evaluation of the polynomial of degree n-1 on the domain of size 16 * n. Example of how it can be [done](https://github.com/matter-labs/bellman/blob/4f01fbd6ec3264c500796bd01ef8831a22dafefa/src/plonk/polynomials/mod.rs#L620) The code should have some form of the trivial validity checks and benchmarks versus already implemented routines. Guidance and assistance will be provided, but we expect independent research.
Last changed by  
 
Alexander
456

Read more

Current performance of EIP-2537 and EVM384

In recent progress reports there were a lot of improvements on the execution speed of EVM384 based on the EVMOne implementation of EVM. It was claimed that implementation of the miller loop + final exponentiation for the pairing of two pairs takes around 4.8 ms, that is a great result, but unfortunately it can only be considered as a wonderful academic achievement that unfortunately have nothing to do with the final cost of this operation to end-users. There is a fundamental difference between the precompile and the EVM384 based contract from perspective of heavy cryptography: in precompile the final cost covers everything: parsing input validation control flow (fast and native) arithmetics (fast and native)

11/5/2020
New tree structure for circuit tests

Simple binary Merkle tree contains 2^N items. Each item is an "account" that follows this declaration and follow this procedure for serialization into the vector of field elements. After serialization item is hashed with Rescue hash in a form of "committer" created like here There are few fields that are must have certain default values: pub balances_tree_root: E::Fr - must be a merkle root of the simple binary merkle tree with 2^K items each of them being zero (as field element) pub sync_pubkey_hash: E::Fr - is zero by default pub self_state: E::Fr - is zero by default pub contract_code_root: E::Fr - is zero by default

9/7/2020
Balance and transfer amount precision

11/12/2019
FPGA requirements

10/29/2019
Read more from Alexander
Published on HackMD