A BrainFuck zkVM implementation using Halo2. Zkvm_brainfuck is a zero-knowledge BrainFuck VM, designed as a custom, STARK-inspired version of PSE's Halo2. It's only for learning purposes only, out of a desire to gain a deeper, detailed understanding of Halo2 and VM arithmetization.

For what's about Brainfuck language and it's constraints, please read the BrainSTARK introduction and Arithmetization of Brainfuck VM first.

1. In BrainSTARK, the author uses Permuation Running Product to do permutation check, which requires some challeges values chosen by the Fiat-Shamir public oracle, thus might incur potential security risk. Here we use Halo2's in-house lookup_any API to do the Permuation check.

2. In BrainSTARK, the author uses Running Evaluation to verify that one table contains rows that are an (order-preserving) sublist of another table. Here, by combining lookup and a order-perservating gate, we can constrait the same thing on output table and input table.

Because we can directly do the above two constraints in halo2, there is no need to introduce a Instrcution table as a bridge fullfill the Permuation Running Product and Running Evaluation.

For clarity, the two gates involved with memory inverse inv required by Processor table in Arithmetization of Brainfuck VM is replace by IsZeroChip.

A range table is used to constrain the memory value and cycle offset, here the chosen range is [0,255].

Credits to cryptape to VM implementation. We made some minor changes to the Matrix structure in bf_vm/src/matrix.rs for easier lookup integration.

cd bf_vm && cargo test

In bf_zk/tests dir, we provide two basic test cases, of which one is without inputs while the other is with inputs.

cd bf_zk
cargo test test_vmcircuit -- --show-output