Contributions and suggestions are always welcome; open issues or pull requests with any changes you want to be made.

contents

• contents
  • projects
  • Technical details
  • bench
  • Independent/third-party Benchmarks
  • papers
    • Cairo
    • Cairo M
    • Ceno
    • Jolt
    • Nexus
    • SP1
    • Risc Zero
    • EDEN
  • resources
  • tutorials / educational zkVM
  • related tooling
  • related awesome lists

projects

[!NOTE]
Maintained by @0xpiapark and @alexanderlhicks. Some details may be outdated; feel free to open an issue or PR. For discussions on fair tracking methods, see the open issues.

• ISA (Instruction Set Architecture): The fundamental “language” of the VM, defining all its basic operations and how they interact with data.
• Continuations: Also known as chunking/sharding. A technique to break oversized computations — too big for a single run — into smaller segments that get proven individually and recursively (proof of segment n+1 includes the proving of segment n's verifier). How self-contained the proving of each segment is (no commitment passed from one segment to the other) and how efficiently parallelizatable it is (minimal inter-thread comm) differs from one implementation to another.
• Precompiles (Built-ins, Chiplets, Accelerate etc): Specialized, pre-built functions for complex tasks (like cryptography) that boost efficiency and reduce proof overhead.
• GPU: Indicates whether proving on GPU is supported (based on publicly exposed Metal/CUDA code).
• Proving Frontend: The programming language the programmer expresses their business logic in, which then get compiled down into the VM’s supported ISA for constrained execution.

Technical details

Proof systems

• Arithmetization: The process of turning an execution trace into an algebraic statement (polynomial equations) that can be verified.
• Optimizations: Ingredients in the proof system that can optimize the size and complexity of the constraints overall.
• Backends: The proof system, typically in the form of a (Polynomial) Interactive Oracle Proof (IOP) and Polynomial Commitment Scheme (PCS), used for the (typically non-interactive) prover-verifier checks.
• Verifiers: Programs that can do the (typically non-interactive) verification given a proof and public inputs.

zkVM	Arithmetization	Optimizations	Backends	Verifiers
cairo	AIR		FRI
cairo m	AIR	Lookup	FRI	Rust
ceno	GKR	Lookup, Sumcheck	Brakedown	Rust
eigen zkvm	eAIR		FRI, Groth16	Solidity
jolt	R1CS	Lookup, Sumcheck, Offline Mem Check	Spartan	WASM
miden	AIR (winterfell)	Lookup,	Winterfell	Rust
mozak vm	AIR (Starky)	Lookup,	FRI	Rust
nexus	Folded Accumulated Relaxed R1CS	Accumulated Folding	Spartan + {Zeromorph, PSE-Halo2 (KZG)}	Rust
o1vm	Plonkish	Lookup	IPA	Rust
olavm	AIR (plonky2)	Lookup	FRI	Rust
openvm	AIR (plonky3), GKR		FRI	Rust
pico	AIR (plonky3)	Lookup	FRI	Rust, Solidity
powdrVM	AIR -ish (PIL, plonky3)	-	PSE-Halo2 (KZG), Plonky3, FRI(eSTARK)	Solidity
risc0	PLONK	Plookup	DEEP-FRI & ALI	Rust, Solidity
sp1	AIR (plonky3)	Lookup	FRI	Rust, Solidity
sphinx	AIR (core), PLONK (wrap)	Lookup,	FRI	Rust
triton vm	AIR	Lookup, Contiguity	FRI	Rust
valida	AIR (plonky3)		FRI	?
zisk	?	?	?	?
zkm	AIR (plonky2)	Lookup,	FRI	Rust
zkWasm	PLONK	-	IPA?	Rust

bench

• benchmarks (kkrt-labs) | code
• benchmarks (lita) | code
• benchmark (risc0) | code
• zkvm-benchmarks (a16z) | code
• zkvm perf (succinct) | code
• zkvm bench (brevis) | code

Independent/third-party Benchmarks

• Benchmarks of VM proving times made by Aligned | results code
• Benchmarking of π² ZK Metamath checkers | code, including results
• definitive guide to zkVMs | article
• Lurk 0.5 Benchmarks | article
• benchmark of zkVMs and proving schemes | code
• zkvm testing | article
• prooflab benchmarks | page
• Agglayer pessimistic Proof Benchmarks using zkVMs | code

papers

Cairo

• Cairo – a Turing-complete STARK-friendly CPU architecture
• A Verified Algebraic Representation of Cairo Program Execution
• A Proof-Producing Compiler for Blockchain Applications

Cairo M

• Cairo M Design Document

Ceno

• Ceno: Non-uniform, Segment and Parallel Zero-knowledge Virtual Machine

Jolt

• Jolt: SNARKs for Virtual Machines via Lookups

Nexus

• Nexus zkVM 3.0 Specification

SP1

• SP1 V4 Turbo: Memory Argument via Elliptic Curve based Multiset Hashing
• Succint Network: Prove the World's software

Risc Zero

• RISC Zero zkVM: Scalable, Transparent Arguments of RISC-V Integrity

EDEN

• EDEN

resources

• Projects That Shaped Modern zkVMs (Part 1)
• a zero-knowledge paradigm series
• cairo – a turing-complete stark-friendly cpu architecture - shahar papini
• lasso + jolt playlist
• new paradigm in ethereum l2 scaling: multi-proving and zk-vms
• the nexus v1.0 zkvm - daniel marin (nexus)
• understanding jolt: clarifications and reflections
• zk whiteboard sessions – module seven: zero knowledge virtual machines (zkvm) with grjte
• zk10: analysis of zkvm designs - wei dai & terry chung
• zk11: o1vm: building a real-world zkvm for mips - danny willems
• zk12: memory checking in ivc-based zkvm - jens groth
• zk7: miden vm: a stark-friendly vm for blockchains - bobbin threadbare – polygon
• zeroing into zkvm
• zkvm design walkthrough with max and daniel
• Verification of zkWasm in Coq
• zk11: polynomial acceleration for stark vms
• what does risc v have to do with risc zero's zkvm
• risc zero architecture presentation @ stanford
• continuations: scaling in zkvm
• Getting the bugs out of SNARKs: The road ahead
• ~tacryt-socryp on Zorp, the Nock zkVM | Reassembly23
• Automatic Circuit Acceleration of Guest Programs
• Introducing Twist and Shout
• zkVM 系列课程 | Coset

tutorials / educational zkVM

• brainfuck tutorial
• chip0
• continuous read only memory constraints an implementation using lambdaworks
• fri from scratch
• stark by hand
• stark brainfuck
• stark 101
• stwo brainfuck
• useless zkvm
• Anatomy of a STARK

related tooling

• zkaleido
• zkRust
• any zkVM
• ere

related awesome lists

• awesome risc0
• awesome sp1
• awesome starknet #cryptography-and-maths
• awesome zkp
• awesome miden
• awesome plonky3
• awesome stwo