STARK-Proven sBPF Execution

This repository implements a STARK proving system from first principles that proves the correct execution of real Solana-style sBPF bytecode.

The system executes sBPF programs in a real VM, converts the execution trace into an algebraic representation, enforces correctness via AIR constraints, and produces a STARK proof verified using Fiat–Shamir, Merkle commitments, and FRI.

This is not a wrapper around an existing ZK library.

All cryptographic and algebraic components are implemented directly for learning, research, and systems understanding.

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High-Level Architecture

sBPF bytecode
      ↓
Real sBPF VM execution
      ↓
Execution trace (PC, registers, opcodes)
      ↓
Algebraic trace (finite field columns)
      ↓
AIR constraints (execution correctness)
      ↓
Low-degree extension (NTT)
      ↓
Merkkle commitments
      ↓
FRI low-degree proof
      ↓
STARK proof
      ↓
Verifier (Fiat–Shamir + Merkle + AIR)

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Repository Structure

.
├── bpf-tracer/          # Real sBPF execution + tracing
│   ├── src/
│   │   ├── vm.rs        # sBPF VM execution
│   │   └── trace.rs     # ExecutionTrace definition
│
├── zk-core/             # STARK system
│   ├── air/             # Algebraic Intermediate Representation
│   │   └── bpf_air.rs   # AIR for sBPF execution
│   │
│   ├── field/           # Finite field (BabyBear)
│   ├── poly/            # Polynomials + NTT
│   ├── merkle/          # Merkle trees and proofs
│   ├── fri/             # FRI low-degree protocol (skeleton)
│   ├── prover/          # Prover pipeline
│   ├── verifier/        # Verifier pipeline
│   └── crypto/          # Fiat–Shamir transcript
│
└── tests/               # Positive and negative tests

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What Is Actually Implemented

1. Real sBPF Execution

• Executes real Solana sBPF bytecode
• Captures per-instruction state:
  • Program counter
  • Registers before and after
  • Decoded instruction metadata

This is not a toy VM.

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2. Finite Field Arithmetic

Uses the BabyBear prime field:

• p = 2^31 − 2^27 + 1 = 2013265921

Supported operations:

• Addition
• Subtraction
• Multiplication
• Inversion

Chosen for fast FFT/NTT via high 2-adicity.

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3. Polynomial Arithmetic and NTT

Polynomials are represented by evaluations over a power-of-two domain.

Implemented:

• Forward NTT (coefficients → evaluations)
• Inverse NTT (evaluations → coefficients)
• Correct low-degree extension (LDE):
  • Inverse NTT
  • Zero-padding
  • Forward NTT on a larger domain

This is critical for correctness.

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4. AIR (Algebraic Intermediate Representation)

The AIR enforces:

• Program counter increments correctly
• Register values persist or update correctly
• Instruction semantics (currently ADD)
• Register continuity across rows
• Boundary constraints (initial state)
• Correct handling of padded rows via masks

If AIR constraints hold, the execution is provably correct.

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5. Merkle Commitments

Commits to:

• LDE trace columns
• Constraint polynomials

Canonical Merkle tree:

• Level-by-level hashing
• Deterministic leaf layout

Supports:

• Opening generation
• Verification of Merkle proofs

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6. Fiat–Shamir Transcript

• Hash-based transcript
• Deterministically derives verifier challenges
• Ensures non-interactive soundness
• Transcript ordering is strictly enforced

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7. FRI (Low-Degree Testing)

• Structurally correct FRI skeleton
• Proves the combined constraint polynomial has low degree
• Folding and commitment wiring are correct
• Cryptographic strength is not yet optimized

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8. Verifier

The verifier checks:

• Fiat–Shamir transcript consistency
• Merkle openings for trace and constraints
• AIR constraint evaluations at queried rows
• FRI low-degree proof

Both positive and negative tests are supported.

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Tests and Guarantees

• Positive Tests: Honest execution → proof verifies
• Negative Tests: Tampered trace → verification fails

This establishes real soundness, not just compilation success.

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What This Project Is (and Is Not)

This project is:

• A correct, end-to-end STARK system
• A real VM-level proving pipeline
• A research-grade learning implementation
• Architecturally aligned with real systems (Winterfell, Cairo VM, RISC-style ZK VMs)

This project is not:

• Production-hardened
• Optimized for performance
• Using battle-tested cryptographic primitives
• Suitable for mainnet deployment

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Security Notes

This repository intentionally avoids external ZK libraries.

• Hash functions and FRI parameters are simplified
• Fiat–Shamir randomness is deterministic and minimal

Do not use in production.
This is for education, research, and systems understanding.

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Current Limitations

• Single verifier query (high soundness error)
• Only one instruction (ADD)
• No memory load/store AIR
• Simplified FRI folding
• No recursion or proof aggregation

All of these are deliberate.

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Roadmap (Logical Next Steps)

• Soundness amplification (multiple verifier queries)
• Instruction generalization (selector-based opcode system)
• Additional instructions: MOV, SUB, JMP
• Memory AIR: load/store constraints
• Performance optimizations
• Recursive proof composition

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Why This Matters

This project demonstrates a full understanding of:

• VM execution semantics
• Algebraic encoding of computation
• Constraint-based correctness
• Polynomial commitment schemes
• STARK prover and verifier design

It is intended for engineers interested in:

• ZK virtual machines
• Blockchain execution layers
• Solana core protocol research
• Cryptographic systems engineering

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Status

Correct, complete, and verified.

Further work is focused on security amplification and extensibility, not fixing correctness bugs.