Editing Zero-knowledge proof (section)

== Security vulnerabilities of zero-knowledge systems ==
While zero-knowledge proofs offer a secure way to verify information, the arithmetic circuits that implement them must be carefully designed. If these circuits lack sufficient constraints, they may introduce subtle yet critical security vulnerabilities.

One of the most common classes of vulnerabilities in these systems is under-constrained logic, where insufficient constraints allow a malicious prover to produce a proof for an incorrect statement that still passes verification. A 2024 systematization of known attacks found that approximately 96% of documented circuit-layer bugs in SNARK-based systems were due to under-constrained circuits.<ref>{{cite book |first1=Stefanos |last1=Chaliasos |first2=Jens |last2=Ernstberger |first3=David |last3=Theodore |first4=David |last4=Wong |first5=Mohammad |last5=Jahanara |first6=Benjamin |last6=Livshits |chapter=SoK: What Don't We Know? Understanding Security Vulnerabilities in SNARKs |title=SEC '24: Proceedings of the 33rd USENIX Conference on Security Symposium |pages=3855–3872 |year=2024 |arxiv=2402.15293 |isbn=978-1-939133-44-1 |chapter-url=https://dl.acm.org/doi/10.5555/3698900.3699116}}</ref>

These vulnerabilities often arise during the translation of high-level logic into low-level constraint systems, particularly when using domain-specific languages such as Circom or Gnark. Recent research has demonstrated that formally proving determinism – ensuring that a circuit's outputs are uniquely determined by its inputs – can eliminate entire classes of these vulnerabilities.<ref>{{cite journal | doi=10.1145/3591282 |doi-access=free | title=Automated Detection of Under-Constrained Circuits in Zero-Knowledge Proofs | date=2023 | last1=Pailoor | first1=Shankara | last2=Chen | first2=Yanju | last3=Wang | first3=Franklyn | last4=Rodríguez | first4=Clara | last5=Van Geffen | first5=Jacob | last6=Morton | first6=Jason | last7=Chu | first7=Michael | last8=Gu | first8=Brian | last9=Feng | first9=Yu | last10=Dillig | first10=Işıl | journal=Proceedings of the ACM on Programming Languages | volume=7 | pages=1510–1532 }}</ref>