Blockchain Firm Certik Achieves Key Milestone, Demonstrating Comprehensive Formal Verification Is Feasible for Complex Zero Knowledge Circuits

Formal verification is a process that mathematically proves the correctness of a system, ensuring it “behaves exactly as intended under all defined conditions.” the CertiK team notes in a blog post.

CertiK explains that given the complexity and the high-stakes nature of blockchain technology, where flaws can lead “to significant financial losses or breaches of privacy, formal verification goes beyond traditional testing or auditing by providing a mathematical proof that certain properties of a program are correct, thereby eliminating a broad class of potential bugs and vulnerabilities.”

As mentioned in the update from CertiK, zero knowledge proofs (ZKPs) are “critical for scaling blockchain.”

The smart contracts of tomorrow “will run on advanced zero knowledge virtual machines (zkVMs), such as zkEVM for Ethereum contracts and zkWasm for Wasm contracts.”

This is a paradigm shift “from traditional VMs to those powered by ZKPs, accommodating a broader range of applications, such as gaming platforms and high-performance computing solutions.”

Certik reveals that it recently “achieved a significant milestone by completing the first full formal verification of a zkVM, the zkWasm circuits.”

According to CertiK, this breakthrough sets “a new standard in the industry, demonstrating that comprehensive formal verification is feasible for complex zero knowledge circuits.”

By ensuring that every zero knowledge proof verified corresponds uniquely and correctly to its intended smart contract execution, CertiK claims it is leading the way in “securing the next generation of blockchain applications.”

For ZKP-based applications, formal verification plays “a crucial role in addressing two principal classes of security and correctness concerns.”

CertiK also noted that the first class “involves verifying the correctness of zero knowledge circuits.”

This verification process ensures “that each zero knowledge proof accepted by a proof checker corresponds precisely to a single, licit transaction specific to that application.”

Since this type of verification is unique to each zero knowledge circuit, it is “typically tailored to specific applications.”

The second class focuses on “the correctness of the zero knowledge proof checker itself, including its underlying cryptography.”

This aspect of formal verification is universal “across applications, ensuring that the foundational components that validate proofs are reliable and function correctly.”

While both classes of formal verification are critical, the formal verification of zero knowledge circuits, “due to their application-specific nature, is an area of high demand and focus.”

CertiK says that it “prioritize this aspect of formal verification, addressing the nuanced and specific needs of zero knowledge circuits to ensure the highest level of security and correctness.”

For zkVM circuits, the actual smart contract code “that runs on the VM circuit also contributes to defining the transaction. FV of these smart contract code’s security and correctness is also highly desirable.”

This has been the case since blockchain and smart contract exist, and CertiK have “been a leader in doing these smart contract FVs in the past.”

Formal verification of ZKPs has been “conducted primarily on application-specific circuits, such as those used for token transfers.”

These efforts should not “be underestimated in terms of complexity.”

However, when it comes to zkVM circuits—used within “more generalized virtual machines like those handling smart contracts—the challenges increase dramatically.”

The inherent complexity of these zkVM circuits, “compounded by the vast size and dynamic nature of the smart contract executions they support, has made their complete formal verification an elusive goal.”

Until recently, no complete formal verification of “a zkVM circuit for an operational blockchain had been successfully demonstrated.”

The daunting nature of this task often led researchers “to limit their formal verification efforts to very small and partial subsets of the zkVM, tackling the easier pieces of the technology before attempting more comprehensive verification.”

CertiK achieved a significant milestone by “conducting the full formal verification of zkWasm circuits based on their Rust implementation.”

This achievement reportedly marks “the world’s first complete formal verification of any zkVM implementation.”

Their verification process ensured that “each zero knowledge proof validated by the zkWasm proof checker was uniquely associated with a corresponding smart contract execution on the zkWasm VM.”

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