In today’s digital systems, we face a growing tension: We need to prove things to one another — identity, correctness, compliance, truth — yet we don’t want to reveal everything in the process.
Traditional methods force us to over-share: a password to log in, a date of birth to prove eligibility, sensitive data to prove solvency. This creates risk, complexity, and a fragile dependence on trusted intermediaries.
Zero-knowledge proofs (ZKPs) offer a radical alternative. With ZKPs, you can prove that something is true without revealing why it’s true. It’s a shift in trust architecture: from trusting people or institutions, to trusting math.
At Nexus, we believe this shift is fundamental. ZKPs aren’t just cryptographic curiosities — they’re a new computing primitive. They enable a Verifiable Internet, where systems can prove their claims by construction. Our zkVM and execution stack are built on this idea: Verifiability isn’t an afterthought — it’s the operating principle.
What Is a zero-knowledge proof?
A zero-knowledge proof (ZKP) is a cryptographic method that allows one party (the prover) to demonstrate to another party (the verifier) that a certain statement is true, without conveying any additional information.
This sounds counterintuitive, but it’s powerful. For example, you can prove you know a password without revealing the password. Or show that you’re eligible to vote without revealing your identity. Or that a transaction is valid without revealing its amount. The verifier becomes convinced of the truth of the claim — but gains no knowledge beyond that.
This property is essential in systems where data privacy and integrity must coexist. ZKPs are non-interactive (in many modern forms), unfakeable, and non-transferrable — meaning they can’t be reused or faked. They make it possible to move from “trust me” to “verify me,” without sacrificing confidentiality.
A brief history of ZKPs
The foundations of zero-knowledge proofs were laid in 1985 by Shafi Goldwasser, Silvio Micali, and Charles Rackoff, who introduced the idea of interactive proofs and knowledge complexity.Their work demonstrated that it was possible to prove a mathematical claim without revealing the witness (i.e., the evidence behind the claim).
In 1986, the Fiat-Shamir heuristic proposed a transformation that made these proofs non-interactive by replacing verifier interaction with a cryptographic hash function. This breakthrough opened the door to scalable applications.
The 2010s saw a wave of practical implementations. zk-SNARKs (2011) introduced a way to create short, quickly verifiable proofs suitable for blockchains and privacy-preserving computation.
Bulletproofs (2017) removed the need for trusted setup while enabling compact range proofs.
zk-STARKs (2018) pushed further, offering transparency, scalability, and post-quantum resistance.
Each step in this evolution removed friction — either in trust assumptions, computational cost, or proof size — bringing ZKPs from theory to production-grade cryptographic infrastructure.
How ZKPs work
At a high level, a ZKP involves a prover generating a cryptographic proof that they possess certain knowledge, and a verifier checking that proof without learning anything beyond its correctness.
There are two primary classes:
Interactive ZKPs, where the verifier challenges the prover with random prompts, and
Non-interactive ZKPs, where a single message suffices (thanks to cryptographic hashing).
Modern zero-knowledge systems rely on a suite of deep cryptographic techniques — e.g., elliptic curve pairings, polynomial commitment schemes, and low-degree testing — combined with clever encoding of computations into constraint systems.
These mechanisms enforce three key guarantees:
Completeness: If the statement is true, an honest prover can convince the verifier.
Soundness: If the statement is false, no malicious prover can convince the verifier.
Zero-knowledge: The verifier learns nothing beyond the truth of the statement.
These properties underpin the shift from trusting authorities to trusting computation itself.
Listen to this episode of Exponential to learn more about how we use ZKPs to build the zkVM.
Where ZKPs are already working
Despite their complexity, ZKPs are not just research artifacts — they’re running in production today.
In privacy-focused cryptocurrencies like Zcash, ZKPs enable shielded transactions where values and addresses are hidden but still verifiable.
In decentralized identity systems like Polygon ID, users can prove things about themselves (age, citizenship, KYC compliance) without revealing sensitive documents. In voting systems like Semaphore, ZKPs allow users to cast votes anonymously while preserving verifiability and preventing double voting.
In DeFi, ZKPs are used to prove solvency, collateralization, or order validity without exposing full balance sheets or transaction details.
Platforms like Aztec andzkSync use zk-rollups to bundle and verify thousands of transactions off-chain, dramatically reducing cost and congestion while preserving Ethereum’s security guarantees.
These examples hint at a larger truth: ZKPs aren’t just about privacy—they’re about selective disclosure. The ability to prove just enough, and nothing more.
From ZKPs to zkVMs: Verifiability as a platform
While individual ZKPs are useful, the real transformation happens when you can prove entire programs — not just statements. This is where the Nexus zkVM comes in.
A zkVM (zero-knowledge virtual machine) is an execution environment that outputs a cryptographic proof of its own execution. Instead of saying “this transaction is valid,” a zkVM can say “this entire program ran correctly on this input, and here’s a proof.”
This unlocks a new category of applications:
Trustless bridges, where off-chain computation or cross-chain data can be proven before being accepted.
Verifiable AI, where model inferences can be validated without exposing data or weights.
Auditable infrastructure, where systems generate cryptographic attestations of what they’ve done, and what they haven't
At Nexus, the zkVM is at the core of our architecture. It allows us to define verifiable compute protocols that run anywhere, prove anything, and disclose only what’s necessary. It’s how we move from systems that are secure by policy to systems that are secure by proof.
Challenges and frontiers
Of course, ZKPs are not a silver bullet. They introduce non-trivial overhead. Proof generation can be slow, and some systems require trusted setups (though these are being phased out). Developers face steep learning curves due to complex tooling and cryptographic primitives.
Yet the ecosystem is maturing quickly. New languages likeNoir,Cairo, andLeo are making ZKP programming more accessible. Recursive proving and hardware acceleration are improving performance. And open-source proving systems likeHalo2,Plonky2, STWO are pushing proof generation into real-time territory.
Meanwhile, research into zkML, zero-knowledge machine learning, is accelerating — enabling AI outputs that can be verified without being reverse-engineered.
Why Nexus is building with zero-knowledge proofs
At Nexus, we see zero-knowledge not as a feature, but as a foundation.
Our mission is to build the Verifiable Internet — a world where trust comes not from brand or bureaucracy, but from proof. That requires new primitives, and the zkVM is one of the most important among them. It’s what allows arbitrary programs to be proven, interoperable protocols to be validated, and AI decisions to be audited without compromising data or privacy.
We’re investing in zero-knowledge because we believe the next internet won’t just be programmable — it will be provable.
Zero-knowledge proofs may have started as an academic curiosity. But today, they’re quietly transforming how we build trust online. They offer a path beyond surveillance, beyond blind trust, and beyond the limitations of legacy infrastructure.
Daniel McGlynn
