Zero-Knowledge Proofs (ZK): The Key Technology Behind Privacy and Scaling

A zero-knowledge proof (ZKP or ZK) is a cryptographic method that allows a prover to convince a verifier that a statement is true without revealing any information beyond the fact that "the statement is true." Originally developed for cryptography and privacy protection, this technology has in recent years been widely applied to blockchain scaling (via zkRollups) and privacy (private transactions, identity verification). It is considered one of the most important directions in blockchain technology today.

1. Basic Concepts of Zero-Knowledge Proofs

1.1 Intuitive Understanding

A classic analogy is "Ali Baba's Cave":

Imagine a circular cave with a door in the middle that can only be opened with a secret password. Alice wants to prove to Bob that she knows the password without telling him what it is:

1. Bob stands at the cave entrance
2. Alice randomly chooses to enter from the left or right side
3. Bob randomly calls out "come out from the left" or "come out from the right"
4. If Alice truly knows the password, she can always exit from whichever side Bob calls
5. After many repetitions, Bob is almost certain that Alice knows the password — yet he learns nothing about what the password actually is

1.2 The Three Core Properties of ZKP

Property	Description
Completeness	If the statement is true, an honest prover can always convince the verifier
Soundness	If the statement is false, a dishonest prover almost certainly cannot fool the verifier
Zero-Knowledge	The verifier learns nothing beyond the fact that the statement is true

1.3 Interactive vs Non-Interactive

Interactive zero-knowledge proofs: The prover and verifier require multiple rounds of communication.

Non-interactive zero-knowledge proofs (NIZK): The prover generates a single proof that the verifier can verify independently, without any back-and-forth. Blockchain applications primarily use non-interactive ZKP, because the proof must be submitted on-chain and verified by a smart contract.

2. Major ZK Proof Systems

2.1 ZK-SNARK

ZK-SNARK (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge) is currently the most widely used ZK proof system.

Core characteristics:

Feature	Description
Succinct	Proof size is small (a few hundred bytes) and verification is fast
Non-Interactive	Proof is generated once; no multi-round interaction needed
Argument of Knowledge	Provides cryptographic guarantees of computational correctness

Technical flow:

1. The computation problem is converted into an arithmetic circuit
2. The circuit is translated into a polynomial constraint system (R1CS)
3. A polynomial commitment scheme is used to generate the proof
4. The verifier checks the proof using elliptic curve pairing operations

Trusted Setup: Traditional ZK-SNARKs (such as Groth16) require a one-time trusted setup ceremony to generate public parameters. If the "toxic waste" from the setup is not properly destroyed, an attacker could forge proofs. Multi-party computation ceremonies (such as Zcash's Powers of Tau) are used to reduce this risk.

Representative projects: Zcash, Tornado Cash (now sanctioned), some zkRollups

2.2 ZK-STARK

ZK-STARK (Zero-Knowledge Scalable Transparent Argument of Knowledge) was developed by the StarkWare team.

Key differences from ZK-SNARK:

Dimension	ZK-SNARK	ZK-STARK
Trusted setup	Required (traditional schemes)	Not required (transparent setup)
Proof size	Small (~hundreds of bytes)	Larger (~tens of KB)
Verification time	Fast	Slightly slower
Proof generation	Slower	Better scalability
Post-quantum security	No (relies on elliptic curves)	Yes (based on hash functions)
Mathematical basis	Elliptic curve cryptography	Hash functions and polynomials

Advantages:

• No trusted setup required — eliminates the trust assumption in the parameter generation phase
• Post-quantum secure
• More efficient for proofs involving large-scale computation

Representative projects: StarkNet, StarkEx

2.3 PLONK and Other Universal Schemes

PLONK: A universal ZK-SNARK scheme that requires only a single "universal and updateable" trusted setup, which can then be used for any circuit.

Halo2: A recursive zero-knowledge proof system developed by the Zcash team that requires no trusted setup at all. Used by Polygon zkEVM and Scroll.

KZG commitments: An efficient polynomial commitment scheme used in Ethereum's EIP-4844 (Proto-Danksharding).

3. ZK in Blockchain Scaling

3.1 ZK Rollup

ZK Rollup is currently the most anticipated Layer 2 scaling solution. The core idea is: execute a large number of transactions off-chain, generate a ZK proof certifying the correctness of all executions, then submit the compressed transaction data along with the proof to Ethereum.

Workflow:

1. A sequencer collects user transactions
2. Transactions are executed in batches off-chain
3. A ZK proof is generated to certify the correctness of the state transition
4. Transaction data and the proof are submitted to Ethereum L1
5. The L1 contract verifies the proof and confirms the state update

Advantages:

• Mathematically guaranteed security (no fraud-proof challenge period required)
• Fast withdrawals (confirmed immediately after proof verification)
• High data compression efficiency

3.2 zkEVM

A zkEVM is a ZK Rollup that is compatible with the Ethereum Virtual Machine (EVM). It allows developers to migrate Ethereum smart contracts and developer tooling directly to a ZK Rollup.

zkEVM types (per Vitalik's classification):

Type	Compatibility	Proof Efficiency	Representative
Type 1	Fully equivalent to Ethereum	Slowest proof generation	(Theoretical goal)
Type 2	EVM-equivalent but not Ethereum-equivalent	Slower	Scroll, Polygon zkEVM
Type 2.5	Mostly compatible, different gas metering	Medium	—
Type 3	Nearly compatible, minor differences	Faster	—
Type 4	Language-level compatible (not EVM bytecode)	Fastest	zkSync Era, StarkNet

Major zkEVM projects:

• zkSync Era: Type 4 zkEVM using the LLVM compilation framework, supporting Solidity and Vyper
• StarkNet: Uses the Cairo language and STARK proof system; not directly EVM-compatible but provides developer tooling
• Polygon zkEVM: Aims for Type 2 EVM equivalence
• Scroll: A community-driven Type 2 zkEVM
• Linea: A zkEVM developed by ConsenSys

3.3 Validium and Volition

• Validium: Uses ZK proofs to guarantee computational correctness, but stores data off-chain. Suitable for use cases sensitive to data costs, such as gaming.
• Volition: Users can choose whether to store data on-chain (Rollup mode) or off-chain (Validium mode).

4. ZK in Privacy Protection

4.1 Private Transactions

ZK technology can verify the validity of a transaction without revealing the transaction amounts or participants:

• Zcash: Uses ZK-SNARKs to enable optional private transactions (shielded transactions)
• Tornado Cash: An Ethereum privacy mixing protocol (now under US sanctions)

4.2 Private Identity Verification

Users can prove they meet certain conditions (such as being over 18 or holding a particular country's passport) without revealing their specific personal information.

• Worldcoin: Uses ZK proofs to verify a user's uniqueness (via iris scanning) while protecting privacy
• Polygon ID: A ZK-based decentralized identity verification solution

4.3 ZK Machine Learning (ZKML)

Using ZK proofs to verify the correctness of machine learning inference — proving that an inference result is accurate without exposing the model parameters or input data. This is an emerging research direction.

5. Challenges Facing ZK Technology

5.1 Computational Cost

Generating ZK proofs requires enormous computational resources. For complex computations (such as zkEVM execution), proof generation can take minutes to tens of minutes.

Mitigation approaches:

• Hardware acceleration (GPUs, FPGAs, ASIC provers)
• Proof parallelization
• Recursive proofs (aggregating multiple small proofs into one)

5.2 Development Complexity

Writing ZK circuits is far more complex than writing ordinary programs. Although zkEVMs lower the barrier for application developers, the underlying ZK engineering still requires deep cryptographic and mathematical expertise.

5.3 Audit Difficulty

The cryptographic implementations in ZK systems are extraordinarily complex, making auditing and verifying their correctness an enormous challenge. Security vulnerabilities may hide in mathematical proofs or implementation details.

5.4 Lack of Standardization

Different ZK proof systems use different technology stacks and tools, and there is a lack of unified standards and interoperability.

6. ZK Technology Development Trends

6.1 Accelerating Proof Generation

• Decentralized proving networks: Multiple provers collaboratively generate proofs (e.g., Gevulot, Succinct)
• ASIC provers: Dedicated hardware dramatically accelerates proof generation
• Recursion and aggregation: Compressing large numbers of proofs into a single proof

6.2 Generalized zkVMs

Moving from circuits designed for specific computations to general-purpose virtual machines (e.g., RISC Zero's zkRISC-V, SP1), enabling any program to be ZK-proven.

6.3 Proof Markets

Building market mechanisms for proof generation, where users pay specialized provers to generate proofs on their behalf.

6.4 Cross-Chain ZK Verification

Using ZK proofs to verify the state of another chain is the most secure cross-chain verification method.

6.5 Balancing Privacy and Compliance

Developing ZK solutions that both protect user privacy and satisfy regulatory requirements (e.g., selective disclosure, compliant privacy pools).

7. ZK's Place in the Ethereum Roadmap

Vitalik Buterin has identified ZK technology as central to Ethereum's long-term roadmap:

• The Verge: Introducing ZK verification into Ethereum itself, allowing nodes to quickly sync and verify the chain's state via ZK proofs
• ZK-EVM as an Ethereum upgrade: The long-term goal of making Ethereum's own execution layer ZK-provable
• Data availability: EIP-4844 and future full Danksharding provide cheap data space for ZK Rollups

Summary

Zero-knowledge proofs are one of the most impactful breakthroughs in cryptography. Their applications in blockchain span three major domains: scaling (zkRollup), privacy (private transactions, identity verification), and interoperability (cross-chain verification). Despite challenges around computational cost, development complexity, and audit difficulty, ZK technology's unique advantages in security and efficiency make it a core direction in blockchain evolution.

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