Zero-Knowledge Proofs on Bitcoin: A Beginner's Guide

Imagine if Bitcoin transactions could be faster, cheaper, and require less data while still being 100% secure. That’s what Zero-Knowledge Proofs (ZKPs) could bring to Bitcoin.

For years, Bitcoin has been praised for its security and decentralization. However, as the network grows, it faces challenges like high fees, slow transactions, and the need for heavy resources to verify the blockchain.

‍In July 2024, BitcoinOS achieved a significant milestone by successfully verifying the first zero-knowledge proof (ZKP) on Bitcoin's mainnet. This advancement opens new possibilities for Bitcoin, enabling it to support decentralized applications without altering its core structure.

ZKPs could change all of that, helping Bitcoin scale better and, as a bonus, making transactions more private.

Let’s dive into what ZKPs are and how they could improve Bitcoin.

Let’s begin!

Why Zero-Knowledge Proofs Matter?

So, why are ZK proofs such a big deal? Here are just a few reasons:

Scalability

Bitcoin’s current design struggles with high transaction volumes. This leads to network congestion, higher fees, and slower processing times. ZKPs can help by making transactions much more efficient:

1. ‍ZK-Rollups: These combine thousands of transactions into a single proof, reducing the amount of data processed on-chain.‍
2. Lower Fees: With less data to handle, transactions become cheaper.‍
3. Faster Transactions: Fewer individual transactions mean quicker processing for everyone.

Using ZKPs, Bitcoin’s network could handle more transactions at lower costs—without changing its core structure.

Accessibility and Decentralization

Running a full Bitcoin node requires downloading and verifying the entire blockchain, which is a lot of work. With ZKPs, users could verify the network using small, simple proofs instead of gigabytes of data.

This makes it easier for more people to participate in the network, keeping Bitcoin decentralized and accessible.

Privacy

While scalability is the main focus for ZKPs on Bitcoin, they also offer an exciting bonus: privacy.

ZKPs allow you to prove that a transaction is valid without revealing any details, such as:

1. How much Bitcoin is being sent?
2. Who’s sending it or receiving it?

For example, if you’re making a private payment or conducting a sensitive transaction, ZKPs can keep your information secure while still proving to the network that the transaction is legitimate.

The Three Pillars of Zero-Knowledge Proofs

ZKPs are built on three fundamental principles, often called their "pillars." These pillars ensure that ZKPs function effectively, providing security, privacy, and trust in the cryptographic systems they support. Let’s explore each of these pillars in detail.

Completeness

Completeness ensures that an honest verifier can be convinced of its truth if a prover's claim is valid. This principle guarantees that legitimate proof will always demonstrate validity.

For Example; Imagine Alice wants to prove to Bob that she knows the solution to a puzzle. If Alice genuinely knows the answer, the proof she provides will convince Bob every time, without fail.

For Bitcoin:

1. A user can prove they have enough funds to complete a transaction without revealing their total wallet balance.
2. The proof validates the transaction without requiring additional details.

Soundness

Soundness ensures that if a prover’s claim is false, they cannot trick an honest verifier into believing it. This prevents malicious actors from fabricating evidence or manipulating outcomes.

For Example; Let’s say Alice doesn’t actually know the puzzle’s solution but tries to fake proof. Soundness guarantees that Bob, as the verifier, will identify her deception every time.

For Bitcoin:

1. A fraudulent user attempting to prove they own more Bitcoin than they actually do would fail, as the ZKP would expose inconsistencies.
2. This safeguards the network from fraud and maintains trust.

Zero-Knowledge

The cornerstone of ZKPs is zero-knowledge—the ability to prove the truth of a statement without revealing any additional information. This principle ensures privacy, making ZKPs a powerful tool for systems like Bitcoin, where confidentiality is critical.

For Example; Alice can prove to Bob that she knows the puzzle’s solution without actually revealing what the solution is. Bob is convinced, but he gains no insight into the specifics of the answer.

For Bitcoin:

1. A sender could prove they’ve sent 1 BTC to a recipient without revealing their wallet addresses or the transaction amount.
2. The network validates the transaction without compromising the privacy of its participants.

How do these pillars work together?

These three pillars—completeness, soundness, and zero-knowledge—operate in harmony to create a system that is secure, reliable, and private:

1. ‍Completeness ensures that valid proofs succeed.‍
2. Soundness protects against false claims.‍
3. Zero-knowledge guarantees confidentiality.

Types of Zero-Knowledge Proofs (ZKPs)

ZKPs come in various forms, each tailored to different use cases and levels of efficiency, scalability, and security. Broadly, ZKPs can be categorized into two main types, with several subtypes based on how they achieve their goals.

Let’s explore the most common types of ZKPs: Interactive Zero-Knowledge Proofs and Non-Interactive Zero-Knowledge Proofs.

Interactive Zero-Knowledge Proofs

Interactive ZKPs require ongoing communication between the prover and the verifier. The prover must repeatedly respond to challenges posed by the verifier to convince them of the truth of a statement.

For Example; Interactive proofs are used in secure computations where live communication is possible, such as online identity verification or authentication systems.

Non-Interactive Zero-Knowledge Proofs (NIZKs)

Non-interactive ZKPs allow the prover to generate a single proof that the verifier can validate without further interaction. This is more efficient and widely used in blockchain and cryptographic systems.

For Example; NIZKs are the backbone of blockchain applications like Bitcoin and Ethereum, as they allow for transaction validation without requiring live interaction.

ZK-SNARKs (Succinct Non-Interactive Arguments of Knowledge)

ZK-SNARKs are a type of non-interactive proof that is both succinct (small in size) and efficient (quick to verify).

Key Features:

• ‍Succinctness: Proofs are tiny, making them suitable for blockchains with limited storage capacity.‍
• Fast Verification: Verifiers can validate proofs almost instantly, even for complex statements.‍
• Scalability: Great for bundling multiple transactions into a single proof, such as in ZK-rollups.

For Example; ZK-SNARKs are widely used in privacy-focused cryptocurrencies like Zcash for shielding transaction details.

ZK-STARKs (Scalable Transparent Arguments of Knowledge)

ZK-STARKs are similar to ZK-SNARKs but prioritize transparency and scalability. They eliminate the need for a trusted setup, which is required in ZK-SNARKs.

Key Features:

• ‍No Trusted Setup: Enhances trustworthiness by removing reliance on external initializations.‍
• Transparency: All computations are verifiable without hidden parameters.‍
• High Scalability: STARKs can handle larger computations, making them suitable for complex systems.

For Example; ZK-STARKs are used in layer-2 scaling solutions like StarkNet to improve transaction throughput and scalability on blockchains.

Bulletproofs

Bulletproofs are compact and efficient ZKPs designed to verify range proofs. They don’t require a trusted setup, making them highly versatile for blockchain applications.

Key Features:

• ‍No Trusted Setup: Like ZK-STARKs, Bulletproofs avoid dependency on external initialization.‍
• Compact Size: Proofs are small and efficient, reducing the burden on storage and computation.

For Example; Bulletproofs are often used in cryptocurrency systems to hide transaction amounts while ensuring they fall within a valid range.

Comparison of ZKP Types

Which Type of ZKP Does Bitcoin Need?

For Bitcoin, ZK-SNARKs and Bulletproofs are particularly relevant:

1. ZK-SNARKs offer privacy and scalability for confidential transactions.
2. Bulletproofs efficiently validate transaction ranges without revealing sensitive data.

Each type of ZKP brings unique strengths, allowing developers to choose the best tool for enhancing Bitcoin’s privacy, scalability, and efficiency.

What's Next?

Zero-knowledge proofs (ZKPs) are paving the way for Bitcoin’s next evolution. Addressing scalability challenges enables faster, cheaper transactions and reduces the network's data load. With innovations like ZK-Rollups and Bulletproofs, Bitcoin can handle more transactions efficiently while remaining decentralized.

ZKPs are not just a technical upgrade—they’re a step toward making Bitcoin more accessible and scalable for everyone. Keep watching as this technology shapes the future of the Bitcoin network.

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This article is also published on txFusion Medium channel.

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