Zero Knowledge Proofs: Exploring Cryptographic Privacy and Validity

Zero knowledge proofs are a cryptographic method that allows one party (the prover) to prove to another party (the verifier) that they possess certain information without revealing what that information is. The prover can essentially say “I know x” without conveying any information aside from the fact that they know x.

This is done through mathematical algorithms that leverage complex cryptography. A simple example is proving you know a secret password without actually divulging the password itself. Zero knowledge proofs have become an important concept in blockchain technology and cryptocurrencies.

Properties of Zero Knowledge Proofs

• Privacy - No information about the secret data is exposed other than its existence.
• Validity - Proofs can be repeatedly verified and validated.
• Efficiency - They require few resources to compute, often simpler than executing the actual algorithm.
• Non-interactivity - The prover and verifier do not need to interact extensively.

These qualities make zero knowledge proofs highly useful in cryptographic systems for privacy and security. A real world analogy is providing proof of ID without revealing personal details.

Zero Knowledge Proof Examples

Here are two classic examples that demonstrate the “zero knowledge” aspect:

The Ali Baba Cave

Imagine a cave with a secret door that is opened by a password. Alice wants to prove to Bob that she knows the password without revealing the actual password. Here is how:

1. Alice goes into the cave and closes the door
2. Bob shouts a random password
3. Alice opens the door only if Bob shouted the correct password
4. By observing Alice opening the door at the right times, Bob can verify she knows the password without her sharing the actual password.

Graph 3-Coloring

Another common example uses math rather than a physical cave. Here Alice needs to prove a graph can be colored with 3 colors without revealing the actual coloring:

1. Alice colors the nodes on the graph with 3 colors (unknown to Bob)
2. Bob asks Alice to reveal a subset of the colored nodes
3. If the revealed nodes follow the correct 3-color pattern, this proves the whole graph is 3-colorable without exposing the full solution.

Zero knowledge proofs enable privacy-preserving verification of knowledge or truth in these ways.

ZKPs in Blockchain and Cryptocurrency

Zero knowledge proofs are now being adopted in blockchain networks and privacy-focused cryptocurrencies. Here are some potential uses:

Verifying Transactions

Provers (users) can show transactions are valid without revealing sensitive details about senders, receivers, or amounts. Preserves privacy.

Ensuring Minimum Account Balances

Users can prove their account balances exceed a certain amount to participate in staking or validation without exposing their actual holdings.

Providing Identity Credentials

Users can demonstrate they have required credentials like a degree or citizenship to access services while keeping personal info private.

Facilitating Private Transfers

Using zk-SNARKs, senders and receivers can be completely anonymous while still verifying transfers are valid on the blockchain.

Zero knowledge capabilities enhance user privacy, security, and control over data exposure in blockchain systems. Coins adopting zkPs include Zcash, Dash, PIVX, and ZCoin.

ZCash and zk-SNARKs

A major driver of zero knowledge proofs in blockchain is the cryptocurrency ZCash, which uses advanced zk-SNARKs (“Zero Knowledge Succinct Non-Interactive Arguments of Knowledge”). Here’s how ZCash leverages zk-SNARKs:

• Users have a public address and a secret spending key (private info)
• When transferring funds, users generate a proof using the spending key without revealing any account data
• Miners verify the proof is valid without learning any specifics of the transaction

This allows shielded transfers where transaction details are encrypted and unviewable on the blockchain. However, a valid proof confirms funds were transferred properly. ZCash calls these transfers "shielded" because the data is encrypted (or “shielded” from view).

zk-SNARKs enable this high degree of privacy. The “succinct” part means proofs are very small in size. The “non-interactive” part means users don’t need multiple rounds of communication to generate proofs. The technology mathematically guarantees validity without requiring transparency of the process.

How Zero Knowledge Ledger Works

Zero Knowledge Proofs for Anonymous Transactions

Here is how a zero knowledge cryptocurrency like ZCash handles anonymous shielded transactions under the hood using zk-SNARKs:

1. A randomized transaction is created, hiding sender/receiver and amount data.
2. The randomized transaction is used as input to build a zk-SNARK proof.
3. The proof attests the transaction is valid without revealing any specifics.
4. Miners verify the proof checks out without seeing the transaction details.
5. The anonymized, encrypted transaction and proof are added to the blockchain.

This allows private transfer of funds while still proving to the network that the transaction followed consensus rules. No oversight of actual account details is needed.

Scalability Benefits

Zero knowledge proofs also offer scalability and efficiency benefits for blockchains. Transaction validity can be proven without executing the full transaction, reducing computation load. Only small proof data is stored on chain instead of entire transactions.
For example, zkRollups bundle transactions off-chain and submit only compressed proofs to Ethereum. This effectively increases throughput. As zero knowledge proofs advance, they will likely expand privacy and scalability across many cryptocurrency projects.


Zero knowledge proofs enable verification of information without exposure, which has promising applications in blockchain and cryptocurrencies for privacy and efficiency. Coins like ZCash are using zk-SNARKs to enable anonymous transactions. As zero knowledge technology evolves, it could provide the ideal combination of privacy and accountability in the decentralized future.