Introduction to Zero-Knowledge Proofs
Published: 2023-02-06 08:41:07

A zero-knowledge proof ZKP is a method by which one party the `prover`  can authenticate to another party the `verifier` that a statement is true, without revealing any additional information beyond the fact that the statement is indeed true. In simpler terms, it means the ability to prove honest computation without inputs.

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> ZKPs == Honest computation


### Properties of Zero-Knowledge Proofs

There are three properties that are critical for ZKP to be considered and the combination of the three makes it useful in maintaining privacy, security, and sensitive information.
They are;

- **Completeness:** 
The `verifier` must be convinced of the statement's truth if the `prover` is indeed an honest authentication.

- **Soundness:** 
If the `prover` is cheating, the verifier should not be convinced of the statement's authentication therefore tends to fail the process of authentication.

- **Zero Knowledge:**
 If the statement is true, no `verifier` learns anything other than the fact that the statement is true and authentic.


### Types of Zero-Knowledge Proofs

There are several types of zero-knowledge proofs depending on the use case it’s needed, and here 
is a list of the popular ones and what they do:

1. **Interactive-proof-system:**

 The interactive proof system is a ZKP that allows the `prover` and `verifier` to engage in an interactive proof system in order to validate that the statement is true. i.e the `prover` sends the `verifier` an encrypted message and in return, the `verifier` sends messages to challenge the `prover`.

A real-life use case for an interactive proof system is in digital voting systems. 
In these systems, voters want to prove to the voting authority that they have cast their vote, without revealing their actual vote. The voting authority wants to be sure that the voters have cast their votes, without being able to see the vote itself.

An interactive proof system can be used to verify that the voters have cast their vote, without revealing the actual vote to the voting authority. Voters can generate proof that they have cast their vote, and send it to the voting authority. The voting authority can then verify the proof without seeing the actual vote. This way, the voter's privacy is protected, while the voting authority is able to ensure the integrity of the voting process.

**Non-Interactive-Proof-system:**

This is the process by which the `prover` generates proof that the `verifier` can verify without any interaction with the `prover`. This is useful when the `prover` and `verifier` are not active at the same time.

A real-life use case for a non-interactive proof system can be found in supply chain management where a producer and a consumer come into place. In this scenario, the producer wants to prove to the consumer that the product was made using sustainable materials without revealing the material used, On the other hand, the consumer wants to verify that the material used in the product is sustainable without having access to the producer supply-chain information.

A non-interactive proof system is used to create proof that the product is made from a sustainable material and attach it to the product. The consumer can then verify the proof without having to interact with the producer. This way, the manufacturer's supply chain information is protected, while the customer is able to verify the sustainability of the product.

**Succinct non-interactive arguments of knowledge (SNARKs):**

SNARKS are a type of ZKP that are succinct and non-interactive i.e They have small-size proofs. They’re widely used in blockchain technology and other decentralized systems, where the proof size needs to be small to allow for efficient verification.

An example can be seen in a secure multi-party computation, where different parties want to jointly compute a function, without revealing their inputs to each other.

SNARKs can be used to prove that the function was computed correctly, without revealing the inputs used. This way, the privacy of the parties' inputs is protected, while the accuracy of the computation is ensured.

4. **Proof of Knowledge (PoK):**

This is a type of ZKP that proves that the `prover` knows a secret without revealing the secret itself. PoKs are often used in secure authentication systems and digital signatures.

An example is when a user wants to deploy computations to a cloud provider without revealing the inputs used. SNARK  can be used to prove that the computations were performed correctly, without revealing the inputs. 

**Proof of Confidential Knowledge (PoCK):**
The PoCK is a type of ZKP that proves that the `prover`  knows a secret and the secret is encrypted.

An example can be found in the authentication of an online financial transaction.

A user wants to prove to a financial institution that they have the necessary knowledge to perform a transaction, without revealing the actual information.

When a user wants to transfer stock from their account, they need to prove that they know the correct account password. A PoCK can be used to prove that the user knows the password, without actually revealing the password. The financial institution can then verify the PoCK and confirm the authenticity of the user, without having access to the password.
    
### Advantages of Zero Knowledge

1. **Privacy-preserving:** ZKPs allows for the verification of information without revealing any additional details about the `prover's` secret, thus preserving their privacy and data.

2. **Secure verification:** ZKPs provide a secure process for verifying information, as the verifier can be sure that the `prover` knows the secret, without learning the secret themselves.
3. **Scalability:** ZKPs can be used to verify large amounts of data, making them suitable for use in decentralised systems and blockchain technology.

4. Flexibility: ZKPs can be used in a variety of contexts, such as secure identification, privacy-preserving transactions, and more.

5. **Non-interactive:** Some ZKPs are Non-interactive, which means that the `prover` and the `verifier` do not need to communicate with each other in order to complete the proof.


### Application of Zero-Knowledge Proofs

Zero-knowledge proofs have several potentials which include:

1. **Secure identification:** ZKPs can be used to verify a person's identity without revealing any additional information about their identity.

2. **Privacy-preserving transactions:** ZKPs can be used to verify transactions on a blockchain network while preserving the privacy of the transaction details.

3. **Secure voting systems:** ZKPs can be used to verify the validity of votes in a secure and private manner.

4. **Data privacy:** ZKPs can be used to protect sensitive information, such as medical records, financial information, and more.


### Conclusion

Zero-knowledge proofs are a powerful tool for maintaining the privacy and security of sensitive information, while still allowing for the verification of that information. With their ability to verify information without revealing any additional details, ZKPs have the potential to revolutionize many different areas, from secure identification to privacy-preserving transactions and more. As the use of ZKPs continues to grow, we can expect to see even more innovative applications of this technology in the future.