Fully Homomorphic Encryption and Zero Knowledge: Data security secrets

Illy’s Web3 blog
6 min readAug 26, 2023


In a recent conversation with Eiger, Aleo’s CEO, Alex Pruden, emphasized that the realm of advanced cryptography extends beyond just ZK. There are lesser-known yet powerful techniques like MPC and FULLY HOMOMORPHIC ENCRYPTION (FME). Let’s dive deep into FME topic today!

1. Introduction

1.1 Definition of Fully Homomorphic Encryption (FHE)

Fully Homomorphic Encryption (FHE) is an encryption method that allows computations to be performed on encrypted data without the need for prior decryption. This means that arithmetic operations or even more complex calculations can be carried out on data while maintaining their confidentiality. FHE represents a revolutionary approach in the field of cryptography, as it provides a high level of security when processing data.

1.2 Definition of Zero Knowledge (ZK)

Zero Knowledge (ZK) is a cryptographic protocol that allows one party to prove to another that it knows certain information without revealing the information itself. The essence of ZK is to prove knowledge of a secret without disclosing it. This is especially useful in situations where it is necessary to confirm authenticity or compliance with certain conditions without revealing confidential data.

2. Historical Context

2.1 Development of FHE

The idea of Fully Homomorphic Encryption was first proposed in 1978, but the first truly functional prototype was created only in 2009. Over these years, many scientists and researchers tried to create an efficient FHE algorithm but encountered numerous challenges. However, with the advancement of technology and mathematical methods, as well as thanks to the efforts of the community, FHE became a reality. Today, FHE is used in various applications, from cloud computing to medical research, ensuring a high level of data security.

2.2 Development of ZK

The concept of Zero Knowledge was first introduced in the 1980s. Since then, ZK has become the foundation for many cryptographic protocols and systems. The primary application of ZK is the creation of secure authentication systems where a user can prove their identity without revealing a password or other secret information. With the development of blockchain technologies and cryptocurrencies, ZK has found widespread use in creating private transactions and secure smart contracts.

3. Basic principles and mechanisms of FHE

3.1 How does FHE work?

FHE operates based on complex mathematical algorithms and principles. At the heart of FHE is the idea that data can be encrypted in such a way that calculations can then be performed directly on the encrypted data. The result of these calculations will also be encrypted, and upon decryption, it will match the result that would have been obtained by performing calculations on the original data. This is achieved through the use of special encryption algorithms and mathematical transformations.

3.2 Application of FHE

FHE is used in various fields where confidential data processing is required. For example, in medicine, FHE can be used to analyze medical data without disclosing it. In the financial sector, FHE can assist in conducting secure transactions and analyzing financial information without the risk of data leakage. FHE is also actively used in cloud computing to process data on third-party servers without revealing the original information.

4. Fundamental Principles and Mechanisms of Zero Knowledge

4.1 What is ZK

Zero Knowledge (ZK) is a cryptographic protocol that allows one party to prove to another party that they know certain information without revealing the information itself.

4.2 How does ZK work?

Zero-knowledge protocols typically involve two participants: the prover and the verifier. The prover tries to convince the verifier that they know certain information without revealing it. This is achieved through a series of mathematical challenges and responses. It’s important that the verifier cannot extract any specific information about what the prover actually knows from these challenges and responses.

For example, the prover can prove that they know the solution to a certain problem without revealing the solution itself. Instead, they can provide a mathematical proof that they have a solution, which the verifier can check without knowing the solution itself.

4.3 Applications of ZK

Zero-knowledge protocols are widely used in cryptography to ensure confidentiality and security. They can be used for authentication, secure key exchange, and even for creating cryptocurrencies that provide complete transaction anonymity.

5. Comparison of FHE and ZK

5.1 Similarities and Differences

Both FHE and ZK are cryptographic methods that allow data processing without revealing the original information. However, they operate on different principles. While FHE allows computations directly over encrypted data, ZK allows proving knowledge of information without revealing it.

5.2 Advantages and disadvantages of each approach

FHE has the advantage of allowing complex computations over encrypted data, which can be useful in cloud computing and other applications. However, it requires complex mathematical algorithms and can be computationally expensive.

ZK, on the other hand, is a lighter and faster method for proving knowledge of information. It can be used for authentication and other tasks where data processing is not required.

6. Joint use of FHE and ZK

The combined use of Fully Homomorphic Encryption (FHE) and Zero-Knowledge Protocols (ZKP) represents an advanced approach in the field of cryptography, which combines the advantages of both methods to create more secure and efficient systems. This approach ensures data confidentiality while simultaneously confirming its authenticity without disclosure.

6.1 Potential Applications

  • Secure cloud computing:

Using FHE for data encryption and ZK for verifying its correctness, computations can be securely performed in the cloud without disclosing the original data.

  • Electronic voting:

Combining FHE and ZK can ensure the confidentiality of a voter’s vote and simultaneously confirm that the vote was counted correctly.

  • Financial transactions:

In the financial sector, transaction confidentiality can be ensured, allowing parties to verify the correctness of operations without access to detailed information about them.

  • Medical diagnostics:

Patients can provide encrypted medical information for diagnosis, and medical institutions can confirm the accuracy of the diagnosis without access to the patient’s personal information.

6.2 Advantages of Joint Use

  • Enhanced Privacy:

Combining FHE and ZK provides the highest level of data protection, allowing users to maintain the confidentiality of their information even during processing.

  • Proof without disclosure:

ZK allows for the verification of information without the need to disclose it, which perfectly complements FHE’s ability to compute on encrypted data.

  • Flexibility and Scalability:

The joint use of FHE and ZK can be adapted for various applications, from simple operations to complex computations, ensuring efficient and secure data processing.

  • Risk Reduction:

Combining these technologies reduces the likelihood of data leakage or compromise, as an attacker needs to overcome both layers of protection to access the information.

In conclusion, the joint use of FHE and ZK opens up new horizons in the field of cryptographic security, providing tools for creating more reliable and efficient systems

7. Practical examples and case studies

7.1 Examples of FHE in real life:

Fully Homomorphic Encryption (FHE) is becoming an increasingly popular tool in the field of cybersecurity. One of the most well-known examples of its use is cloud computing. Companies such as Google and Microsoft have already begun integrating FHE into their cloud services to ensure the secure storage and processing of client data without revealing its content. Another example is the medical industry, where FHE can be used to analyze patient medical data without violating their privacy.

7.2 Examples of ZK in real life:

Zero-Knowledge Proof (ZK) has found widespread use in the cryptocurrency sector. One of the most well-known examples is the cryptocurrency Zcash, which uses ZK to ensure transaction anonymity. Additionally, ZK can be used in electronic voting systems to confirm the legitimacy of a vote without revealing the voter’s actual choice.

8. Future of FHE and ZK
8.1 Current research and development:

At the moment, active work is being done on the optimization and improvement of FHE and ZK algorithms. Scientists and engineers around the world are working on creating faster and more efficient encryption methods that could be integrated into everyday applications and services.

8.2 Potential changes and innovations:

It is expected that in the coming years new methods and technologies based on FHE and ZK will emerge. These innovations can radically change the approach to data processing and storage, making it even more secure and confidential.

9. Conclusion
9.1 Summary of the main points of the article:

The article discussed the basic principles and advantages of FHE and ZK, as well as practical examples of their use. These technologies represent promising directions in the field of cybersecurity and cryptography.

9.2 Conclusions and recommendations:

FHE and ZK provide powerful tools for ensuring data confidentiality and security. It is recommended to keep an eye on new research and developments in this area to stay updated on the latest innovations and trends.

Stay curious, keep learning, and delve deeper into the Aleo ecosystem — the journey is just beginning. Join the community here: