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Last updated on 2024年5月15日

How can you learn more about homomorphic encryption and its applications?

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Homomorphic encryption is a fascinating and powerful technique that allows you to perform computations on encrypted data without decrypting it first. This can have many applications in fields like cloud computing, machine learning, healthcare, and finance, where you want to protect the privacy and security of your data while still benefiting from the services of third parties. But how can you learn more about homomorphic encryption and its applications? Here are some suggestions to help you get started.

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Sunil Vanmullem

solutions architect focussed on customer success
Amir Reza Nazarizadeh

Sr. Security Engineer, DevSecOps @ Snapp! | PhD Candidate

1 Basics and history

Homomorphic encryption is based on the idea that some mathematical operations can be performed on encrypted data in such a way that the result is the same as if they were performed on the original data. For example, if you add two encrypted numbers, you get the same result as if you added the plain numbers and then encrypted them. This property is called homomorphism, and it can be applied to different kinds of operations, such as addition, multiplication, or even more complex functions. The concept of homomorphic encryption was first proposed by Rivest, Adleman, and Dertouzos in 1978, but it took decades to develop practical and efficient schemes that could support more than one operation.

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2 Types and challenges

There are different types of homomorphic encryption schemes, depending on how many and which operations they support. The simplest ones are called partially homomorphic encryption (PHE), which only support one operation, such as addition or multiplication. For example, the RSA cryptosystem is partially homomorphic with respect to multiplication. A more advanced type is called somewhat homomorphic encryption (SHE), which supports multiple operations, but with some limitations on the number or complexity of the computations. For example, the BGV scheme can handle both addition and multiplication, but it introduces some noise in the encrypted data that grows with each operation and eventually makes it unreadable. The most powerful and desirable type is called fully homomorphic encryption (FHE), which supports unlimited operations without compromising the security or accuracy of the encrypted data. However, FHE is also the most challenging to achieve, as it requires overcoming several technical and theoretical obstacles, such as efficiency, bootstrapping, and circuit complexity.

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3 Resources and tutorials

If you want to learn more about homomorphic encryption and its applications, there are many resources and tutorials available online that can help you understand the concepts and techniques behind it. For example, you can watch some videos from experts and researchers who explain the basics and the state of the art of homomorphic encryption, such as this one by Craig Gentry, who proposed the first FHE scheme in 2009. You can also read some books or papers that provide a more detailed and rigorous introduction to the theory and practice of homomorphic encryption, such as this one by Pascal Paillier, who designed a widely used PHE scheme based on addition. You can also try some online courses or workshops that offer hands-on exercises and demonstrations of homomorphic encryption, such as this one by IBM Research, which uses a Python library called HElib to implement various applications of SHE and FHE.

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Sunil Vanmullem

solutions architect focussed on customer success
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The link to Craig's dissertation at Stanford University Department of Computer Science: https://crypto.stanford.edu/craig/craig-thesis.pdf A youtube link to the recording of a meeting about fully homomorphic encryption by Pascal Paillier: https://www.youtube.com/watch?v=aruz58RarVA

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4 Applications and use cases

Homomorphic encryption has many potential applications and use cases in various domains that require privacy-preserving computations on sensitive data. For example, you can use homomorphic encryption to outsource your data analysis or machine learning tasks to a cloud service provider without revealing your data or your queries. You can also use homomorphic encryption to enable secure multi-party computation, where different parties can collaborate on a joint computation without disclosing their inputs or outputs. You can also use homomorphic encryption to enhance the security and efficiency of cryptographic protocols, such as digital signatures, zero-knowledge proofs, or verifiable computation. Some examples of real-world applications of homomorphic encryption include encrypted search engines, encrypted genomic analysis, encrypted face recognition, and encrypted credit scoring.

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Amir Reza Nazarizadeh

Sr. Security Engineer, DevSecOps @ Snapp! | PhD Candidate
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Data breach in a cyber attack is mainly done by accessing the target database. Now, if the database can be encrypted, when a security incident occurs, the data cannot be exploited by threat actors. But the data in the database is often used for operations such as data analysis that involve calculations. Also, applications need this data to function. But if the database is encrypted, it is necessary to be able to perform these calculations on encrypted data so that the results are exactly the same as the results of calculations on plain data. In this case, Homomorphic Encryption(HE) can solve the problem. In this case, in addition to maintaining privacy, it is possible to prevent data breaches during a security incident.

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5 Limitations and trade-offs

Homomorphic encryption is not a magic bullet that can solve all the problems of data privacy and security. It has some limitations and trade-offs that you need to be aware of before using it. For instance, homomorphic encryption is still computationally expensive and requires more resources and time than conventional encryption. It also introduces some overhead and complexity in the data representation and the encryption scheme. It also depends on some assumptions and parameters that may affect its security and performance. It also faces some legal and ethical challenges that may limit its adoption and acceptance. Therefore, you need to carefully evaluate the costs and benefits of using homomorphic encryption for your specific scenario and purpose.

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Amir Reza Nazarizadeh

Sr. Security Engineer, DevSecOps @ Snapp! | PhD Candidate
(已编辑)
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Often, when talking about Homomorphic Encryption(HE), the first thing that comes to mind is efficiency and speed. One thing that affects the performance of HE is the operation on the ciphertext generated by HE, which is significantly larger than the plaintext. Also, the transmission of these ciphertexts affects the efficiency of the communication link. But another important point is the verifiable computing. HE does not inherently provide verifiable computing. Currently, such cases have made it impossible or very difficult to use HE in practice, especially on a large scale, but it seems that the potential of HE can be used in practice in the future with continuous research and more efficient algorithms.

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6 Future and trends

Homomorphic encryption is a rapidly evolving and exciting field that has many opportunities and challenges for the future. Some of the current research directions and trends include improving the efficiency and scalability of homomorphic encryption schemes, developing new applications and use cases that leverage homomorphic encryption, exploring the connections and synergies between homomorphic encryption and other cryptographic techniques, such as differential privacy or secure multiparty computation, and addressing the social and regulatory implications of homomorphic encryption. If you are interested in following the latest developments and innovations in homomorphic encryption, you can check some online platforms and communities that share news and events related to homomorphic encryption, such as this one by Microsoft Research, which hosts an annual workshop on homomorphic encryption.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you learn more about homomorphic encryption and its applications?

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1 Basics and history

2 Types and challenges

3 Resources and tutorials

4 Applications and use cases

5 Limitations and trade-offs

6 Future and trends

7 Here’s what else to consider

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