Homomorphic encryption is a cryptographic technique that lets you perform computations on encrypted data without decrypting it first. In other words, it enables computations on sensitive information while it remains encrypted. It is vital for privacy and security when data needs to be processed or analyzed, but its raw form is sensitive and should not be exposed.

Did you know that the term “homomorphic” comes from the Greek words “homo,” meaning “same,” and “morphe,” meaning “form”? In the context of encryption, homomorphism is a property where you can perform certain functions on encrypted data, and when the result is decrypted, it is the same as if the operations were done to its unencrypted form.

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Homomorphic encryption is critical, especially in the digital age where online data theft abounds.

What Are the Main Types of Homomorphic Encryption?

Several homomorphic encryption schemes exist, each with its properties and use cases. The three main types, however, are:

  • Partially Homomorphic Encryption (PHE): This type allows you to perform only one type of operation (either addition or multiplication) on encrypted data.
  • Somewhat Homomorphic Encryption (SHE): This type allows you to perform limited addition and multiplication operations on encrypted data. As such, practical limitations apply to the number of operations you can do before the noise in the encrypted data makes further computations unreliable.
  • Fully Homomorphic Encryption (FHE): This type allows unlimited addition and multiplication operations on encrypted data. It is the most advanced form of homomorphic encryption but is generally more computationally intensive.

How Does Homomorphic Encryption Work?

Like other encryption schemes, homomorphic encryption starts with key generation. A user generates a pair of keys—a public key and a private key. The public key encrypts data, while the private key is kept secret and used for decryption. 

Next, the user encrypts the plaintext data using the public key. The resulting ciphertext appears as random data and reveals no information about the original content. 

The user then performs certain mathematical operations on the encrypted data using PHE, SHE, or FHE. 

After that, The user can decrypt the result using the private key, revealing the result of the computations in plaintext form. FHE requires reducing noise (produced when computations are performed on the data) to produce the correct decryption result.

Homomorphic Encryption Steps

What Are the Applications of Homomorphic Encryption?

Homomorphic encryption has several applications in various domains where privacy and security are critical concerns. Here are some notable applications.

  • Securing cloud computing: Homomorphic encryption lets users store their data in the cloud in encrypted form. A cloud service provider can perform computations on the encrypted data without decrypting it, ensuring the confidentiality of the sensitive information.
  • Preserving privacy during data analysis: In scenarios where multiple parties want to jointly analyze data without revealing its raw form, homomorphic encryption enables secure and private collaboration. Each party can encrypt its data, share it with others, and perform computations on the other entity’s encrypted data.
  • Securing computation outsourcing: Homomorphic encryption enables organizations to outsource computations to third-party service providers while keeping data confidential. The service provider can perform computations on the encrypted data without having access to the plaintext.
  • Preserving machine learning (ML) privacy: Homomorphic encryption is increasingly being explored in relation to ML, where models can be trained on encrypted data. It allows organizations to collaborate on building ML models without sharing the raw training data.
  • Securing healthcare data sharing: In healthcare, homomorphic encryption allows users to share patient data with healthcare providers or researchers securely. It enables collaborative research without compromising patient privacy.
  • Processing financial data: Homomorphic encryption in the financial sector lets users perform computations on encrypted data. It allows financial institutions to collaborate and analyze aggregated data without exposing sensitive customer information.
  • Securing multiparty computations: Homomorphic encryption is a key component in secure multiparty computation, where multiple parties want to compute a function over inputs while keeping them private jointly. Each party encrypts its input, and computations are performed on encrypted data.
  • Securing searches in encrypted databases: Homomorphic encryption allows you to perform secure searches on encrypted databases. Users can submit queries without revealing search details to the database owner.

While homomorphic encryption offers significant advantages in terms of privacy and security, it also comes with computational overhead. Performing operations on encrypted data is more resource-intensive than doing so on plaintext data.

Homomorphic encryption is crucial in processes that require utmost privacy and security. However, it is computationally expensive compared to using traditional encryption methods. As such, its performance overhead may be limiting its widespread adoption. Researchers are thus actively improving its efficiency and practicality for broader use.

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