What is Homomorphic Encryption?

What is Homomorphic Encryption?

Homomorphic Encryption (HE) is an advanced form of encryption that allows computations to be performed on encrypted data without ever decrypting it. The result of the computation, once decrypted, matches the output as if the operations were performed on the raw, unencrypted data.

In simpler terms: you can run mathematical operations on encrypted information while keeping it private and secure. This makes it a powerful tool for data security, especially in environments where sensitive information needs to be processed by third parties.

A Brief History of Homomorphic Encryption

  • 1978 – Rivest, Adleman, Dertouzos (RAD paper): The concept was first introduced in their work on “Privacy Homomorphisms,” which explored how encryption schemes could support computations on ciphertexts.
  • 1982–2000s – Partial Homomorphism: Several encryption schemes were developed that supported only one type of operation (either addition or multiplication). Examples include RSA (multiplicative homomorphism) and Paillier (additive homomorphism).
  • 2009 – Breakthrough: Craig Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme as part of his PhD thesis. This was a landmark moment, proving that it was mathematically possible to support arbitrary computations on encrypted data.
  • 2010s–Present – Improvements: Since Gentry’s breakthrough, researchers and companies (e.g., IBM, Microsoft, Google) have been working on making FHE more practical by improving performance and reducing computational overhead.

How Does Homomorphic Encryption Work?

At a high level, HE schemes use mathematical structures (like lattices, polynomials, or number theory concepts) to allow algebraic operations directly on ciphertexts.

  1. Encryption: Plaintext data is encrypted using a special homomorphic encryption scheme.
  2. Computation on Encrypted Data: Mathematical operations (addition, multiplication, etc.) are performed directly on the ciphertext.
  3. Decryption: The encrypted result is decrypted, yielding the same result as if the operations were performed on plaintext.

For example:

  • Suppose you encrypt numbers 4 and 5.
  • The server adds the encrypted values without knowing the actual numbers.
  • When you decrypt the result, you get 9.

This ensures that sensitive data remains secure during computation.

Variations of Homomorphic Encryption

There are different types of HE based on the level of operations supported:

  1. Partially Homomorphic Encryption (PHE): Supports only one operation (e.g., RSA supports multiplication, Paillier supports addition).
  2. Somewhat Homomorphic Encryption (SHE): Supports both addition and multiplication, but only for a limited number of operations before noise makes the ciphertext unusable.
  3. Fully Homomorphic Encryption (FHE): Supports unlimited operations of both addition and multiplication. This is the “holy grail” of HE but is computationally expensive.

Benefits of Homomorphic Encryption

  • Privacy Preservation: Data remains encrypted even during processing.
  • Enhanced Security: Third parties (e.g., cloud providers) can compute on data without accessing the raw information.
  • Regulatory Compliance: Helps organizations comply with privacy laws (HIPAA, GDPR) by securing sensitive data such as health or financial records.
  • Collaboration: Enables secure multi-party computation where organizations can jointly analyze data without exposing raw datasets.

Why and How Should We Use It?

We should use HE in cases where data confidentiality and secure computation are equally important. Traditional encryption secures data at rest and in transit, but HE secures data while in use.

Implementation steps include:

  1. Choosing a suitable library or framework (e.g., Microsoft SEAL, IBM HELib, PALISADE).
  2. Identifying use cases where sensitive computations are required (e.g., health analytics, secure financial transactions).
  3. Integrating HE into existing software through APIs or SDKs provided by these libraries.

Real World Examples of Homomorphic Encryption

  • Healthcare: Hospitals can encrypt patient data and send it to cloud servers for analysis (like predicting disease risks) without exposing sensitive medical records.
  • Finance: Banks can run fraud detection models on encrypted transaction data, ensuring privacy of customer information.
  • Machine Learning: Encrypted datasets can be used to train machine learning models securely, protecting training data from leaks.
  • Government & Defense: Classified information can be processed securely by contractors without disclosing the underlying sensitive details.

Integrating Homomorphic Encryption into Software Development

  1. Assess the Need: Determine if your application processes sensitive data that requires computation by third parties.
  2. Select an HE Library: Popular libraries include SEAL (Microsoft), HELib (IBM), and PALISADE (open-source).
  3. Design for Performance: HE is still computationally heavy; plan your architecture with efficient algorithms and selective encryption.
  4. Testing & Validation: Run test scenarios to validate that encrypted computations produce correct results.
  5. Deployment: Deploy as part of your microservices or cloud architecture, ensuring encrypted workflows where required.

Conclusion

Homomorphic Encryption is a game-changer in modern cryptography. While still in its early stages of practical adoption due to performance challenges, it provides a new paradigm of data security: protecting information not only at rest and in transit, but also during computation.

As the technology matures, more industries will adopt it to balance data utility with data privacy—a crucial requirement in today’s digital landscape.