Homomorphic Encryption: Process Encrypted Data Without Decryption
Homomorphic encryption is a type of data security that lets users perform calculations on encrypted information without decrypting it first. This method keeps sensitive data private while allowing computations to take place. The system works by converting regular data into an encrypted format that maintains mathematical relationships.
Users can add, subtract, multiply, or analyze the encrypted data, and the results remain accurate when decrypted. This technology helps businesses, healthcare providers, and financial institutions process confidential information securely in cloud computing environments.
Companies use homomorphic encryption to protect customer data while still performing necessary operations and analytics.
Key Properties of Homomorphic Encryption
Homomorphic encryption schemes have some key properties that enable computation on encrypted data:
- Homomorphic addition: Adding two ciphertexts produces a third ciphertext that encrypts the sum of the plaintexts.
- Homomorphic multiplication: Multiplying two ciphertexts produces a third ciphertext that encrypts the product of the plaintexts.
- Format-preserving: Ciphertext keeps the same form as plaintext so computations can be carried out.
- Probabilistic encryption: The same plaintext doesn’t always produce the same ciphertext.
- Compact ciphertext: Ciphertext size is roughly the same as plaintext size.
These properties allow complex computations to be carried out through additions and multiplications directly on the encrypted data.
Why Homomorphic Encryption is Important
Homomorphic encryption enables computation on encrypted data, which was previously thought to be impossible. This brings several major advantages:
- Privacy: Computations can be carried out on sensitive data without accessing the underlying plaintext.
- Secure outsourcing: Data processing tasks can be outsourced without exposing data.
- Cloud computing: Enables computations in the cloud while data remains encrypted.
- Searchable encryption: Allows searches on encrypted data.
- Other applications: Useful for things like machine learning, statistics, etc.
Homomorphic encryption solves major privacy and security challenges associated with data processing and cloud outsourcing. It allows sensitive computations to be carried out while maintaining confidentiality.
Brief History of Homomorphic Encryption
The concept of homomorphic encryption schemes has been studied since the 1970s, but fully homomorphic encryption remained elusive for decades. Here’s a brief overview of the history:
- 1978: RSA public-key encryption proposed, allowing multiplication of encrypted data.
- 1996: First partially homomorphic encryption scheme proposed by Pascal Paillier.
- 2009: First fully homomorphic encryption scheme proposed by Craig Gentry.
- 2011-Present: Ongoing research to improve efficiency and applicability.
Partially vs. Fully Homomorphic Encryption
In 1978, RSA public-key encryption was proposed, enabling multiplication operations on encrypted data. However, early schemes could only handle either addition or multiplication alone, but not both. These “partially homomorphic” schemes paved the way for “fully homomorphic” encryption.
Partially homomorphic schemes:
- Can perform either addition or multiplication on encrypted data.
- But not both addition and multiplication together.
Fully homomorphic encryption:
- Enables both addition and multiplication operations.
- Allows arbitrary computations on encrypted data.
It wasn’t until 2009 that Craig Gentry proposed the first fully homomorphic encryption scheme that could handle both addition and multiplication operations. This opened the door to widespread adoption and research into homomorphic encryption.
How Does Homomorphic Encryption Work?
At a high level, homomorphic encryption works by transforming plaintext data into ciphertext that can be operated on directly. The ciphertext produces a result that matches computations done on the plaintext. When decrypted, the result is revealed.
Let’s break down the process step-by-step:
- Plaintext data is encrypted via the public key, transforming it into ciphertext.
- Computations are directly performed on the ciphertext.
- The computations produce a result ciphertext.
- The resulting ciphertext is decrypted via the secret key.
- The decrypted result matches the output of computations done on the plaintext data.
The computations work on the ciphertext because of the encryption algorithm’s special mathematical structure. Additions and multiplications on the ciphertext effectively implement additions and multiplications on the underlying plaintext numbers.
This structure is simplified, but it allows computing directly on the encrypted data while retaining the ability to decrypt the results.
Homomorphic Encryption Algorithms
Many homomorphic encryption algorithms have been proposed with different properties:
- RSA: Partial, allows multiplication but not addition.
- ElGamal: Partial, allows addition but not multiplication.
- Paillier: Partial, allow addition but not multiplication.
- BGN: Somewhat homomorphic, support limited additions and multiplications.
- GGH: Somewhat homomorphic based on lattices.
- BGV: Somewhat homomorphic based on lattices.
- FHEW: Fully homomorphic encryption.
- TFHE: Fast, fully homomorphic encryption.
Each scheme makes tradeoffs between the complexity of computations allowed versus encryption/decryption speed. Active research is still developing new and improved algorithms.
Implementation Challenges with Homomorphic Encryption
While homomorphic encryption offers groundbreaking capabilities, it also comes with some substantial challenges:
Performance Overhead
- Homomorphic encryption schemes are often computationally demanding.
- It can be millions of times slower compared to computations on plaintext.
- Requires significant processing overhead.
Encryption/Decryption Time
- Complex public key encryption algorithms require more time.
- Encryption and decryption may take up to several seconds, depending on the scheme.
Computational Limits
- Fully homomorphic encryption schemes have limits on the complexity of supported computations.
- Beyond a certain limit, the noise grows too large, and decryption fails.
Storage Expansion
- Ciphertexts tend to be much larger than plaintext.
- Storage requirements inflated by encryption.
Implementation Complexity
- Correctly implementing these cryptographic schemes is very challenging.
- Difficult to guard against side-channel attacks.
- Prone to implementation vulnerabilities if not careful.
Lack of Standardization
- No dominant standard encryption algorithm or implementation.
- Encrypted data portability issues between different schemes.
Continued research is seeking to improve the efficiency, applicability, and standardization of homomorphic encryption systems. But they remain complex and computationally heavy processes.
How to Implement Homomorphic Encryption
Here is a general outline for implementing homomorphic encryption in an application:
1. Select a Homomorphic Encryption Library
A number of homomorphic encryption libraries are available, such as:
- SEAL (Microsoft Research)
- HELib (HomomorphicEncryption.org)
- HElib (IBM)
- Palisade (Duality Technologies)
2. Generate Key Pairs
Use the library’s API to generate a public/private key pair. The public key will encrypt the data while the private key decrypts.
3. Encrypt Data
Encrypt the plaintext data via the public key into ciphertext. Make sure to save the ciphertext.
4. Execute Computations
Perform computations directly on the ciphertext as needed by the application.
5. Decrypt Results
Use the secret key to decrypt the computed ciphertext. It will reveal the result matching the plaintext computations.
6. Integrate the Library
Integrate the homomorphic encryption library into the broader application architecture. Orchestrate key management, encryption, computations, and decryption.
Proper integration and use of the cryptographic primitives require expertise. However, the libraries provide the core algorithms to enable homomorphic encryption.
Comparison of Homomorphic Encryption Libraries
Here is an overview of some leading open-source homomorphic encryption libraries:
Microsoft SEAL
- Developed by Microsoft Research.
- Supports BGV and BFV encryption schemes.
- Written in C++ with .NET & Python wrappers.
- Mature library with optimizations.
- Can integrate with TensorFlow and PyTorch.
HElib (IBM)
- Developed by IBM.
- Implements BGV encryption.
- Written in C++ with Python bindings.
- High-performance parallel implementation.
- Supports GPU acceleration.
Palisade (Duality Technologies)
- Developed by Duality Technologies.
- Supports BFV, CKKS, and other schemes.
- Written in C++ and Go with Python bindings.
- Easy to use API and tooling.
- GPU acceleration support.
HElib (HomomorphicEncryption.org)
- Provides an implementation of the BGV scheme.
- Developed by researchers for prototyping.
- Written in C++ with Python bindings.
- More focused on research than production use.
Other newer libraries include HEAAN, NFLlib, and cuHE. Evaluate them to choose the one best suited to your needs and environment.
What are the Limitations of Homomorphic Encryption
While homomorphic encryption enables groundbreaking new applications, it’s important to be aware of current limitations:
- Performance: Still very computationally heavy in most cases.
- Encryption schemes: A limited set of encryption algorithms to choose from.
- Computational complexity: Restrictions on complexity of supported computations.
- Space complexity: Ciphertext can be much larger than plaintext.
- Implementation difficulty: It is not easy to implement correctly and securely.
- Standardization: No single dominant library or standard yet.
- Maturity: Still an emerging technology requiring more maturity.
These limitations mean homomorphic encryption may not be suitable for many performance-sensitive or simple use cases today. However, ongoing innovation is rapidly improving capabilities.
What are the Future of Homomorphic Encryption
Homomorphic encryption is an area of very active research and rapid innovation. Here are some key areas of expected progress:
New Encryption Schemes
- New homomorphic encryption algorithms and variants are continuously emerging.
- Schemes are becoming more advanced and efficient.
Implementation Optimizations
- Libraries are optimizing performance with parallelization, batching, and hardware acceleration.
- Big improvements in execution times are expected.
Standardization
- Increased standardization of algorithms, formats, and APIs.
- It will improve interoperability.
Applications
- A wider range of applications is becoming possible as performance improves.
- Adoption is increasing in fields like health, finance, ML, etc.
Post Quantum Security
- Most homomorphic encryption schemes already provide post-quantum security not vulnerable to quantum attacks.
Cloud Services
- Cloud services providing homomorphic encryption are emerging, removing the implementation burden.
Homomorphic encryption is reaching viability for real-world applications and will increasingly impact privacy-preserving computation.
Final Thoughts
Homomorphic encryption enables computations to be carried out on encrypted data without decrypting it first. This groundbreaking technique has major implications for privacy and security.
While still a relatively new and complex technology, homomorphic encryption schemes are advancing rapidly. Performance and usability have reached levels that make many practical applications possible.
Major corporations and researchers are actively innovating in homomorphic encryption. As the ecosystem matures and adoption increases, homomorphic encryption can become a mainstream technology enabling privacy-preserving computation. The future looks bright for this transformational cryptography capability.
Frequently Asked Questions About Homomorphic Encryption
Here are answers to some common questions about homomorphic encryption:
Is homomorphic encryption secure?
Yes, homomorphic encryption can be highly secure against cryptanalysis when implemented correctly using strong encryption algorithms. Leading schemes are considered secure against both classical and quantum attacks.
Does homomorphic encryption have any vulnerabilities?
Like any complex cryptography, a careless implementation may introduce vulnerabilities. Side-channel attacks could compromise keys. However, no major theoretical weaknesses are known in leading schemes.
Can you break homomorphic encryption?
No efficient attacks are known that can realistically break the encryption for leading schemes like BGV and BFV. Brute-forcing the keys is infeasible.
What are the risks of homomorphic encryption?
The main risks are potential flaws in implementation, configuration, and key management. Chosen ciphertext attacks could also threaten some schemes. Proper implementation by experts is important.
Is homomorphic encryption used in the real world?
Use is still somewhat limited, but major companies like Microsoft, Google, IBM, and Intel are researching and implementing homomorphic encryption, and adoption is rapidly increasing.
Is homomorphic encryption commercially viable?
Performance and usability limitations initially prevented widespread use. But performance is now reaching practical levels for many applications, making it commercially viable.
Does homomorphic encryption have a public key?
Yes, homomorphic encryption uses public/private key pairs. The public key encrypts data while the private key decrypts, allowing computation on data encrypted with the public key.
Is homomorphic encryption available as a cloud service?
Some cloud services provide hosted homomorphic encryption services, eliminating the need to implement it directly. Adoption by major cloud providers is growing.
Priya Mervana
Verified Web Security Experts
Priya Mervana is working at SSLInsights.com as a web security expert with over 10 years of experience writing about encryption, SSL certificates, and online privacy. She aims to make complex security topics easily understandable for everyday internet users.
