When we upload a file to the cloud, the server typically has to open it to process it. To search for a word in a document, to train a model, or to calculate an average, the machine needs to read the data in the clear. This poses an obvious risk: anyone with access to the server —or an attacker who compromises it— can see the information. Homomorphic encryption proposes a radical solution: allowing the server to perform operations on encrypted data without ever decrypting it.
The problem with traditional encryption
Current symmetric and asymmetric encryption protects data at rest and in transit. When a user sends a file to a cloud service, it is encrypted on the client side and decrypted on the server for processing. That is, data is protected during transit and while stored, but not while being used. This state, known as "data in use," is the weakest link. Homomorphic encryption aims to fill that gap.
What does "homomorphic" mean?
In mathematics, a function is homomorphic if it preserves structure between two sets. Applied to cryptography, an encryption scheme is homomorphic if it allows operations to be applied to ciphertexts such that the result, when decrypted, is equivalent to having operated on the plaintexts. Simply put: if you encrypt 3 and 5, and then add the encrypted values, decrypting the result yields 8. The server never saw the 3 or the 5, but it performed the addition.
How it works under the hood (the math)
Modern homomorphic encryption schemes are based on hard mathematical problems, such as Ring Learning With Errors (RLWE). The core idea is to introduce a small "noise" or error into the encryption. Without the secret key, the noise makes the ciphertext appear random. With the key, one can remove the noise and recover the message. Each homomorphic operation (addition or multiplication) increases this noise. If too many operations are performed, the noise grows so much that decryption fails.
The noise problem and bootstrapping
To solve the growth of noise, Craig Gentry introduced a technique called "bootstrapping" in 2009. It consists of running the scheme’s own decryption algorithm homomorphically on the ciphertext, but using an encrypted version of the secret key. This "refreshes" the ciphertext and reduces the noise, allowing an unlimited number of operations. It is a computationally very expensive process, but it is the basis of fully homomorphic encryption (FHE).
Types of homomorphic encryption
Not all schemes allow the same operations. They are classified as:
- Partially homomorphic (PHE): allows only one type of operation, usually addition or multiplication, but not both.
- Somewhat homomorphic (SHE): allows both operations, but only a limited number of times before the noise destroys the message.
- Leveled (LHE): allows both operations up to a predefined depth level.
- Fully homomorphic (FHE): allows both operations indefinitely, thanks to bootstrapping.
Real-world applications
Homomorphic encryption is already being tested in several fields. In healthcare, it allows hospitals to share patient data with researchers without the researchers seeing personal information. In the cloud, it enables training artificial intelligence models on encrypted data, so the service provider cannot spy on the training data. It is also used in finance to detect fraud without accessing individual transactions.
The performance challenge
The main obstacle to mass adoption is computational overhead. Homomorphic operations are between 1,000 and 1,000,000 times slower than plaintext operations. Newer schemes, such as CKKS (for real and complex numbers), BFV (for integers), and TFHE (for fast boolean operations), have improved efficiency. In addition, specific hardware accelerators, such as FPGA and ASIC chips, are emerging and promise to close this gap.
Conclusion
Homomorphic encryption represents a paradigm shift in cloud security. Although it is still far from being a mass-market consumer technology, its development is advancing rapidly. As privacy regulations tighten and cloud computing becomes more ubiquitous, the ability to process data without seeing it becomes a necessity, not a luxury. Homomorphic encryption is the missing piece to complete the puzzle of digital trust.
