What is Fully Homomorphic Encryption (FHE)?

Encryption has a problem. Traditional encryption methods protect data by encoding it, ensuring that only authorized parties can decode it using a specific key. While these methods are effective at keeping data secure during storage and transmission, they require decryption for computation, which exposes the data to potential threats.

User data has been lost in hacks as a result of this. Data on centralized servers must be decrypted before it can be processed, meaning that pretty much anything you give to another party on the Internet is exposed at some point. The solution to this issue has been to keep data in protected siloes, but even if these can be adequately protected and no data is leaked, it prevents data from being processed efficiently, and users must put a lot of trust into whoever they give their data to—you’re just entrusting your medical records, financial history, and other sensitive data to some faceless security engineers and hoping they keep it safe.

Blockchains solve many of the problems presented by the centralized model of the Internet, but their encryption model is also an issue. If centralized approaches to processing data are problematic, public blockchains don’t even have a model for processing this data without exposing it. Blockchains like Ethereum are transparent by design, meaning that anything you put on them is viewable by anyone with an Internet connection. So while receiving your salary directly without having to trust a bank or sending a payment directly to a friend without an intermediary might seem cool and useful, the encryption methods used by blockchains are currently not able to shield the amounts you’re sending and receiving. Truly private methods of onchain interaction, like privacy chains underpinned by zero-knowledge technology, sacrifice many of the advantages of blockchains, such as their composability, trading them for hardcore anonymity.

Luckily, there’s a solution to all of these problems. Fully Homomorphic Encryption (FHE) represents a paradigm shift in cryptography and data security. FHE breaks these limitations by allowing computations to be performed directly on encrypted data without ever decrypting it. This means that sensitive information remains protected throughout its lifecycle—even when it is being processed. By enabling secure computation on encrypted data, FHE unlocks new possibilities for privacy-preserving applications across various sectors, including blockchains.

How Fully Homomorphic Encryption Works

So what is FHE?

To put it simply, FHE is a form of encryption that enables computations to be executed on encrypted data, producing an encrypted result. When this result is decrypted, it corresponds precisely to the outcome of operations as if they had been performed directly on the plaintext. Sounds like magic right?

Here’s a simple example. Say you have a JPEG image file of a yellow banana. Let’s encrypt the file so no one can see it. Now, with FHE, someone could run a function to change the color of the image. They never even knew it was a yellow banana in the first place, but they’ve computed upon the encrypted image to turn it green. So we have a green banana, but no one knows it’s a green banana apart from the person who originally encrypted the image. They can decrypt it when they want to, revealing the green banana. 

This is an abstract example, but when you have something like financial data, it becomes more interesting. So you could have your private financial records on a public server, and a bank could run a function on it to assign interest to it without ever revealing the amount. This would stop any danger of your financial information being exposed. Pretty cool.

Let’s go a step deeper. FHE allows for mathematical operations to be performed on encrypted data, producing an encrypted result that, when decrypted, matches the result of operations performed on the plaintext. If you’re a math person, you might think of it like this: 

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Enc(a + b) = Enc(a) + Enc(b)
Enc(a x b) = Enc(a) x Enc(b)

And here are some core principles of FHE.

• Public and Private Keys: FHE relies on asymmetric encryption. A public key encrypts the data, and a private key decrypts it.
• Homomorphic Operations: Certain operations—such as addition and multiplication—can be executed directly on ciphertexts. These operations correspond to their plaintext equivalents.
• Decryption: The output remains encrypted until it is decrypted by the party holding the private key, ensuring security at all stages.

If you’re a technical person, here are some more insights.

• Noise Management: As FHE is based on lattice-based LWE setups (link to LWE post), during computation, ciphertexts accumulate noise. To handle this noise management problem, FHE schemes use techniques like bootstrapping (introduced by Craig Gentry) (link to Gentry post) to control this noise, ensuring the correctness of results.
• Efficiency Challenges: Early FHE systems were computationally expensive, but modern schemes like BFV (Brakerski-Fan-Vaikuntanathan) and TFHE (Fast Fully Homomorphic Encryption over the Torus) have made significant strides in improving efficiency.

So where are we at with the development of FHE?

From academic proofs to open-source libraries like Zama’s TFHE.rs/Concrete and Microsoft’s SEAL, FHE is steadily transitioning into practical implementations. Collaborative efforts across academia and industry continue to refine and optimize these techniques for broader adoption. There’s still some way to go, but FHE is now at a point where it can begin being implemented. Very exciting.

Use Cases of Fully Homomorphic Encryption

One of the coolest things about FHE is the new use cases it unlocks. There are so many useful applications that could be built if there was just a way to provide privacy without sacrificing utility. As it is, many modes of encryption require data to be siloed and protected—and definitely not computed upon without decryption. FHE provides a fantastic solution to this problem.

Here are just some of the use cases that become possible with FHE.

Healthcare

Currently, patient data is siloed and protected to safeguard patient privacy. Health records are, rightly, kept with a high level of confidentiality, with patients’ data protected at all costs. This often means that it can’t be processed or used to garner insights that would be beneficial to the public.

With FHE, researchers could garner insights into pools of patient data without getting access to the data itself. Computations could be run on data without exposing the data itself, with researchers able to see how frequent a comorbidity was among a specific demographic without the medical data ever being exposed. This could lead to a revolution in how medical research is executed, with a vast amount of previously siloed data suddenly available—all with privacy being protected.

Finance

There are many potential FHE use cases within finance. Let’s touch on just a few.

Financial institutions frequently collaborate with external partners, such as auditors, regulators, or analytics firms. Sharing sensitive data with these third parties can introduce significant privacy and security risks, particularly when data must be transferred or stored externally. FHE offers a transformative solution by enabling encrypted data to be shared and processed without revealing its contents. For instance, an auditor could verify compliance or analyze trends in encrypted transaction logs without ever seeing the raw data. 

AI and Machine Learning

The AI revolution is underway, but the massive volume of data presents a series of privacy questions. 

You might be reluctant to contribute data to a machine learning model if there’s a risk it might be leaked, or if the dataset is open-source or publicly available. But with FHE, the data could be used to train the model without exposing it, opening up a vast volume of new data to improve AI training processes.

These are just a few examples of what’s possible with FHE. But there’s one we haven’t yet touched on: FHE can be used to bring a great amount of utility to blockchain technology by fueling it with confidentiality.

FHE and Blockchains: A Powerful Combination

Public blockchains like Ethereum and Bitcoin excel at transparency but fall short when it comes to confidentiality. Every transaction and smart contract interaction is visible to all participants, which can be a major barrier for applications requiring sensitive data. FHE offers a transformative solution by enabling computations on encrypted data while keeping the underlying data private.

Currently, executing payroll or even paying a friend through a public blockchain would involve displaying the amount you received or sent to anyone in the world. This is a major barrier to adoption, as the public and institutions rightly feel reluctant to divulge this information. Other encryption modes, such as zero-knowledge proofs, sacrifice the strengths of blockchains, such as composability, and make transactions much more cumbersome, and private blockchains require bridging, presenting further user experience barriers. With FHE, nothing has to change—users can use the most established public blockchains, such as Ethereum, and just shield the details of their transactions. For more on this, check out the confidential ERC20 (cERC20) framework from Inco and Circle Research. 

Elsewhere, financial institutions looking to bring equities, commodities, and other assets onchain need certain confidentiality protections and the ability to grant specific access to regulators. With FHE, they can shield the details of onchain activity while granting access to select parties. Inco is working on how to implement FHE into the ERC3643 token standard, which is built specifically for bringing real-world assets onchain.

There are many other onchain uses cases for FHE, including gaming and infrastructure issues such as cross-chain confidential transfers.

The Future of Fully Homomorphic Encryption

Technological progress is steadily pushing the boundaries of what FHE can achieve. While the speed and computation load of FHE is currently an issue, forward progress is being made on a frequent basis.

Researchers continue to develop more efficient FHE schemes, focusing on reducing computational overhead and improving noise management. Techniques like batching and ciphertext packing allow multiple operations to be performed simultaneously, further enhancing efficiency.

Furthermore, the integration of hardware acceleration, such as GPUs, FPGAs, and ASICs designed for FHE, is a game-changer. These technologies significantly reduce the time required for homomorphic computations, making them more suitable for real-time applications.

Open-source libraries like Zama’s Concrete, Microsoft’s SEAL, and IBM’s HELib are evolving rapidly, offering user-friendly APIs and optimized algorithms that simplify the integration of FHE into existing systems.

Finally, combining FHE with other cryptographic techniques, such as Multi-Party Computation (MPC) or Zero-Knowledge Proofs (ZKPs), is gaining traction. These hybrid approaches balance efficiency and privacy, paving the way for practical deployment in complex use cases.

The sky is the limit for this powerful form of encryption. Inco is leveraging FHE to create a confidential layer for existing blockchains, which will unlock mainstream use cases that are a no-brainer in the existing Internet. Everything from receiving your salary onchain to buying bonds and equities could soon be a part of everyday life for millions of people in the same way that online shopping or email is as a result of FHE—confidentiality is a real game-changer.

For more about Inco, check out our documentation.