Homomorphic Encryption

#programming

To put in plain words, Homomorphic Encryption is a technique of encryption that allows mathematical operations and manipulations on encrypted data without needing to decrypt it first, so that the underlying results, when decrypted, matches the operations performed.

It essentially allows a company or a service to work on sensitive, encrypted data, without being able to see the data itself, boosting security and privacy, while not losing the nature of the data itself.

This leads us to a world of "blind computing", where we don't need to know or observe the data to do operations on it.
It removes the need for "trust" in digital relationships. Third party service providers can freely provide their services on data without the customer having to worry about privacy.

The initial problem

Every encryption methods adds a little bit of "noise" or randomness to hide the original data.
This "noise" is propogated through operations, like addition and multiplications, growing in magnitude until it becomes so large that it overwrites the data itself and the original data is lost.

Breakthrough in concept : "Bootstrapping"

In 2009, A researcher named Craig Gentry solved the problem with an idea called bootstrapping.

Research and expand on the concept of "bootstrapping"
Read the paper : Fully Homomorphic Encryption Using Ideal Lattices

Current accelerations

The problem that remained that even though we know the concept and it works in theory, it was just too computationally expensive. A supercomputer would take hours to do a simple operation.

Three specific technological shifts changed this :

1. Lattice-Based Cryptography

Most modern FHE uses Lattices—complex, high-dimensional grids of points. Finding a specific point in a 1,000-dimensional lattice is an "NP-Hard" problem, making it incredibly secure (even against future quantum computers).

Because these lattices are based on simple linear algebra (vector and matrix addition), they are much more efficient for computers to process than the heavy prime-number math used in RSA (traditional encryption algorithms).

2. The "Flavor" Specialization

We stopped trying to use one math formula for everything. Instead, we developed "flavors" for specific tasks:

TFHE (Torus FHE): Optimized for Boolean Gates (AND, OR, NOT). It’s incredibly fast for logic and is used for things like encrypted smart contracts.
CKKS: Optimized for Floating Point numbers. It allows for "approximate" math, which is perfect for AI and Machine Learning where a 0.00001% error doesn't matter.

3. Hardware Acceleration (ASICs)

Just like Bitcoin has ASICs and AI has GPUs, we now have FHE Accelerators. Companies are building chips specifically designed to handle the massive polynomial multiplications that FHE requires. In the last 24 months, we’ve seen speedups of 1,000x to 10,000x, bringing processing times down.