Homomorphic Encryption: The cryptographic revolution that allows data to be processed without decrypting it

In the classic computer security paradigm, data goes through three protection states: in transit (protected by SSL/TLS), at rest (protected by disk or database encryption), and in use (processed in RAM). Historically, to analyze or manipulate data, it was mandatory to decrypt it in memory, leaving it vulnerable to memory leaks or server intrusions.

Homomorphic Encryption (HE) solves this dilemma by allowing operations on data directly in its encrypted state.

The mathematical concept of homomorphism

The term "homomorphism" comes from abstract algebra and describes a structured correspondence between two algebraic groups. In cryptography, it means that if we encrypt a message $A$ as $E(A)$ and a message $B$ as $E(B)$, we can apply a mathematical operator on both ciphertexts to obtain $E(A \otimes B)$ so that, when decrypting the result, we obtain the exact result of the operation in plaintext.

There are three levels of homomorphic encryption depending on the operations supported:

1. Partial Homomorphic Encryption (PHE): Supports only addition or only multiplication (like RSA or ElGamal algorithms).
2. Shameless Homomorphic Encryption (SHE): Supports addition and a very limited number of consecutive multiplications before mathematical noise corrupts the message.
3. Full Homomorphic Encryption (FHE): It allows arbitrary additions and multiplications to be evaluated in an unlimited way, allowing any computer algorithm to be executed on encrypted data. The first viable FHE scheme was proposed by Craig Gentry in 2009.

Revolutionary use cases

The ability to process without decrypting transforms entire industries:

• Medical and Genomics: Researchers can run machine learning models on encrypted patient DNA databases to identify disease markers without knowing the identity or explicit medical history of individuals.
• Financial Services: Banks can detect fraudulent transactions by sending their encrypted transaction history to external AI engines without revealing balances or customer names.
• Electronic Voting: Allows votes to be counted and audited in a public and encrypted manner, guaranteeing the absolute anonymity of voters and the immutability of the final count.

The challenge of efficiency

Despite its immense theoretical potential, mass adoption of Full Homomorphic Encryption (FHE) faces a performance barrier: computational overhead. Processing data under FHE can be between $10,000 and $1,000,000 times slower than processing in clear text.

However, joint efforts in the development of specialized hardware (such as ASIC accelerators and FPGAs dedicated to cryptography) and new simplified mathematical algorithms are paving the way for homomorphic encryption to become commercially viable this decade.