Private AI Inference with Homomorphic Encryption: A Practical Guide to Computing on Encrypted Data

In 2009, Craig Gentry demonstrated that it is feasible to perform computations on encrypted data without decrypting it, which was initially regarded as a theoretical curiosity. Fast forward to 2026, and homomorphic encryption has moved from academic papers to practical applications, with banks screening transactions against encrypted watchlists, hospitals running diagnostic models on confidential data, and Google announcing private AI features built on the same principles.

However, the gap between theoretical possibilities and practical usability remains significant, but it is no longer a deterrent to exploring this technology. This report delves into the intricacies of homomorphic encryption, specifically focusing on the CKKS scheme, which enables machine learning computations on encrypted data, and the cost considerations that determine the feasibility of implementing such private inference pipelines.

The Promise of Homomorphic Encryption:

Ordinary encryption algorithms, such as AES-CTR, ChaCha20, and RSA, scramble data in a way that makes it impossible for attackers to retrieve the original message without the key. However, this same property becomes a hindrance for computation. Traditional encryption methods render data unreadable, even to supercomputers, once decrypted for processing, thus compromising the confidentiality boundary from storage to memory layers.

Homomorphic encryption alters this paradigm by allowing operations on ciphertexts that correspond to operations on the original plaintext. This is achieved through the property Enc(a) ⊕ Enc(b) = Enc(a + b), which enables servers to add, multiply, and combine encrypted values, ultimately returning the encrypted result. The server remains oblivious to the inputs, intermediate values, or the output, ensuring data confidentiality.

Challenges in Computing with Plain Encryption:

Conventional encryption methods, while ensuring security, present challenges for computation. AES, for example, employs an S-box substitution and multiple rounds of ShiftRows and MixColumns that thoroughly mix input bits, resulting in a completely unpredictable output. This avalanche effect, which underpins AES's security, also makes it unsuitable for computations, as no algebraic relationship exists between plaintext and ciphertext.

Fully Homomorphic Encryption (FHE) offers a contrasting approach, starting with an algebraic structure naturally accommodating both addition and multiplication operations. It initiates with an algebraic structure that supports both operations, rather than attempting to adapt a scrambling cipher for arithmetic purposes. The classic FHE construction operates over polynomial rings, where plaintexts are small polynomials, ciphertexts are pairs of larger polynomials, and these structures maintain the algebraic operations necessary for computation.