Homomorphic Encryption: Capabilities and Practical Applications

Homomorphic encryption (HE) is a class of cryptographic technique that permits computation on ciphertext, producing an encrypted result that, when decrypted, matches the output of the same operation performed on the plaintext. This property fundamentally changes the threat model for data-in-use, a problem that conventional encryption — which requires decryption before processing — cannot address. The page covers the mechanics of HE schemes, their classification, regulatory relevance, practical tradeoffs, and deployment considerations for cryptographers, compliance officers, and applied security researchers.

• Definition and Scope
• Core Mechanics or Structure
• Causal Relationships or Drivers
• Classification Boundaries
• Tradeoffs and Tensions
• Common Misconceptions
• Checklist or Steps (Non-Advisory)
• Reference Table or Matrix

Definition and Scope

Homomorphic encryption describes any encryption system that preserves an algebraic structure such that operations on ciphertext correspond to operations on plaintext. Under a homomorphic scheme, a third party — a cloud provider, analytics platform, or federated node — can process encrypted data without ever obtaining the plaintext or the decryption key.

The scope is broader than a single algorithm. HE encompasses a family of constructions ranging from schemes supporting only one operation type to fully general systems capable of arbitrary computation. NIST, through its Cryptographic Standards and Guidelines program, has actively tracked HE research and maintains documentation on its standardization trajectory, recognizing its relevance to long-term privacy infrastructure.

Regulatory relevance surfaces under frameworks including HIPAA (45 CFR Parts 160 and 164), which governs protected health information processed by cloud-based analytics platforms, and the NIST Privacy Framework, which categorizes data-in-use as a distinct exposure surface from data-at-rest and data-in-transit. The Federal Risk and Authorization Management Program (FedRAMP) baseline controls reference data-in-use protections, creating a compliance rationale for agencies evaluating HE as a supplemental control layer.

Core Mechanics or Structure

The algebraic foundation of HE derives from the Learning With Errors (LWE) problem and its ring variant Ring-LWE (RLWE), both of which are believed to be resistant to quantum adversaries (NIST, Post-Quantum Cryptography Standardization). This quantum resistance distinguishes HE from RSA-based constructions detailed in the RSA encryption reference.

Noise and the Bootstrapping Problem

HE ciphertexts carry an inherent noise term introduced during encryption. Each arithmetic operation — addition or multiplication — increases this noise. When noise exceeds a threshold, decryption fails. Controlling noise accumulation is the central engineering challenge:

• Addition increases noise linearly.
• Multiplication increases noise quadratically or exponentially depending on the scheme.
• Bootstrapping (introduced by Craig Gentry in his 2009 IBM thesis) resets noise by homomorphically evaluating the decryption circuit, enabling continued computation but at significant computational cost.

Key Components

Scheme implementations such as BFV (Brakerski/Fan-Vercauteren), BGV (Brakerski-Gentry-Vaikuntanathan), CKKS (Cheon-Kim-Kim-Song), and TFHE (Fast Fully Homomorphic Encryption over the Torus) each manage noise differently, favoring integer arithmetic, modular arithmetic, approximate real-number arithmetic, or gate-level Boolean computation respectively.

Causal Relationships or Drivers

Three structural forces explain the growing deployment pressure for HE:

1. Cloud adoption and data custody separation. As federal agencies and regulated industries migrate processing to third-party clouds, decrypting data for analysis creates custody exposure. FedRAMP-authorized cloud environments require documented data-in-use controls. HE is one of two primary architectural responses, the other being secure multiparty computation.

2. Privacy regulation proliferation. The California Consumer Privacy Act (CCPA), as amended by CPRA (California Civil Code § 1798.100 et seq.), the Illinois Biometric Information Privacy Act (BIPA, 740 ILCS 14), and sector-specific federal rules under HIPAA collectively impose requirements that create liability for plaintext exposure during analytics workflows. HE shifts the exposure surface by eliminating plaintext-in-use.

3. Machine learning on sensitive datasets. Privacy-preserving machine learning — training models on health records, financial data, or biometric inputs — requires computation without decryption. Research consortia including the OpenMined project and IBM's HElib library have produced open-source infrastructure that makes HE-based inference computationally feasible for constrained model architectures.

Classification Boundaries

HE is not a single standard but a spectrum of capability classes. The boundaries matter for deployment decisions because each class has fundamentally different computational scope.

Partially Homomorphic Encryption (PHE)

Supports one operation type (addition or multiplication) an unlimited number of times. RSA (multiplicative) and Paillier (additive) are PHE systems. PHE is computationally efficient but limited to use cases requiring only one operation class, such as encrypted vote tallying (additive) or private set intersection.

Somewhat Homomorphic Encryption (SHE)

Supports both addition and multiplication but only for a bounded circuit depth. No bootstrapping is required. SHE is suitable for fixed-depth computations such as encrypted database queries with known query structure.

Leveled Fully Homomorphic Encryption (Leveled FHE)

Supports arbitrary computation up to a predetermined circuit depth, established at key generation. Deeper circuits require larger parameters. No bootstrapping is used; depth is bounded by the noise budget at parameter selection.

Fully Homomorphic Encryption (FHE)

Supports arbitrary computation of unbounded depth via bootstrapping. Gentry's 2009 construction was the first theoretical proof of FHE feasibility. FHE is computationally intensive: benchmarks from the HomomorphicEncryption.org community standard (version 1.1, published 2020) document latency factors of 10,000x to 1,000,000x compared to plaintext computation for representative workloads.

Tradeoffs and Tensions

Performance vs. Security Parameter Depth

Larger ring dimensions and modulus sizes increase security margins against both classical and quantum adversaries but scale ciphertext size and computation time polynomially. The CKKS scheme, optimized for approximate arithmetic on real numbers (relevant to neural network inference), accepts bounded decryption error in exchange for orders-of-magnitude performance improvement over exact-arithmetic schemes. This tradeoff is unsuitable for applications requiring exact results — payroll, cryptographic key derivation, or legal records.

FHE vs. Secure Multiparty Computation

FHE and secure multiparty computation address overlapping problems but differ in trust and communication models. FHE requires no interaction between parties after key distribution; MPC requires multiple rounds of communication between participants. For single-server computation on a dataset owned by one party, FHE is architecturally simpler. For computations spanning data held by distinct parties who distrust each other, MPC protocols may be more efficient. The choice is not universal; the correct architecture depends on threat model and data topology.

Standardization Lag

Unlike AES (FIPS 197) or SHA-3 (FIPS 202), no FIPS-grade HE standard exists as of the NIST post-quantum standardization process timeline. The HomomorphicEncryption.org security standard provides community-consensus parameter recommendations, but these are not FIPS publications and carry no regulatory presumption of adequacy under frameworks that require FIPS-validated cryptography. This creates a compliance gap for federal contractors bound by FIPS 140 requirements.

Common Misconceptions

Misconception: Homomorphic encryption eliminates all data privacy risk.
HE protects plaintext from the computing party but does not protect against inference attacks on outputs. If a malicious computing party can submit chosen inputs and observe encrypted outputs, side-channel analysis may still leak information about the plaintext function. NIST SP 800-188 (draft, "De-Identifying Government Datasets") addresses output-privacy risks that persist even in encrypted computation contexts.

Misconception: FHE is ready for general production deployment.
FHE performance benchmarks from HomomorphicEncryption.org (v1.1) place practical FHE throughput at 3 to 4 orders of magnitude below plaintext computation for non-trivial circuits. Production FHE is confined to limited use cases: encrypted inference on shallow neural networks, private database lookups, and encrypted genome analysis. General-purpose cloud replacement of plaintext computation is not achievable at current performance levels.

Misconception: Bootstrapping is free in computational terms.
Bootstrapping is the most expensive operation in FHE. A single bootstrapping operation in TFHE takes approximately 0.1 seconds on a modern CPU core for a single bit (per TFHE library documentation), meaning deep circuits requiring frequent noise resets incur costs measured in CPU-hours rather than milliseconds.

Misconception: HE replaces zero-knowledge proofs.
HE and zero-knowledge proofs solve distinct problems. HE enables computation on encrypted data. ZKPs enable proving properties of data without revealing the data itself. The two constructions are complementary and are combined in privacy-preserving protocol stacks.

Checklist or Steps (Non-Advisory)

The following discrete steps reflect the operational sequence for evaluating HE applicability in a constrained data-processing workflow. This is a structural reference, not professional guidance.

1. Identify the computation class — Determine whether the target computation requires addition only, multiplication only, both, or arbitrary depth. This maps directly to PHE, SHE, leveled FHE, or full FHE requirements.
2. Define the threat model — Specify whether the untrusted party is a cloud provider (single-server model), a joint analytics partner (multi-party model), or an internal compartment with access restrictions.
3. Select scheme family — Match scheme to computation type: BFV/BGV for exact integer arithmetic; CKKS for approximate real-number arithmetic; TFHE for Boolean gate-level computation.
4. Set security parameters — Apply HomomorphicEncryption.org security standard parameter tables (128-bit, 192-bit, or 256-bit security levels) appropriate to data sensitivity and regulatory classification.
5. Benchmark against plaintext baseline — Measure latency and throughput of the HE implementation against equivalent plaintext operations to determine operational feasibility.
6. Assess noise budget — For SHE and leveled FHE, calculate the maximum circuit depth the parameter set supports before noise causes decryption failure.
7. Evaluate bootstrapping necessity — If computation depth exceeds the noise budget, determine whether FHE with bootstrapping is required and quantify the associated latency cost.
8. Document key management architecture — HE requires public keys, secret keys, and evaluation keys. Align key custody with existing encryption key management policy and key lifecycle controls.
9. Verify library provenance — Confirm the HE library (HElib, Microsoft SEAL, OpenFHE, TFHE-rs) has undergone third-party audit; none currently hold FIPS 140-2/3 validation.
10. Map to compliance framework — Document whether the HE deployment satisfies data-in-use requirements under the applicable regulatory framework (HIPAA, FedRAMP, CMMC) or serves only as a supplemental control.

Reference Table or Matrix

HE Scheme Comparison Matrix

Regulatory Mapping Reference

The encryption compliance landscape reflects a regulatory environment where HE is recognized as technically relevant but has not yet been incorporated into prescriptive FIPS-validated control sets. Deployment in regulated industries therefore requires documented compensating controls and legal review of whether HE satisfies applicable statutory encryption definitions.

References

• NIST Homomorphic Encryption Project — csrc.nist.gov
• NIST Post-Quantum Cryptography Standardization — csrc.nist.gov
• HomomorphicEncryption.org Security Standard v1.1
• NIST SP 800-53 Rev 5, SC-28: Protection of Information at Rest — csrc.nist.gov
• NIST Privacy Framework — nist.gov
• FedRAMP Program — fedramp.gov
• HIPAA Security Rule, 45 CFR Part 164 — hhs.gov
• FIPS 140-3 Standard — csrc.nist.gov
• CMMC Program, 32 CFR Part 170 — acq.osd.mil
• California Consumer Privacy Act (CCPA/CPRA) — oag.ca.gov
• OpenFHE Library — openfhe.org
• Microsoft SEAL Documentation — microsoft.com