Homomorphic Encryption

Supports unlimited operations of a single type—either addition or multiplication, but not both.

• RSA encryption is multiplicatively homomorphic: E(x) * E(y) = E(x * y)
• Paillier cryptosystem is additively homomorphic: E(x) * E(y) = E(x + y)
• Computationally efficient with small ciphertext expansion
• Used in federated GWAS for secure allele frequency aggregation
• Cannot evaluate arbitrary functions; limited to linear operations

Supports both addition and multiplication but only for circuits of limited depth. Each operation increases ciphertext noise, and decryption fails once noise exceeds a threshold.

• Based on ideal lattices and ring learning with errors (RLWE)
• Can evaluate low-degree polynomials before noise overwhelms the signal
• Serves as a building block for fully homomorphic schemes via bootstrapping
• Suitable for simple statistical computations like chi-squared tests on encrypted genotype counts

Supports arbitrary computation on encrypted data by enabling both addition and multiplication an unlimited number of times. Achieved through bootstrapping, a technique that recursively decrypts and re-encrypts ciphertexts to reset accumulated noise.

• Gentry's 2009 breakthrough proved FHE is theoretically possible using ideal lattices
• Modern schemes: BGV, BFV, CKKS, TFHE
• CKKS supports approximate arithmetic on real numbers, ideal for genomic model inference
• Enables encrypted neural network inference on private variant data without exposing patient genomes

A practical variant of FHE that supports computation up to a pre-determined multiplicative depth without bootstrapping. Parameters are chosen to accommodate a specific circuit before noise becomes unmanageable.

• BGV and BFV operate in leveled mode by default
• Eliminates the extreme computational cost of bootstrapping for known-depth circuits
• Ideal for fixed-architecture neural networks where layer count is known in advance
• Enables encrypted polygenic risk score calculation with a bounded number of arithmetic operations

A fundamental security property ensuring that an adversary cannot distinguish between encryptions of two different plaintexts, even when allowed to choose the plaintexts. Formally defined as IND-CPA security.

• Guarantees that ciphertexts reveal no partial information about the underlying genomic data
• Achieved through probabilistic encryption—the same plaintext encrypts to different ciphertexts each time
• Prevents allele frequency inference from repeated encryptions of identical genotypes
• Essential for compliance with GDPR and HIPAA when processing encrypted patient data in untrusted cloud environments

A stronger security notion ensuring that the evaluated ciphertext reveals nothing about the computation itself, only the final result. Without circuit privacy, an adversary could infer which genomic analysis was performed.

• Protects proprietary algorithms running on encrypted data from reverse engineering
• Achieved through noise flooding or rerandomization after homomorphic evaluation
• Critical when a pharmaceutical company runs encrypted drug-target prediction on a hospital's encrypted genomic data
• Prevents leakage of model architecture or variant weights during federated inference

The strongest form of homomorphic encryption, supporting arbitrary computation (both addition and multiplication) on ciphertexts without any limit on circuit depth. FHE schemes, such as CKKS and TFHE, enable complex genomic algorithms like neural network inference directly on encrypted DNA sequences, but incur substantial computational overhead—often 4-5 orders of magnitude slower than plaintext operations. Recent hardware acceleration and scheme optimizations are closing this gap for production deployment.

A restricted form of homomorphic encryption supporting only one operation type—either addition or multiplication, but not both. The Paillier cryptosystem provides additive homomorphism and is widely used in federated learning for secure aggregation of genomic model gradients. PHE is significantly more efficient than FHE, making it practical for production systems that only require summation of encrypted updates.

An intermediate scheme that supports both addition and multiplication but only for limited-depth circuits before noise accumulation corrupts the ciphertext. SHE is often used as a building block in bootstrapped FHE constructions. For genomic applications, SHE can handle shallow computations like variant frequency counting across encrypted cohorts without the full overhead of FHE bootstrapping.

A complementary cryptographic paradigm where multiple parties jointly compute a function over their private inputs without revealing them to each other. Unlike homomorphic encryption, which operates on encrypted data at rest, SMPC distributes computation across participants using secret sharing and oblivious transfer. In genomic federated learning, SMPC is often combined with HE in hybrid protocols—HE handles local encryption while SMPC manages the interactive aggregation phase.

A hardware-based isolation mechanism, such as Intel SGX or AMD SEV, that creates an encrypted enclave within the CPU where code and data are protected from the host operating system. TEEs offer a higher-performance alternative to HE for genomic computation, operating at near-native speed, but require trust in the hardware manufacturer and are vulnerable to side-channel attacks. Many production genomic pipelines use TEEs for heavy computation and HE for data in transit.

A mathematical framework providing provable privacy guarantees by injecting calibrated noise into computation outputs. While HE protects data during computation, DP protects against inference from the output itself—preventing membership inference attacks on trained genomic models. The combination of HE and DP creates a defense-in-depth strategy: HE secures the computation pipeline, while DP bounds what an adversary can learn from the final released model or statistics.