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Homomorphic Encryption
A cryptographic technique that allows performing mathematical operations directly on encrypted data without decrypting it. The decrypted result corresponds to the operation performed on the plaintext, ensuring confidentiality during processing.
FHE (Fully Homomorphic Encryption)
A complete homomorphic encryption scheme that allows an unlimited number of addition and multiplication operations on encrypted data. Considered the Holy Grail of modern cryptography for secure processing of sensitive data.
SHE (Somewhat Homomorphic Encryption)
A partial homomorphic encryption scheme that supports a limited number of operations before noise makes decryption impossible. Offers a trade-off between performance and functionality for practical applications.
PHE (Partially Homomorphic Encryption)
An encryption system that supports only one type of operation (addition OR multiplication) but in an unlimited manner. Used in specific protocols like electronic voting or secure statistical aggregation.
Homomorphic Bootstrapping
A process of refreshing the noise in a homomorphic ciphertext to enable unlimited computations. It involves homomorphically decrypting a ciphertext under a different key, thereby reducing the accumulated noise.
BGV Scheme
A homomorphic encryption scheme based on lattice cryptography developed by Brakerski, Gentry, and Vaikuntanathan. Particularly efficient for operations on bits and deep boolean circuits.
BFV Scheme
A homomorphic encryption scheme optimized for integers, developed by Brakerski, Fan, and Vercauteren. Enables precise arithmetic operations on integers without approximation.
CKKS Scheme
A homomorphic encryption scheme that supports floating-point numbers, created by Cheon, Kim, Kim, and Song. Ideal for machine learning applications requiring calculations on real numbers with controlled approximation.
Ring-LWE
Ring Learning with Errors problem, mathematical foundation of many modern FHE schemes. Provides efficient security parameters with reduced-size keys and ciphertexts.
Noise level
Measure of the error introduced during encryption that accumulates with each homomorphic operation. Determines the maximum depth of circuits that can be evaluated before requiring bootstrapping.
Circuit depth
Maximum number of logic gates or arithmetic operations that can be composed in a homomorphic circuit. Determines the complexity of algorithms that can be executed on encrypted data.
Encryption modulus
Cryptographic parameter defining the computation space and security level in homomorphic schemes. Directly influences the size of keys, ciphertexts, and computation capacity.
Circuit evaluation
Process of sequential application of homomorphic operations to evaluate a function on encrypted data. Requires careful optimization to minimize multiplication and circuit depth.
Evaluation key
Special key in some FHE schemes allowing efficient homomorphic multiplications. Usually created for a specific level of multiplication in the circuit.
Slot rotation
Homomorphic SIMD operation allowing permutation of elements in an encrypted vector without decryption. Essential for optimizing parallel computations in ring-based schemes.
Homomorphic tensor
Encrypted data structure enabling tensor operations directly in the encrypted domain. Crucial for neural networks and privacy-preserving deep learning algorithms.
Security parameters
Set of cryptographic values ensuring resistance to quantum and classical attacks on FHE schemes. Includes module size, polynomial degree, and noise standard deviation.
Homomorphic latency
Additional time introduced by homomorphic encryption/decryption operations in processing pipelines. Critical factor for practical adoption in real-time systems.