Definition
Homomorphic Encryption (HE) is a class of cryptographic schemes that allow computations to be performed directly on encrypted data (ciphertexts) without decrypting them. The result remains encrypted and, upon decryption, matches the outcome of performing the same operations on plaintext data.
Classification of HE Schemes
- Partially Homomorphic Encryption (PHE) - supports unlimited operations of a single type (e.g. only addition or only multiplication).
- Somewhat Homomorphic Encryption (SHE) - supports a limited number of mixed operations (addition and multiplication), up to a defined complexity limit.
- Leveled HE - permits evaluation of arithmetic circuits of predetermined depth.
- Fully Homomorphic Encryption (FHE) - enables arbitrary computations (arithmetic and logic) of unbounded depth on ciphertexts.
Operational Model
- KeyGen - generate cryptographic keys (public/private, optional evaluation keys).
- Enc(pk, m) - encrypt plaintext m into ciphertext c.
- Evaluate - execute operations (addition, multiplication, logic) on ciphertexts without decryption.
- Dec(sk, c′) - decrypt result c′, obtaining the same result as operations on plaintext.
Technical Parameters and Costs
Attribute | Implication |
Ciphertext size | Much larger than plaintext, increasing storage and transmission overhead. |
Computation cost | Homomorphic operations consume significantly more CPU/memory than plaintext ones. |
Circuit depth / operation limit (SHE / leveled HE) | Limits number/complexity of permissible operations without bootstrapping. |
Noise growth | Each operation increases noise; too many operations can make decryption impossible. |
Bootstrapping / relinearization overhead (FHE) | Required for deep computations; entails high computational cost. |
Advantages
- Enables computation on sensitive data in untrusted or external environments (e.g. cloud), without exposing plaintext.
- Protects data during processing (data‑in‑use), not only during storage or transport.
- Allows combining privacy and functionality - data analysis, aggregation, ML - on encrypted data.
Limitations and Practical Challenges
- High computational and memory requirements compared to plaintext processing.
- Large ciphertexts and keys, leading to storage, bandwidth, and performance overhead.
- Some schemes restrict number or complexity of operations; full schemes require expensive bootstrapping.
- No universal HE scheme optimal for all use cases; trade‑offs między bezpieczeństwem, wydajnością i funkcjonalnością.
Relevance in Image and Video Anonymization Contexts
While HE is typically designed for numeric or structured data, it can support privacy-preserving workflows in image/video systems - not by bezpośrednie szyfrowanie obrazów, lecz przez ochronę metadanych lub wyników analizy. Przykłady zastosowań:
- Aggregated statistics from video surveillance (e.g. counts of detections, number of events) - without exposing raw footage.
- Processing extracted features or metadata (e.g. bounding boxes, detection outputs) via external ML/cloud services, while keeping raw images encrypted.
- Sharing analytics or reports between organizations while preserving confidentiality of source media.
In data protection architectures, HE can complement visual anonymization, metadata masking, and access control.