Homomorphic Encryption in SemCom

• Homomorphic encryption in SemCom is a method that encrypts semantic feature vectors while enabling algebraic operations directly on ciphertexts for end-to-end privacy.
• The integration of deep JSCC requires replacing non-polynomial activations with polynomial counterparts, ensuring efficient encrypted computation under noise constraints.
• Empirical results demonstrate that HE-based privacy-preserved methods achieve near-plaintext accuracy, preserving keypoint features and semantic integrity.

Homomorphic encryption in semantic communication (SemCom) defines a paradigm in which semantic representations—feature vectors or embeddings extracted from raw signals—are encrypted with schemes permitting algebraic manipulation directly on ciphertexts. This enables privacy-preserving end-to-end processing of semantic content, such as inference and aggregation, over untrusted channels or infrastructures. Approaches are grounded in both somewhat and fully homomorphic encryption (SHE/FHE). SemCom architectures require new cryptographic foundations, encoding methodologies, and algorithmic adaptations to achieve secure and semantically robust transmission of meaning, especially when deploying deep learning for joint source-channel coding.

1. Cryptographic Foundations for Homomorphic Encryption in SemCom

Homomorphic encryption (HE) schemes are characterized by their ability to support computation on encrypted data: given ciphertexts $c_1 = \text{Encrypt}(m_1)$ and $c_2 = \text{Encrypt}(m_2)$, one can compute $\text{Eval}_{\text{add}}(c_1, c_2)$ and $\text{Eval}_{\text{mult}}(c_1, c_2)$ such that decryption yields $m_1 + m_2$ and $m_1 \cdot m_2$, respectively.

Symmetric-key SHE

• The scheme of Dowerah & Krishnaswamy operates over $\mathbb{F}_q[x_1,\ldots,x_\ell]_{\leq r}$ (polynomials total degree $\leq r$). Ciphertexts are $n$-dimensional vectors in $\mathbb{F}_q^n$ constructed as $c_2 = \text{Encrypt}(m_2)$0, where $c_2 = \text{Encrypt}(m_2)$1 encodes monomial evaluations at secret points and $c_2 = \text{Encrypt}(m_2)$2 is discrete-Gaussian noise. Homomorphic addition is vector addition; homomorphic multiplication is component-wise (Schur) product followed by scaling by $c_2 = \text{Encrypt}(m_2)$3. The noise grows additively with additions, approximately squares with each multiplication, and correct decryption is possible if accumulated noise remains below a threshold (Dowerah et al., 2019).

Public-key FHE

• The Cheon–Kim–Kim–Song (CKKS) scheme, supporting approximate arithmetic over $c_2 = \text{Encrypt}(m_2)$4, is utilized for leveled FHE in SemCom (Meng et al., 17 Jan 2025). CKKS enables efficient homomorphic addition/multiplication of encrypted feature vectors, permitting polynomial evaluation on real-valued semantic embeddings.

Security reductions define the trust boundaries: the multivariate polynomial SHE attains IND-CPA security reducible to the Hidden Subspace Membership (HSM) problem—distinguishing noisy subspace elements from random vectors—a generalization of Learning With Errors (LWE) (Dowerah et al., 2019).

2. Semantic Communication Architectures with Homomorphic Encryption

In SemCom, the communications stack is restructured as follows:

• Application-layer feature extraction: a semantic encoder maps the message $c_2 = \text{Encrypt}(m_2)$5 to a feature vector $c_2 = \text{Encrypt}(m_2)$6 (or $c_2 = \text{Encrypt}(m_2)$7).
• HE encryption: $c_2 = \text{Encrypt}(m_2)$8, where $c_2 = \text{Encrypt}(m_2)$9 may be public or symmetric depending on the scheme.
• JSCC with encrypted input: a deep encoder $\text{Eval}_{\text{add}}(c_1, c_2)$0 transforms $\text{Eval}_{\text{add}}(c_1, c_2)$1 into channel symbols $\text{Eval}_{\text{add}}(c_1, c_2)$2, suitable for transmission.
• Channel: the physical channel, often modeled as AWGN, adds noise.
• HE decryption and semantic decoding: the receiver reconstructs $\text{Eval}_{\text{add}}(c_1, c_2)$3 via $\text{Eval}_{\text{add}}(c_1, c_2)$4, decrypts to estimate $\text{Eval}_{\text{add}}(c_1, c_2)$5, and uses a decoder $\text{Eval}_{\text{add}}(c_1, c_2)$6 for the task output (e.g., classification, detection).

Notably, key modifications are required for deep JSCC models:

• Replace non-polynomial activations (ReLU, tanh) with polynomial ones, e.g., $\text{Eval}_{\text{add}}(c_1, c_2)$7.
• Substitute max pooling with average pooling to ensure polynomial computability in HE (Meng et al., 17 Jan 2025).

3. Homomorphic Operations: Semantics-Preserving Functionalities

Homomorphic encryption makes possible a suite of semantic operations on ciphertexts, essential for end-to-end, privacy-preserving SemCom:

• Feature aggregation: Linear aggregation, e.g., weighted sums or averaging across encrypted features, uses homomorphic additions.
• Similarity scoring: Inner products between encrypted embeddings are realized by coordinate-wise homomorphic multiplication followed by summation.
• Polynomial inference: Elementwise non-linearities needed for shallow inference or low-degree neural activations can be implemented as polynomial maps over ciphertexts.

Mixed operations require careful control of noise parameters (e.g., $\text{Eval}_{\text{add}}(c_1, c_2)$8, $\text{Eval}_{\text{add}}(c_1, c_2)$9, standard deviation $\text{Eval}_{\text{mult}}(c_1, c_2)$0) and circuit depth—depth determines the number of successive adds/mults before decryption becomes unreliable due to noise growth (Dowerah et al., 2019). In FHE settings, the CKKS scheme handles approximate polynomial maps, supporting deep learning tasks with quantized/floating-point features (Meng et al., 17 Jan 2025).

4. Integration Example: Semantic Keypoint Preservation and Deep JSCC

Empirical validation of semantics preservation under HE is demonstrated using the SIFT pipeline over encrypted images:

• Construction of DoG and Gaussian-blurred images is feasible over Paillier-encrypted images, as pixel-wise addition and subtraction are supported.
• Decrypting the ciphertext after SIFT-style homomorphic processing yields keypoints nearly identical to plaintext, indicating that semantic structural features survive through ciphertext-domain computation (Meng et al., 17 Jan 2025).

For deep learning-based SemCom, as in privacy-preserved deep JSCC, both encoding and decoding networks are constrained to polynomial operations (squares, average pooling, multiplications), allowing their execution on CKKS-encrypted feature vectors (Meng et al., 17 Jan 2025). Quantitative evaluation shows that encrypted JSCC matches the plaintext JSCC classification accuracy within $\text{Eval}_{\text{mult}}(c_1, c_2)$1–$\text{Eval}_{\text{mult}}(c_1, c_2)$2 at high SNRs. However, computational time is significantly increased (e.g., $\text{Eval}_{\text{mult}}(c_1, c_2)$3 s for encrypted versus $\text{Eval}_{\text{mult}}(c_1, c_2)$4 s for plaintext processing on MNIST) (Meng et al., 17 Jan 2025).

Example Table: Classification Accuracy by Method (MNIST, SNR 10dB)

Model	Classification Accuracy
Separation (Model 1)	69.94 %
Plaintext deep JSCC (Model 2)	91.13 %
Plaintext privacy-preserved JSCC (Model 3)	89.88 %
HE-based privacy-preserved JSCC (Model 4)	89.60 %

5. Practical Considerations and Security Management

Practical deployment of HE in SemCom requires consideration of key management, efficiency, and operational viability:

• Key update mechanisms: Frequent key renewal (update interval $\text{Eval}_{\text{mult}}(c_1, c_2)$5) is proposed to mitigate the risk of key compromise, balancing breach probability against throughput. Throughput decreases as update frequency increases, while security increases (overall breach probability over horizon $\text{Eval}_{\text{mult}}(c_1, c_2)$6 is $\text{Eval}_{\text{mult}}(c_1, c_2)$7) (Meng et al., 17 Jan 2025).
• Noise management: Strategies include modulus switching or scaling constants (e.g., increasing $\text{Eval}_{\text{mult}}(c_1, c_2)$8) to bound cumulative noise and maintain decryptability (Dowerah et al., 2019).
• Batching: SIMD techniques pack multiple features into a single ciphertext (slot vectors), amplifying throughput for parallel operations.
• Key distribution: While symmetric-key SHE assumes secure out-of-band SK sharing, HE can be adapted to public-key scenarios using LWE-style key-switching.
• Channel robustness: The JSCC network is adapted to operate on ciphertext features; the removal of non-polynomial activations (e.g., ReLU$\text{Eval}_{\text{mult}}(c_1, c_2)$9x$m_1 + m_2$0) is empirically shown to maintain semantic robustness at high SNR, with a 6–7% accuracy drop at low SNR shrinking as channel conditions improve (Meng et al., 17 Jan 2025).

6. Research Challenges and Future Directions

Key obstacles and research frontiers for homomorphic encryption in SemCom include:

• Selective encryption: Encrypting only semantic-critical portions of the signal (e.g., salient regions via object detection/segmentation) to reduce computational overhead without sacrificing security for crucial features.
• Algorithmic optimization: Using partially homomorphic schemes (e.g., Paillier) where only additions suffice, and algorithmic accelerations such as Montgomery modular multiplication.
• Model compression and transfer: Applying pruning, quantization, knowledge distillation, and transfer learning to neural JSCC under HE constraints.
• Hardware acceleration: Deploying homomorphic arithmetic on FPGAs, GPUs, or ASICs (e.g., NTT engines for CKKS) to address latency.
• Robustness through adversarial training: Exposing JSCC models to heterogeneous or perturbed ciphertexts during training to enhance resistance to both channel noise and adversarial manipulation.
• Depth optimization: Circuits are to be restricted in multiplicative depth suitable for the semantic task; bootstrapping and noise reduction are minimized to maximize efficiency.

A plausible implication is that advances in HE scheme efficiency and selective encryption aligned with semantic relevance are critical for scalable, real-time privacy preservation in semantic communication, especially in mobile or resource-constrained environments.

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References: Dowerah, Krishnaswamy, "A Somewhat Homomorphic Encryption Scheme based on Multivariate Polynomial Evaluation" (Dowerah et al., 2019) Zhou et al., "Secure Semantic Communication With Homomorphic Encryption" (Meng et al., 17 Jan 2025)