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+---
+id: wiki-2026-0508-homomorphic-encryption
+title: Homomorphic Encryption (HE)
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [HE, FHE, homomorphic encryption, fully homomorphic, CKKS, BFV, BGV, TFHE, privacy-preserving ML]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.93
+verification_status: applied
+tags: [cryptography, fhe, privacy, encryption, ml-privacy, secure-computation]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: C++ / Python
+  framework: Microsoft SEAL / OpenFHE / Concrete / TFHE-rs
+---
+
+# Homomorphic Encryption
+
+## 매 한 줄
+> **"매 encrypted data 의 의 의 직접 의 compute"**. 매 plaintext 의 reveal X. 매 Gentry 2009 (FHE breakthrough). 매 modern: 매 CKKS (real / approximate), BFV/BGV (integer), TFHE (Boolean). 매 응용: 매 privacy-preserving ML, 매 cloud, 매 medical.
+
+## 매 핵심
+
+### 매 levels
+- **Partial HE** (PHE): 매 single op (add or mul).
+- **Somewhat HE** (SHE): 매 limited depth.
+- **Leveled HE**: 매 known depth.
+- **Fully HE** (FHE): 매 unlimited depth via bootstrapping.
+
+### 매 schemes
+- **CKKS**: 매 approximate arithmetic on real / complex (modern ML).
+- **BFV / BGV**: 매 exact integer.
+- **TFHE**: 매 fast bootstrapping, Boolean.
+- **NTRU**, **GSW**: 매 historical / specialized.
+
+### 매 modern library
+- **Microsoft SEAL** (CKKS, BFV).
+- **OpenFHE** (모든 schemes).
+- **Concrete** (Zama, TFHE).
+- **TFHE-rs** (Rust).
+- **PySEAL**, **TenSEAL** (Python).
+
+### 매 응용
+1. **Privacy-preserving ML inference**.
+2. **Medical** (encrypted genomic).
+3. **Financial** (encrypted query).
+4. **Cloud compute** (zero-knowledge).
+5. **Federated learning** + HE.
+6. **Smart contract** (FHEVM).
+
+### 매 cost
+- 매 100x-10000x slowdown vs plaintext.
+- 매 modern hardware (GPU FHE) 의 의 의 reduce.
+- 매 ciphertext 매 100-1000x larger.
+
+## 💻 패턴
+
+### TenSEAL (CKKS, Python)
+```python
+import tenseal as ts
+
+context = ts.context(ts.SCHEME_TYPE.CKKS, poly_modulus_degree=8192,
+                      coeff_mod_bit_sizes=[60, 40, 40, 60])
+context.global_scale = 2**40
+context.generate_galois_keys()
+
+# 매 encrypt
+v1 = ts.ckks_vector(context, [1.0, 2.0, 3.0])
+v2 = ts.ckks_vector(context, [4.0, 5.0, 6.0])
+
+# 매 compute on ciphertext
+add = v1 + v2  # 매 [5, 7, 9]
+mul = v1 * v2  # 매 [4, 10, 18]
+dot = v1.dot(v2)  # 매 32
+
+# 매 decrypt only when needed
+print(add.decrypt())
+```
+
+### Microsoft SEAL (BFV, C++)
+```cpp
+#include "seal/seal.h"
+using namespace seal;
+
+EncryptionParameters parms(scheme_type::bfv);
+parms.set_poly_modulus_degree(4096);
+parms.set_coeff_modulus(CoeffModulus::BFVDefault(4096));
+parms.set_plain_modulus(1024);
+
+SEALContext context(parms);
+KeyGenerator keygen(context);
+PublicKey public_key; keygen.create_public_key(public_key);
+SecretKey secret_key = keygen.secret_key();
+
+Encryptor encryptor(context, public_key);
+Evaluator evaluator(context);
+Decryptor decryptor(context, secret_key);
+
+Plaintext x_plain("5"); Ciphertext x_encrypted;
+encryptor.encrypt(x_plain, x_encrypted);
+
+Ciphertext result;
+evaluator.square(x_encrypted, result);  // 매 5² = 25 (encrypted)
+```
+
+### Encrypted ML inference (logistic regression)
+```python
+def encrypted_logistic_regression(encrypted_x, weights_plaintext, bias_plaintext):
+    """매 매 매 weights / bias 매 plaintext, 매 input 매 encrypted."""
+    z = encrypted_x.dot(weights_plaintext) + bias_plaintext
+    # 매 sigmoid approximation (poly degree 3)
+    z2 = z * z
+    z3 = z2 * z
+    sigmoid_approx = 0.5 + 0.197 * z - 0.004 * z3  # 매 around 0
+    return sigmoid_approx
+```
+
+### Sigmoid polynomial approx (CKKS)
+```python
+def sigmoid_poly_approx(z):
+    """매 매 [-5, 5] 의 의 의 valid."""
+    # 매 deg 3 Taylor-like
+    z2 = z * z
+    z3 = z2 * z
+    z5 = z3 * z2
+    return 0.5 + 0.197 * z - 0.004 * z3 + 0.0001 * z5
+```
+
+### Encrypted neural net (CKKS)
+```python
+def encrypted_dense_layer(enc_x, weights, bias):
+    """매 매 layer 의 linear part 는 가능, 매 ReLU 는 polynomial approx."""
+    z = enc_x.mm(weights) + bias  # 매 matrix-vector
+    return polynomial_relu_approx(z)
+
+def polynomial_relu_approx(z):
+    """매 ReLU(x) ≈ a + b*x + c*x²."""
+    z2 = z * z
+    return 0.375 * z + 0.5 + 0.125 * z2  # 매 매 small range
+```
+
+### Bootstrapping (FHE refresh)
+```python
+# 매 SEAL CKKS 의 native bootstrap
+# 매 OpenFHE
+import openfhe
+parameters = openfhe.CCParamsCKKSRNS()
+parameters.SetMultiplicativeDepth(20)
+cc = openfhe.GenCryptoContext(parameters)
+cc.Enable(openfhe.PKESchemeFeature.PKE)
+cc.Enable(openfhe.PKESchemeFeature.LEVELEDSHE)
+cc.Enable(openfhe.PKESchemeFeature.ADVANCEDSHE)
+cc.Enable(openfhe.PKESchemeFeature.FHE)
+
+# 매 bootstrap
+ct_refreshed = cc.EvalBootstrap(ct)
+```
+
+### TFHE (Boolean fast)
+```rust
+use tfhe::boolean::prelude::*;
+
+let (client_key, server_key) = gen_keys();
+let ct1 = client_key.encrypt(true);
+let ct2 = client_key.encrypt(false);
+
+// 매 server side
+let result = server_key.and(&ct1, &ct2);
+
+// 매 client side
+let dec = client_key.decrypt(&result);  // 매 false
+```
+
+### Concrete-ML (Zama)
+```python
+from concrete.ml.sklearn import LogisticRegression
+
+model = LogisticRegression(n_bits=8)
+model.fit(X_train, y_train)
+
+# 매 compile to FHE
+model.compile(X_train)
+
+# 매 encrypted inference
+y_pred = model.predict(X_test_encrypted)
+```
+
+### Multi-party (HE + secret share)
+```python
+def hybrid_compute(encrypted_data_party_a, encrypted_data_party_b, secure_aggregator):
+    # 매 매 party 매 encrypt own data
+    # 매 aggregator 의 의 의 sum (HE)
+    sum_encrypted = encrypted_data_party_a + encrypted_data_party_b
+    # 매 only authorized 매 decrypt
+    return sum_encrypted
+```
+
+### Performance benchmark
+```python
+import time
+def benchmark_he(scheme='ckks'):
+    setup_t = time.perf_counter()
+    context = create_context(scheme)
+    keys = setup_keys(context)
+    setup_t = time.perf_counter() - setup_t
+    
+    enc_t = time.perf_counter()
+    ct = encrypt([1, 2, 3], context, keys.pub)
+    enc_t = time.perf_counter() - enc_t
+    
+    op_t = time.perf_counter()
+    ct2 = ct * ct
+    op_t = time.perf_counter() - op_t
+    
+    return {'setup': setup_t, 'encrypt': enc_t, 'op': op_t}
+```
+
+### Threshold HE (multi-key)
+```python
+# 매 multi-party with shared secret
+# 매 매 party 매 partial decryption share
+def threshold_decrypt(ciphertext, partial_shares, threshold):
+    if len(partial_shares) >= threshold:
+        return combine_shares(partial_shares, ciphertext)
+    raise ThresholdNotMet()
+```
+
+### FHEVM (smart contract on encrypted)
+```solidity
+// 매 fhEVM (Zama)
+import "fhevm/lib/TFHE.sol";
+
+contract EncryptedAuction {
+    euint64 highestBid;  // 매 encrypted
+    
+    function bid(bytes calldata encryptedAmount) public {
+        euint64 amount = TFHE.asEuint64(encryptedAmount);
+        highestBid = TFHE.max(highestBid, amount);
+    }
+}
+```
+
+## 매 결정 기준
+| 상황 | Scheme |
+|---|---|
+| ML inference (real) | CKKS |
+| Exact integer | BFV / BGV |
+| Boolean / lookup | TFHE |
+| Smart contract | FHEVM (TFHE-based) |
+| Multi-party | Threshold HE |
+| Best library | OpenFHE / SEAL / Concrete |
+
+**기본값**: 매 ML = CKKS + 매 polynomial activation. 매 boolean = TFHE. 매 always benchmark before commit (100-1000x cost).
+
+## 🔗 Graph
+- 부모: [[Practical-Cryptography|Cryptography]]
+- 응용: [[Privacy-Preserving-ML]] · [[Federated-Learning]]
+- Adjacent: [[Differential-Privacy]] · [[Secure Multi-party Computation]]
+
+## 🤖 LLM 활용
+**언제**: 매 medical / financial. 매 cloud trust. 매 multi-party compute.
+**언제 X**: 매 latency-critical. 매 plaintext 의 가능.
+
+## ❌ 안티패턴
+- **FHE for everything**: 매 cost overkill.
+- **No polynomial approx of activation**: 매 deep ReLU 의 hard.
+- **Wrong scheme**: 매 BFV for real-valued ML.
+- **No bootstrap when deep**: 매 noise overflow.
+
+## 🧪 검증 / 중복
+- Verified (Gentry 2009, CKKS 2017, OpenFHE / SEAL / Concrete docs).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-04-26 | Auto |
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — schemes + 매 TenSEAL / SEAL / TFHE / Concrete / FHEVM code |