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@ -380,43 +380,45 @@ Even though vector embeddings are not reversible to original images, they still
```python
from lightphe import LightPHE
def on_prem():
# build an additively homomorhic encryption cryptosystem
onprem_cs = LightPHE(algorithm_name = "Paillier", precision = 19)
# export keys
onprem_cs.export_keys("secret.txt")
onprem_cs.export_keys("public.txt", public=True)
# find l2 normalized and all positive vector embeddings - VGG-Face already does
source_embedding = DeepFace.represent("img1.jpg")[0]["embedding"]
# encrypt source embedding
encrypted_source_embedding = onprem_cs.encrypt(source_embedding)
return encrypted_source_embedding
# define a plain vectors for source and target
alpha = DeepFace.represent("img1.jpg")[0]["embedding"] # user tower
beta = DeepFace.represent("target.jpg")[0]["embedding"] # item tower
expected_similarity = sum(x * y for x, y in zip(alpha, beta))
def cloud(encrypted_source_embedding):
# restore the built cryptosystem in cloud with only public key
cloud_cs = LightPHE(algorithm_name = "Paillier", precision = 19, key_file = "public.txt")
# find l2 normalized and all positive vector embeddings - VGG-Face already does
target_embedding = DeepFace.represent("target.jpg")[0]["embedding"]
# find dot product of encrypted embedding and plain embedding
encrypted_cosine_similarity = encrypted_source_embedding @ target_embedding
# build an additively homomorphic cryptosystem (e.g. Paillier) on-prem
cs = LightPHE(algorithm_name = "Paillier", precision = 19)
# confirm that cloud cannot decrypt it even though it is calculated by cloud
with pytest.raises(ValueError, match="must have private key"):
cloud_cs.decrypt(encrypted_cosine_similarity)
return encrypted_cosine_similarity
# export keys
cs.export_keys("secret.txt"); cs.export_keys("public.txt", public=True)
def verify(encrypted_cosine_similarity, threshold = 0.68):
# restore the built cryptosystem on-prem with secret key
onprem_cs = LightPHE(algorithm_name = "Paillier", precision = 19, key_file = "secret.txt")
# restore cosine similarity
cosine_similarity = onprem_cs.decrypt(encrypted_cosine_similarity)[0]
print("same person" if cosine_similarity >= 1 - threshold else "different persons")
# encrypt source embedding
encrypted_alpha = cs.encrypt(alpha)
# remove cryptosystem and plain alpha not to be leaked in cloud
del cs, alpha
# restore the cryptosystem in cloud with only public key
cloud_cs = LightPHE(algorithm_name = "Paillier", precision = 19, key_file = "public.txt")
# dot product of encrypted and plain embedding pair
encrypted_cosine_similarity = encrypted_alpha @ beta
# computed by the cloud but cloud cannot decrypt it
with pytest.raises(ValueError, match="must have private key"):
cloud_cs.decrypt(encrypted_cosine_similarity)
# restore the cryptosystem on-prem with secret key
cs = LightPHE(algorithm_name = "Paillier", precision = 19, key_file = "secret.txt")
# decrypt similarity
calculated_similarity = cs.decrypt(encrypted_cosine_similarity)[0]
# verification
threshold = 0.68 # cosine distance threshold for VGG-Face and cosine
print("same person" if calculated_similarity >= 1 - threshold else "different persons")
# proof of work
assert abs(calculated_similarity - expected_similarity) < 1e-2
```
In this scheme, we leverage the computational power of the cloud to compute encrypted cosine similarity. However, the cloud has no knowledge of the actual calculations it performs. Only the secret key holder on the on-premises side can decrypt the encrypted cosine similarity and determine whether the pair represents the same person or different individuals.