CKKS Bootstrappping

When a ciphertext is created, it has a fixed multiplication count called a level. When two cipehrtexts are multiplied, the resulting ciphertext will have the level reduced by one compared to the input ciphertexts. A ciphertext with level 0 can no longer be multiplied. It is possible to reset this level to a higher value by the bootstrapping operation.

Bootstrapping operation requires the bootstrap key. The bootstrap key incorporates every single fixed rotation key that is needed by the bootstrap operation. Because of this, the bootstrap key is quite large (about 14GB).

from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
bootstrap_key = engine.create_bootstrap_key(secret_key, stage_count=3)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(ciphertext, relinearization_key, conjugation_key, bootstrap_key)

Alternatively, the bootstrapping operation can be performed using the rotation key and the small bootstrap key instead of the bootstrapping key. This approach reduces memory usage to around 6GB but makes the operation slower.

from desilofhe import Engine

engine = Engine(use_bootstrap=True)
secret_key = engine.create_secret_key()
public_key = engine.create_public_key(secret_key)
relinearization_key = engine.create_relinearization_key(secret_key)
conjugation_key = engine.create_conjugation_key(secret_key)
rotation_key = engine.create_rotation_key(secret_key)
small_bootstrap_key = engine.create_small_bootstrap_key(secret_key)

message = [-1, 0, 1]
ciphertext = engine.encrypt(message, public_key, level=0)
bootstrapped = engine.bootstrap(ciphertext, relinearization_key, conjugation_key, rotation_key, small_bootstrap_key)

bootstrapped_stage_count_5 = engine.bootstrap(ciphertext, relinearization_key, conjugation_key, rotation_key, small_bootstrap_key, stage_count=5)