lossy_bootstrap

Engine.lossy_bootstrap(ciphertext, relinearization_key, conjugation_key, lossy_bootstrap_key)

Restores the level, which is the remaining number of multiplications you can do with a ciphertext, of a ciphertext. Using the lossy bootstrap key is faster but requires more memory than using the small bootstrap key. This function can only be used if the engine is initialized for bootstrapping.

• Input:
  • Ciphertext: The ciphertext to be bootstrapped. The values must be within the range [−1,1]. The level of the ciphertext must be at least the stage_count of the lossy bootstrap key
  • RelinearizationKey
  • ConjugationKey
  • LossyBootstrapKey
• Output:
  • Ciphertext: restored to a level of 16 - stage_count.

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)
lossy_bootstrap_key = engine.create_lossy_bootstrap_key(
    secret_key, stage_count=3
)

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

Engine.lossy_bootstrap(ciphertext, relinearization_key, conjugation_key, rotation_key, small_bootstrap_key, stage_count=3)

Restores the level, which is the remaining number of multiplications you can do with a ciphertext, of a ciphertext. Using the small bootstrap key requires less memory than using the lossy bootstrap key, but is slower. This function can only be used if the engine is initialized for bootstrapping.

• Input:
  • Ciphertext: The ciphertext to be bootstrapped. The values must be within the range [−1,1]. The level of the ciphertext must be at least the stage_count input value.
  • ConjugationKey
  • RotationKey
  • SmallBootstrapKey
  • stage_count: optional
    • Specifies the number of levels used in coefficient to the slot function and the slot to coefficient function of bootstrapping algorithm. The default value is 3, and values from 3 to 5 are supported. The larger the stage count, the faster the bootstrapping, but the lower level of the final result.
• Output:
  • Ciphertext: restored to a level of 16 - stage_count.

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.lossy_bootstrap(
    ciphertext,
    relinearization_key,
    conjugation_key,
    rotation_key,
    small_bootstrap_key,
)

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

Stage Count

Stage counts of 3, 4, and 5 are supported by default. For sparse bootstrapping, the following values are supported.

key_size	slot_count	1	2	3	4	5
medium	1	✅
medium	2	✅
medium	3	✅
medium	4	✅	✅
medium	5	✅	✅
medium	6		✅
medium	7		✅	✅
medium	8		✅	✅
medium	9		✅	✅
medium	10		✅	✅	✅
medium	11			✅	✅
medium	12			✅	✅
medium	13			✅	✅	✅
medium	14			✅	✅	✅
large	3	✅
large	4	✅
large	5	✅
large	6		✅
large	7		✅
large	8		✅
large	9		✅	✅
large	10		✅	✅
large	11			✅
large	12			✅	✅
large	13			✅	✅
large	14			✅	✅