Fully homomorphic encryption from a circular-secure bootstrappable scheme #
One sampled base key and its self-encrypted secret define a fixed-key scheme permitting every
finite Boolean circuit, without a depth parameter in key generation. The actual algorithms have
perfect correctness, unchanged polynomial secret and ciphertext widths, polynomial decryption
circuits, uniform native efficiency and IND-CPA security. FixedKey.evaluate_spec additionally
allows prior evaluation outputs as inputs and preserves their width and plaintext under that
same key.
The input assumptions concern the base scheme and its actual decryption circuits. In particular,
Encryption.CircularSecure is the explicit joint one-key real-versus-zero experiment, in addition
to ordinary base IND-CPA. This is a conditional bootstrapping construction, not an instantiation
of the premises by a concrete lattice scheme. No circuit privacy or exact concrete-security
loss is asserted.
Main results #
Cslib.Crypto.Homomorphic.FixedKey.fullyHomomorphic: correctness for all finite circuits, compactness, native efficiency and security of the same constructed algorithms.
References #
A circular-secure bootstrappable base scheme yields one compact, efficient, IND-CPA scheme
for all finite Boolean circuits. All conclusions refer to scheme D; its key generator takes
only the security parameter, and its decryption circuits are exactly those generated by D.
The stronger evaluate_spec also certifies arbitrary repeated evaluation.