Security for the GSW family with a growing noise budget

The explicit depth-compatible family supplies the native dimension routines and entropy surplus required by the actual-algorithm security reduction. Its exact decision-LWE assumption remains a hypothesis; hardness for the earlier parameter family does not establish hardness for this one. No decryption-circuit, bootstrappability or circular-security premise is hidden here.

Main results

• DepthParameters.indCPA: actual serialized encryption security under this family's exact LWE.

References

• Gentry, Sahai and Waters, Sections 3.1–3.2

theorem Cslib.Crypto.Homomorphic.GSW.DepthParameters.indCPA (hLWE : DecisionLWE Parameters.dimension samples width fun (k : ℕ) => noiseLaw (width k) (Parameters.noise k)) : Encryption.INDCPA (fun (k : ℕ) => keyGenSerialized (Parameters.dimension k) (samples k) (width k) (Parameters.noise k)) fun (k : ℕ) => encryptSerialized (Parameters.dimension k) (samples k) (width k)

The actual serialized algorithms are IND-CPA under decision LWE for this exact new family. The LWE premise for the earlier, narrower modulus family is not used.