Somewhat homomorphic encryption (SHE) ⇒ HE

Somewhat homomorphic encryption (SHE) implies HE.

Statement

Migrated verbatim from homomorphic-encryption:

Supports both additions and multiplications, but only up to a bounded number (bounded by the multiplicative depth of the circuit).

Migrated verbatim from homomorphic-encryption:

Supports arbitrary polynomial-time computation via bootstrapping: a special homomorphic evaluation of the decryption circuit that refreshes the noise in a ciphertext. First construction based on ideal lattices — Gen09.

Notes

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

This relation is stated on 2 pages; the statements above are all of them.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Variation section; SHE ⇒ HE is implicit, never asserted. No citation.
• No wiki slug ‘somewhat-homomorphic-encryption’.
• The bootstrapping reduction needs the SHE scheme to be bootstrappable (able to evaluate its own decryption circuit) and, for unbounded FHE without leveling, a circular-security assumption - neither is listed as a hypothesis here (circular security is mentioned only at line 66).
• No wiki slugs for SHE / FHE as distinct objects.