Leveled Multi-Hop Multi-Identity Fully Homomorphic Encryption

Gentry, Sahai, and Waters (CRYPTO 2013) proposed the notion of multi-identity fully homomorphic encryption (MIFHE), which allows evaluation data encrypted under multiple identities. Subsequently, Clear McGoldrick (CANS 2014, CRYPTO 2015) leveled MIFHE candidates. However, is either based on i O , a nonstandard assumption or single hop; that is, an arbitrary “evaluated” ciphertext set identities difficult to further evaluate when new ciphertexts are additional To overcome these drawbacks, we propose multi-hop scheme. In scheme, one can group obtain ciphertext, be evaluated with other We also show scheme secure against selective identity chosen-plaintext attacks (IND-sID-CPA) learning errors (LWE) assumption.