Gentry, Sahai, and Waters (CRYPTO 2013) proposed the notion of multi-identity fully homomorphic encryption (MIFHE), which allows homomorphic evaluation of data encrypted under multiple identities. Subsequently, Clear and McGoldrick (CANS 2014, CRYPTO 2015) proposed leveled MIFHE candidates. However, the proposed MIFHE is either based on i O , which is a nonstandard assumption or single hop; that is, an arbitrary “evaluated” ciphertext under a set of identities is difficult to further evaluate when new ciphertexts are encrypted under additional identities. To overcome these drawbacks, we propose a leveled multi-hop MIFHE scheme. In a multi-hop MIFHE scheme, one can evaluate a group of ciphertexts under a set of identities to obtain an “evaluated” ciphertext, which can be further evaluated with other ciphertexts encrypted under additional identities. We also show that the proposed MIFHE scheme is secure against selective identity and chosen-plaintext attacks (IND-sID-CPA) under the learning with errors (LWE) assumption.
With the continuous and rapid development of Cloud Computing, Big Data and Internet of Things, it is extremely critical to protect data with homomorphism, privacy and integrity. For this, Rezaeibagha et al. proposed a new cryptographic primitive, called homomorphic signcryption. However, the current homomorphic signcryption schemes either only support linear computation or are built on nonstandard assumption. Therefore, it is interesting to design a leveled fully homomorphic signcryption (FHSC) scheme from the standard assumption. In this work, we present a leveled FHSC scheme from lattices. For this, we exert classical sign-then-encrypt method and surmount the difficulty of homomorphic multiplicative evaluation in the way of encrypting every elements. Moreover, we prove its indistinguishability against chosen plaintext attacks (IND-CPA) and strong unforgeability (SUF) under hard problems of standard lattices.INDEX TERMS Fully homomorphic signcryption, learning with errors, short integer solution.
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