Cryptology ePrint Archive: Report 2014/798

Multi-Identity and Multi-Key Leveled FHE from Learning with Errors

Michael Clear and Ciarán McGoldrick

Abstract: Gentry, Sahai and Waters recently presented the first (leveled) identity-based fully homomorphic (IBFHE) encryption scheme (CRYPTO 2013). Their scheme however only works in the single-identity setting; that is, homomorphic evaluation can only be performed on ciphertexts created with the same identity. In this work, we extend their results to the multi-identity setting and obtain a multi-identity IBFHE scheme that is selectively secure in the random oracle model under the hardness of Learning with Errors (LWE). We also obtain a multi-key fully-homomorphic encryption (FHE) scheme that is secure under LWE in the standard model. This is the first multi-key FHE based on a well-established assumption such as standard LWE. The multi-key FHE of López-Alt, Tromer and Vaikuntanathan (STOC 2012) relied on a non-standard assumption, referred to as the Decisional Small Polynomial Ratio assumption.

Category / Keywords: public-key cryptography / fully homomorphic encryption, identity-based FHE, multi-key FHE

Original Publication (with minor differences): IACR-CRYPTO-2015

Date: received 5 Oct 2014, last revised 2 Sep 2015

Contact author: clearm at scss tcd ie

Available format(s): PDF | BibTeX Citation

Note: Extended version of paper from CRYPTO 2015

Version: 20150902:125221 (All versions of this report)

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