Paper 2014/798

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

Michael Clear and Ciarán McGoldrick


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.

Note: Extended version of paper from CRYPTO 2015

Available format(s)
Public-key cryptography
Publication info
A minor revision of an IACR publication in CRYPTO 2015
fully homomorphic encryptionidentity-based FHEmulti-key FHE
Contact author(s)
clearm @ scss tcd ie
2015-09-02: last of 3 revisions
2014-10-10: received
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Creative Commons Attribution


      author = {Michael Clear and Ciarán McGoldrick},
      title = {Multi-Identity and Multi-Key Leveled FHE from Learning with Errors},
      howpublished = {Cryptology ePrint Archive, Paper 2014/798},
      year = {2014},
      note = {\url{}},
      url = {}
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