An immediate corollary is that known schemes that are based on the hardness of decoding in the presence of low hamming-weight noise cannot be fully homomorphic. This applies to known schemes such as LPN-based symmetric or public key encryption.
Using these techniques, we show that the recent candidate fully homomorphic encryption, suggested by Bogdanov and Lee (ePrint '11, henceforth BL), is insecure. In fact, we show two attacks on the BL scheme: One that uses homomorphism, and another that directly attacks a component of the scheme.
Category / Keywords: public-key cryptography / homomorphic encryption Date: received 24 Apr 2012, last revised 1 Sep 2012 Contact author: zvika at stanford edu Available format(s): PDF | BibTeX Citation Version: 20120901:225611 (All versions of this report) Discussion forum: Show discussion | Start new discussion