On Constructing Homomorphic Encryption Schemes from Coding Theory

Abstract. Homomorphic encryption schemes are powerful cryptographic primitives that allow for a variety of applications. Consequently, a variety of proposals have been made in the recent decades but none of them was based on coding theory. The existence of such schemes would be interesting for several reasons. First, it is well known that having multiple schemes based on different hardness assumptions is advantageous. In case that one hardness assumption turns out be wrong, one can switch over to one of the alternatives. Second, fo some codes decoding (which would represent decryption in this case) is a linear mapping only (if the error is known), i.e., a comparatively simple operation. This would make such schemes interesting candidates for constructing of fully-homomorphic schemes based on bootstrapping (see Gentry, STOC’09). We show that such schemes are indeed possible by presenting a natural construction principle. Moreover, these possess several non-standard positive features. ...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Frederik Armknecht, Daniel Augot, Ludovic Perret, Ahmad-Reza Sadeghi
• Keywords: Construction Principle, Cryptographic Primitives, Homomorphic Encryption, IACR 2011