On Public Key Encryption from Noisy Codewords

Several well-known public key encryption schemes, including those of Alekhnovich (FOCS 2003), Regev (STOC 2005), and Gentry, Peikert and Vaikuntanathan (STOC 2008), rely on the conjectured intractability of inverting noisy linear encodings. These schemes are limited in that they either require the underlying field to grow with the security parameter, or alternatively they can work over the binary field but have a low noise entropy that gives rise to sub-exponential attacks. Motivated by the goal of efficient public key cryptography, we study the possibility of obtaining security over the binary field by using different noise distributions. Inspired by an abstract on scheme of Micciancio (PKC 2010), we consider an abstract encryption scheme that unifies all the three schemes mentioned above and allows for arbitrary choices of the underlying field and noise distributions. Our main result establishes an unexpected connection between the power of such encryption schemes and additive...

• Type: Journal
• Year: 2016
• Where: PKC
• Authors: Eli Ben-Sasson, Iddo Ben-Tov, Ivan Damgård, Yuval Ishai, Noga Ron-Zewi
• Keywords: Cryptology, PKC 2016