Achieving Perfect Secrecy with One Bit Keys
Mohsen Karimzadeh Kiskani, Hamid R. Sadjadpour · 2018
Shannon perfect secrecy, also known as one-time pad, can only be achieved by using exactly a different key bit for each information bit. This requirement makes the implementation of perfect secrecy impractical in most applications. In this paper, a novel coding scheme for security is proposed that achieves perfect secrecy with only half a bit key per packet or equivalently, one bit key per two packets, regardless of the size of the packet. This surprising result implies that the ratio of key to the ratio of the data can asymptotically go to zero. The coding scheme has been applied to distributed cloud storage systems. Further, optimal code for security is defined and it has been shown that the proposed approach is optimal.