Hamming Distortion Based Secrecy Systems: To Foil the Eavesdropper With Finite Shared Key

Rate-distortion based secrecy is introduced in communication systems recently, where security is measured by the distortion that an eavesdropper can be forced to attain when reconstructing secret source symbols from an encrypted message. To maximize the distortion, previous works show that at least an unbounded number of secret keys growing with the block length is required for general distortion measure. Instead, in this letter, we will show that if hamming distortion, i.e. symbol error probability, is considered in secrecy systems, maximal hamming distortion is achievable with only a finite and constant number of shared secret keys, no matter how long the block length grows.