Stream Cipher by Reed-Solomon Code

Reed-Solomon code or RS code is widely used for error corrections of data in transmission and storages. However, it is thought of as insecure for direct implementation in code based cryptography due to plaintext-known attacks. In recent years, McEliece cryptosystem with enhanced public key security by generalized RS code and Goppa code are discussed for hardware implementation. In this work, from another point of view a stream cipher based on RS code is proposed for communications between two parties, with the generalized RS code not used. First, it copies or shifts the stream cipher a few times to XOR with the message composed of a codeword; second, between the RS encoding and decoding it conceals the cipher within the RS code. There are two advantages with this scheme: First, compared with generalized RS code it uses systematic encoding instead of nonsystematic encoding, which decreases the power overhead. Second, the stream cipher requires no extra hardware rather than the RS encoding and decoding modules, which is already included in many computer systems or devices. Third, the stream cipher may depend on the difficulty of a well know NP-complete problem: the difficulty of decoding a random linear code. Meanwhile, since the cipher is a numerical value hidden in the codeword rather than a function with algorithmic definitions, the synchronization of cipher and messages can be easily held as a whole.