Integration of error correction, encryption, and signature based on linear error-correcting block codes

McEliece has proposed a public-key cryptosystem based on algebraic linear error-correcting block codes, in particular Goppa codes. Its security is derived from the intractibility of the general decoding problem. In McEliece's system, the Goppa code is used to correct errors invoked intentionally by the transmitter. A series of modifications are introduced on McEliece's system that allow the Goppa code to be used for the correction and/or detection of errors caused by noise on the communication channel. The channel is modeled as an M-state Markovian chain in which each state is associated with a binary symmetric channel with fixed bit error rate. In the modified system, the code is used as an FEC, type-I hybrid ARQ, and adaptive type-I hybrid ARQ protocols. A tradeoff between reliability and security is thus created, and the modified system provides error-correction and encryption.; Xinmei's scheme and the Harn-Wang modified version of Xinmei's scheme are both true trapdoor digital signature schemes based on linear error-correcting block codes. The securities of the schemes were investigated where it was shown that both schemes are vulnerable to several attacks. A scheme was devised that overcomes the weaknesses of both schemes. Further analysis of this scheme indicated the vulnerability of this scheme to a different attack. Using the previous attacks as guidelines, a new signature scheme was constructed. Extensive security analysis on this new scheme was conducted; the scheme was shown to be secure against all the attacks that were successful on the previous schemes as well as other attacks. The new scheme is designed to be used with the modified McEliece's system, and thus a provision for encryption, error correction, and signature is achieved.