| Given the continuing growth in computer networks and the associated communication demands, an increased awareness of the necessity for data security is expected. As the number of nodes in networks increases, the logistical problems associated with conventional (i.e., symmetric key) encryption will also increase. Thus, public key encryption seems destined to play a role in the solution of security problems. McEliece (1) proposed a public key system in 1978 based on linear error-correcting codes. Its security is derived from the intractability of the general decoding problem. The systems discussed here are modifications and extensions of the McEliece system. They offer potential solution to modern security problems.; The objective of this research is the development and analysis of a series of modifications to the McEliece system. These modifications are compared to the best-known public key system; RSA (2). The security of the integrated scheme (combined encryption and error-correction) is investigated through the development of an attack based on majority logic decoders. Several important observations are pointed out regarding the integrated scheme.; In 1990, Riek (3) proposed an approach to improve the information rate of McEliece's system. In this thesis, the analytical basis for this approach is presented. Some new attacks on the improved scheme are found. Also, the trade-off between security and bandwidth of the McEliece system is investigated here. The optimal system parameters to minimize bandwidth demands are found. The objective function is examined both over an error-free channel and noisy channels.; Finally, the separate and combined approaches to the data reliability and secrecy problem are considered. In both approaches a nonbinary code is used as the basis for the system over noisy channels. The possibility of using RS codes directly in McEliece's system is examined and rejected through the development of an attack. Several important features of these modifications are pointed out. The overall goal of establishing an encryption scheme that has a high information rate, security (by present measures), high speed, and reliability over various channels is found here. |
