In this paper, we present a new class of public-key cryptosystem (PKC) using algebraic coding on the basis of superimposition and randomness. The proposed PKC is featured by a generator matrix, in a characteristic form, where the generator matrix of an algebraic code is repeatedly used along with the generator matrix of a random code, as sub-matrices. This generator matrix, in the characteristic form, will be referred to as K-matrix. We show that the K-matrix yields the following advantages compared with the conventional schemes: (i) It realizes an abundant supply of PKCs, yielding more secure PKCs, (ii) It realizes a short public key.

Diagonal algebraic space time (DAST) block codes was proved to achieve the full transmit diversity over a quasi-static fading channel and to maintain 1 symbol/s/Hz. When the number of transmit antennas employed is larger than 2, DAST codes outperform the codes from orthogonal design with the equivalent spectral efficiency. However, due to the limitation on the signal constellation with complex integer points, no good 3bits/symbol DAST block code was given previously. In this paper, we propose a general form of 8-star-PSK constellations with integer points and present some theoretical results on the performance of the equivalent 8-star-PSK modulations. By using our proposed 8-star-PSKs, we present a searching algorithm to construct DAST codes with 3 bits per symbol under some criteria and investigate their performances over flat Rayleigh fading channels. It is shown that (5,2) 8-star-PSK scheme has a comparable performance to conventional 8PSK over additive white Gaussian noise (AWGN) channel and the corresponding DSAT codes constructed can achieve significant performance gain over flat Rayleigh fading channel.