Public-key algebraic encryption (PUAE) has certain advantages that mak
e it attractive in some applications. Variants of PUAE for private-key
algebraic encryption (PRAE) have been proposed subsequently. PRAE is
proven to be insecure under chosen plaintext attack. In the paper, som
e invariants of PRAE are studied, and a private-key cryptosystem based
on concatenation of codes is proposed and analysed. The new system is
composed of short-length codes and is designed to avoid the weaknesse
s in other PRAE systems. The system looks secure against known attacks
. Some methods to improve the system information rate and security are
also suggested.