Private-key algebraic-code encryption with errors up to (dmin − 1) of the code

In most algebraic-code cryptosystems errors are added to the encoded plaintext to form the ciphertext. The number of added errors is usually less than or equal to the error-correcting capability of the code. In this paper we propose a method that permits the addition of almost double the number of these errors. The idea is based on the fact that linear codes can correct twice as many erasures as errors. A method for erasure creation, detection and correction is devised. Such an approach will allow for the addition of a number of errors that can not be corrected without side information about their position. This approach will result in a further increase in the security of these systems compared to systems with errors only. Based on this idea, a private-key cryptosystem with simple codes and permutations only is proposed and its security is evaluated.