Two NP-complete Problems in Coding Theory with an Application in Code Based Cryptography

In this paper it is shown that the reconstruction of a punctured code from a given code is an NP-complete problem. Based on this observation a modification of code-based cryptosystems such as the Niederreiter scheme is suggested. In particular the modification is resistant to the Sidelnikov-Shestakov attack. Some other possible attacks are reviewed, and secure key parameters are estimated