Page 69 - ISCI’2017

Thus, resistant to all known attacks the McEliece and Niederreiter cryptosystems based the binary

Goppa code comparable to the relative data rates. The highest resistance is provided for the relative
data rate 1/2 .. 2/3 and this significant disadvantage is partially removed in the following proposed

cryptosystem.
Proposed authors’ cryptosystem. Inherently the proposed cryptosystem is a further

development of the McEliece scheme with additional encoding of information data according to the
Niederreiter scheme. Cryptographic transformation process using the codes schematically shows in

Fig. 2:

− in the McEliece scheme an information is placed in the code word of the masked code.
Encryption consists of adding the random error vector, which can be interpreted as the session

(one-time) key. Decryption is decoding the code word, i.e. removal of the random error vector

from the code word, which includes an information sequence;
− in the Niederreiter scheme an information is placed in the error vector (by means of

equilibrium encoding). Syndromic sequence of the masked code that is not dependent on code
word calculates by the formed vector, i.e. arbitrary code word (considered to be zero by

default) can be added to original error vector. The syndromic vector can uniquely decode this
word on the receiving side, only this information is not extracted from a code word but from

the error vector;

− an information sequence is divided into two parts in the proposed scheme. The first part is
placed into a code word; the second part is placed into the error vector (by means of

equilibrium encoding). These two parts can be additionally transformed (mixed, encrypted,

etc.) to increasing of a resistance. Further, all transformations are done as in the McEliece
scheme. However, on the receiving side both an information is extracted from a code word

(the first part) and from error vector (the second part).

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