Page 71 - ISCI’2017

This, the proposed authors’ scheme union of the transformation methods of information data

for the McEliece and Niederreiter schemes that allows to significantly increase the relative data rate.
Encryption exists by the rule (19), where I is the first information part of message (as in the McEliece

scheme) and e is the second information part of message (as in the Niederreiter scheme). Assuming
that w ( e =) t , then the relative speed will calculate by the following expression:
h

  n!  
k + log q  q − )1 t t! n ( t − )!   
(

R ** =     , (28)
n
where the first term corresponds to the first part of the of information data I in the numerator, and the
second term corresponds to the second part e.

For a case ≤0 w( e ≤) t the expression (28) will rewrite as

  t n!  

k + log q ∑ ( q − )1 i   

R ** =  i  =0 i! n ( i − )!   . (29)
n
For a case of using of the perfect codes the expression (29), as and (25), reaches a maximum.
Really, by substituting (27) in (29) we will obtain:

k + n − k
R * * = = 1.
n

Furthermore, the proposed scheme by the information encoding of a vector e allows to increase
the relative speed and for imperfect codes. As an example, estimates of relative speed of the

transmission information by using different the binary Goppa codes were been shown in Table 2. It
is obvious that the use of the proposed encryption scheme increases the relative speed of data

transmission by 30-40% compared with the best indicator among the McEliece and Niederreiter

schemes.

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