Page 64 - ISCI’2017

but the total number of operations will be reduced due to the reduced dimension of modules.

3
3
3
Complexity of transformation will be 2 l = 3l and the values in Table 1 correspond to this
2
assessment. The size of the module and the appropriate assessment of resistance (as the equivalent
the length of a symmetric cipher key) was shown in the work [49]. Estimates of the volume of the
quantum resources, which need to solve of some asymmetric cryptographic tasks with the help of

Shor's algorithm at different parameters of these tasks, and a comparison of them with a complexity
of sort out problem solution at searching of symmetric cipher key, were been presented in the work

3
[50]. In particular, the assessment 4m of time complexity of the quantum factorization Shor's
algorithm gives for m-bits number, and the volumes, which were shown in Table 1, correspond to this
assessment.

Description of block symmetric ciphers AES (FIPS-197) and Kalyna (DSTU 7624:2014)

presents in the works [44, 45]. Research complexity of quantum algorithms for cryptanalysis of
symmetric ciphers was performed in the work [51]. In particular, the quantum Grover’s algorithm for

the solution of brute force problems, includes brute force searching of m-bits secret key of symmetric
π
m
cipher, requires of execution of 2 iterations. In practice, this leads to a corresponding reduction
4
in resistance (twice the equivalent length of the key is reduced).
It should be noted to a high speed of crypto-transformation in the McEliece scheme, which

approaching by encryption speed to block symmetric ciphers. Really, at using the Goppa code with

recommended in the author’s manuscript [15] parameters
n = 1024, k = 524, t = 50, d = 2t + 1 = 101,

needs to execute no more than 524 XOR-operations per one processed word for an encryption by

matrix method (calculation IG + ). For example, one from the most fast modern block symmetric
e
X
ciphers AES (American Encryption Standard, FIPS-197) requires to encryption no less 4 XOR-
operations to 32-bits word in each round [44] that at 10 rounds consists no less 40 XOR-operations.

The second important advantage of the McEliece scheme is a possibility to combine a crypto-
transformation with errors resulting control. Really, if at the cryptogram forming (18) a random errors

vector e and weights w(e)< t can be used, then will allow a possibility of a control errors within
correcting capacity simultaneously with the cryptographic data conversion. Weight reducing of vector

e decreases a cryptographic persistence of the McEliece scheme, but increases a data transmission
noise immunity, i.e. changing the w(e) can adaptively respond to the need for appropriate security

services in this “hybrid” scheme.

Let us denote fraction of weight vector error of the vector e, attributable to the artificial
introduction of the cryptogram formation (see to expression (18)) by the symbol ρ = w(e) / t. Then

64