Information Technology Reference
In-Depth Information
3 Cryptosystem Behavior Analysis
The proposed algorithm evaluation was done using essentially three concepts: the
entropy and randomness of the cryptograms and the mutual information of the en-
cryption process. For this evaluation 5 files with different formats and sizes were
used, and the proposed cryptosystem was compared with common cryptosystems as
AES and IDEA.
The entropy is used as a measure of the message diffusion by the encryption proc-
ess. So that, if the cryptogram entropy is maximum, it means that the cryptogram will
be able to have a statistical distribution very near to the uniform distribution. This
condition seeks to affect the statistical distribution of plaintext, and thus the crypto-
gram will achieve the state of greatest uncertainty. In the calculations a maximum
entropy H MAX = 8 has been considered for the cryptograms. Table 1 shows the results
of the entropy for each cryptogram.
Mutual information measures the amount of information that contributes on a vari-
able, the knowledge of another one. In this case, the mutual information is used as a
measure of the relationship between plaintext and its respective cryptogram (see Table
2). A cryptosystem can be considered safe if the amount of information contributed by
the knowledge of the cryptogram C in the entropy of the plaintext M is zero.
The randomness of the produced cryptograms has been evaluated using the NIST
random tests [10]. Table 3 shows the results of applying the suite of NIST tests to a
specific file, which was ciphered with each one of the different cryptosystems. In
order to be able to apply the tests, the cryptosystems were binarized in a stream of 100
million bits. Note that proposed cryptosystem was successful in all the NIST SP800-
22 test suite cases; this means that the cryptogram has the appearance of a random
sequence.
Table 1. Entropy of the cryptograms using the proposed, AES and IDEA cryptosystems
Entropy
File type
Plaintext
Proposed
cryptosystem
AES
IDEA
TXT
5.0802508
7.999173637
7.9989214
7.9992133
DOC
5.8174680
7.999426499
7.9994851
7.9995290
RTF
3.5727449
7.999939016
7.9999467
7.9999444
PPT
6.6895915
7.999671958
7.9995576
7.9996626
XML
5.4487835
7.999824941
7.9998163
7.9998091
Table 2. Mutual information of the proposed, AES, and IDEA cryptosystems
Mu t ual Information
File type
Proposed
cryptosystem
AES
IDEA
TXT
0.069618783
0.0710524
0.0695141
DOC
0.144927532
0.1434934
0.1449023
RTF
0.004785542
0.0047777
0.0047549
PPT
0.100683255
0.1013163
0.1014454
XML
0.017484572
0.0177723
0.0177751
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