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Table 3.
The average
p
-values obtained from Coverage,
ρ
and DP-Coverage tests using
100 different keys (eSTREAM API-compliant source codes are used to test candidates)
Cipher
Coverage Test
ρ Test
DP Coverage Test
12
14
15
20
12
14
Crypt.MT.v3
0.421172
0.502259
0.438767
0.434522
0.491562
0.496520
Decim.v2
0.483673
0.498243
0.515213
0.561964
0.507519
0.434853
Dragon
0.467800
0.524956
0.531447
0.508126
0.475863
0.490167
Edon80
0.503102
0.504606
0.496585
0.506221
0.458080
0.511870
FFCSR-16
0.501281
0.536393
0.522143
0.505929
0.487775
0.501770
Grain128
0.507743
0.546400
0.521265
0.473777
0.514002
0.481063
HC-128
0.453212
0.502525
0.489393
0.475678
0.516889
0.513914
Lex
0.472844
0.497004
0.500221
0.475852
0.473196
0.497984
Mickey-128.v2
0.490894
0.499849
0.510405
0.479021
0.434051
0.544828
NLS.v2
0.508358
0.483571
0.474961
0.477997
0.516875
0.468336
Pomaranch.v1
0.433858
0.320433
0.506190
0.520325
0.483106
0.513709
Rabbit
0.512423
0.473658
0.522667
0.518543
0.470558
0.470504
Salsa20
0.485817
0.527911
0.533091
0.501501
0.430587
0.498490
Sosemanuk
0.439461
0.487562
0.497158
0.527524
0.555262
0.531222
Trivium
0.413683
0.500991
0.491455
0.495252
0.458730
0.508625
Fig. 6.
The number of
p
-values in intervals of length 0.1 versus expected values for
Pomaranch
6Con lu on
Statistical randomness testing plays an important role in analyzing the security
of cryptosystems. In this study, we propose a new framework of randomness test-
ing based on some properties of random mappings, focusing on TMTO attacks
against stream ciphers. Here, we present three chosen IV distinguishers namely;
(i) coverage test, (ii)
ρ
-test and (iii) DP-coverage test. We experimentally ob-
served some statistical deviations in the distribution of
p
-values in Pomaranch.
We observe that Pomaranch fails the Coverage(100,14) test with probability ap-
proximately equal to 0
.
3125 using a type I error
α
=0
.
01. Applying the test
anumberoftimes(
500) using the same secret key, the cipher can be distin-
guished from a random mapping.
≈
