SRG | Security Research Group

RFID

Introduction

This work presents an ultra-light, cryptographic, mutual authentication protocol that is much more secure than its predecessors, for RFID tags. Traditional and rotational cryptanalysis has shown that previous ultra-light schemes based on triangular functions and rotation, suffer from the same vulnerabilities. In this paper, we summarize the successful attacks on previous schemes and demonstrate further attacks on two recent ultra-lightweight protocols. Then a proposal that removes the mentioned weaknesses which resists all known passive attacks is made. The proposal pays attention to the properties and rules of ARX-c systems. It also involves the insertion of parts of AES S-Boxes into the temperings of the Mersenne Twister, which is used as a deterministic random number generator. Apart from previous schemes, the proposal is compared and contrasted against well hashing and encryption algorithms recommended for RFID tags, as well. 

ENT Results

ENT 217Results, Random Inputs from

List of Input files to the ENT:

eMT:

Byte

Bit
Entropy = 7.999876 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 269.73, and randomly
would exceed this value 25.16 percent of the times.

Arithmetic mean value of data bytes is 127.4784 (127.5 = random).
Monte Carlo value for Pi is 3.143188477 (error 0.05 percent).
Serial correlation coefficient is 0.000946 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 0.39, and randomly
would exceed this value 52.99 percent of the times.

Arithmetic mean value of data bits is 0.5001 (0.5 = random).
Monte Carlo value for Pi is 3.143188477 (error 0.05 percent).
Serial correlation coefficient is -0.000437 (totally uncorrelated = 0.0).

eMT(Zi& Zi+1):

Byte

Bit
Entropy = 7.999875 bits per byte.

Optimum compression would reduce the size
of this 1572852 byte file by 0 percent.

Chi square distribution for 1572852 samples is 271.84, and randomly
would exceed this value 22.39 percent of the times.

Arithmetic mean value of data bytes is 127.5183 (127.5 = random).
Monte Carlo value for Pi is 3.141167764 (error 0.01 percent).
Serial correlation coefficient is 0.000223 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582816 bit file by 0 percent.

Chi square distribution for 12582816 samples is 0.34, and randomly
would exceed this value 56.03 percent of the times.

Arithmetic mean value of data bits is 0.5001 (0.5 = random).
Monte Carlo value for Pi is 3.141167764 (error 0.01 percent).
Serial correlation coefficient is 0.000067 (totally uncorrelated = 0.0).

MixBits:

Byte

Bit
Entropy = 7.999910 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 196.23, and randomly
would exceed this value 99.75 percent of the times.

Arithmetic mean value of data bytes is 127.3920 (127.5 = random).
Monte Carlo value for Pi is 3.142623901 (error 0.03 percent).
Serial correlation coefficient is -0.000152 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 3.56, and randomly
would exceed this value 5.91 percent of the times.

Arithmetic mean value of data bits is 0.4997 (0.5 = random).
Monte Carlo value for Pi is 3.142623901 (error 0.03 percent).
Serial correlation coefficient is -0.000043 (totally uncorrelated = 0.0).

MixBits (Zi& Zi+1):

Byte

Bit
Entropy = 7.999885 bits per byte.

Optimum compression would reduce the size
of this 1572852 byte file by 0 percent.

Chi square distribution for 1572852 samples is 250.50, and randomly
would exceed this value 56.78 percent of the times.

Arithmetic mean value of data bytes is 127.6035 (127.5 = random).
Monte Carlo value for Pi is 3.138634786 (error 0.09 percent).
Serial correlation coefficient is -0.000331 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582816 bit file by 0 percent.

Chi square distribution for 12582816 samples is 2.60, and randomly
would exceed this value 10.68 percent of the times.

Arithmetic mean value of data bits is 0.5002 (0.5 = random).
Monte Carlo value for Pi is 3.138634786 (error 0.09 percent).
Serial correlation coefficient is 0.000522 (totally uncorrelated = 0.0).

A:

Byte

Bit
Entropy = 7.999888 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 244.10, and randomly
would exceed this value 67.73 percent of the times.

Arithmetic mean value of data bytes is 127.4395 (127.5 = random).
Monte Carlo value for Pi is 3.149490356 (error 0.25 percent).
Serial correlation coefficient is 0.001624 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 0.02, and randomly
would exceed this value 89.15 percent of the times.

Arithmetic mean value of data bits is 0.5000 (0.5 = random).
Monte Carlo value for Pi is 3.149490356 (error 0.25 percent).
Serial correlation coefficient is 0.000083 (totally uncorrelated = 0.0).

B:

Byte

Bit
Entropy = 7.999879 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 264.93, and randomly
would exceed this value 32.14 percent of the times.

Arithmetic mean value of data bytes is 127.4449 (127.5 = random).
Monte Carlo value for Pi is 3.141967773 (error 0.01 percent).
Serial correlation coefficient is -0.000237 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 1.37, and randomly
would exceed this value 24.14 percent of the times.

Arithmetic mean value of data bits is 0.4998 (0.5 = random).
Monte Carlo value for Pi is 3.141967773 (error 0.01 percent).
Serial correlation coefficient is -0.000279 (totally uncorrelated = 0.0).

C:

Byte

Bit

Entropy = 7.999876 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 269.71, and randomly
would exceed this value 25.19 percent of the times.

Arithmetic mean value of data bytes is 127.4078 (127.5 = random).
Monte Carlo value for Pi is 3.144104004 (error 0.08 percent).
Serial correlation coefficient is -0.000006 (totally uncorrelated = 0.0).

 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 0.94, and randomly
would exceed this value 33.19 percent of the times.

Arithmetic mean value of data bits is 0.4999 (0.5 = random).
Monte Carlo value for Pi is 3.144104004 (error 0.08 percent).
Serial correlation coefficient is -0.000216 (totally uncorrelated = 0.0).

D:

Byte

Bit
Entropy = 7.999899 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 219.72, and randomly
would exceed this value 94.64 percent of the times.

Arithmetic mean value of data bytes is 127.5115 (127.5 = random).
Monte Carlo value for Pi is 3.146194458 (error 0.15 percent).
Serial correlation coefficient is 0.001039 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 0.27, and randomly
would exceed this value 60.12 percent of the times.

Arithmetic mean value of data bits is 0.4999 (0.5 = random).
Monte Carlo value for Pi is 3.146194458 (error 0.15 percent).
Serial correlation coefficient is 0.000021 (totally uncorrelated = 0.0).

IDS:

Byte

Bit
Entropy = 7.999885 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 250.71, and randomly
would exceed this value 56.42 percent of the times.

Arithmetic mean value of data bytes is 127.4951 (127.5 = random).
Monte Carlo value for Pi is 3.139434814 (error 0.07 percent).
Serial correlation coefficient is 0.001224 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 0.10, and randomly
would exceed this value 75.69 percent of the times.

Arithmetic mean value of data bits is 0.5000 (0.5 = random).
Monte Carlo value for Pi is 3.139434814 (error 0.07 percent).
Serial correlation coefficient is -0.000162 (totally uncorrelated = 0.0).

IDS (Zi& Zi+1):

Byte

Bit
Entropy = 7.999884 bits per byte.

Optimum compression would reduce the size
of this 1572852 byte file by 0 percent.

Chi square distribution for 1572852 samples is 253.01, and randomly
would exceed this value 52.35 percent of the times.

Arithmetic mean value of data bytes is 127.4550 (127.5 = random).
Monte Carlo value for Pi is 3.147591763 (error 0.19 percent).
Serial correlation coefficient is 0.000408 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582816 bit file by 0 percent.

Chi square distribution for 12582816 samples is 0.01, and randomly
would exceed this value 92.45 percent of the times.

Arithmetic mean value of data bits is 0.5000 (0.5 = random).
Monte Carlo value for Pi is 3.147591763 (error 0.19 percent).
Serial correlation coefficient is -0.000523 (totally uncorrelated = 0.0)..

K2:

Byte

Bit
Entropy = 7.999879 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 263.92, and randomly
would exceed this value 33.72 percent of the times.

Arithmetic mean value of data bytes is 127.5978 (127.5 = random).
Monte Carlo value for Pi is 3.139389038 (error 0.07 percent).
Serial correlation coefficient is -0.000024 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 3.79, and randomly
would exceed this value 5.16 percent of the times.

Arithmetic mean value of data bits is 0.5003 (0.5 = random).
Monte Carlo value for Pi is 3.139389038 (error 0.07 percent).
Serial correlation coefficient is 0.000261 (totally uncorrelated = 0.0).

K3:

Byte

Bit
Entropy = 7.999892 bits per byte.

Optimum compression would reduce the size
of this 1572864 byte file by 0 percent.

Chi square distribution for 1572864 samples is 236.32, and randomly
would exceed this value 79.35 percent of the times.

Arithmetic mean value of data bytes is 127.4093 (127.5 = random).
Monte Carlo value for Pi is 3.133438110 (error 0.26 percent).
Serial correlation coefficient is 0.000306 (totally uncorrelated = 0.0).		 Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 12582912 bit file by 0 percent.

Chi square distribution for 12582912 samples is 1.41, and randomly
would exceed this value 23.46 percent of the times.

Arithmetic mean value of data bits is 0.4998 (0.5 = random).
Monte Carlo value for Pi is 3.133438110 (error 0.26 percent).
Serial correlation coefficient is 0.000190 (totally uncorrelated = 0.0).

DAVID SEXTON'S BATTERY TEST

 

eMT A

the bit runs statistic = 16.91641 [P = 0.0762]*
the alt. 1 bit runs statistic = 19.12343 [P = 0.0387]*
the alt. 2 bit runs statistic = 7.11588 [P = 0.7145]
the alt. 3 bit runs statistic = 9.08468 [P = 0.5241]
the alt. 4 bit runs statistic = 18.58891 [P = 0.0458]*
the alt. 5 bit runs statistic = 14.44606 [P = 0.1536]
the block bit freq. statistic = 255.44775 [P = 0.4980]
the bit frequency statistic = 1.36189 [P = 0.2432]
the tidbit frequency statistic = 3.58092 [P = 0.3104]
the nibble frequency statistic = 14.66498 [P = 0.4758]
the byte frequency statistic = 262.45264 [P = 0.3608]
the bit 0 statistic = 0.12497 [P = 0.7237]
the bit 1 statistic = 0.95749 [P = 0.3278]
the bit 2 statistic = 2.30304 [P = 0.1291]
the bit 3 statistic = 0.09523 [P = 0.7576]
the bit 4 statistic = 0.63813 [P = 0.4244]
the bit 5 statistic = 0.11024 [P = 0.7399]
the bit 6 statistic = 0.05133 [P = 0.8208]
the bit 7 statistic = 1.00000 [P = 0.3173]
the overall bit statistic = 5.28044 [P = 0.7272]
the 8-bit-sum statistic = 4.67821 [P = 0.7914]
the 16-bit-sum statistic = 9.16262 [P = 0.0102]*
the 32-bit-sum statistic = 1.42806 [P = 0.4897]
the odd/even-bit-sum statistic = 56.58462 [P = 0.7027]
the 64-bit matrix statistic = 313.49121 [P = 0.0073]**
the 128-bit matrix statistic = 273.91650 [P = 0.1985]
the 256-bit matrix statistic = 288.89453 [P = 0.0710]*
the 512-bit matrix statistic = 236.74756 [P = 0.7878]
the 1024-bit matrix statistic = 200.22119 [P = 0.9953]^^
the 2048-bit matrix statistic = 251.10059 [P = 0.5572]
the bit prediction A statistic = 0.24241 [P = 0.6225]
the bit prediction B statistic = 5.24323 [P = 0.0220]*
the bit prediction C statistic = 1.78539 [P = 0.1815]
the bit prediction D statistic = 0.67525 [P = 0.4112]
the bit prediction E statistic = 1.87885 [P = 0.1705]
the byte prediction A statistic = 1.13333 [P = 0.2871]
the byte prediction B statistic = 0.14118 [P = 0.7071]
the byte prediction C statistic = 0.31765 [P = 0.5730]
the byte prediction D statistic = 0.08848 [P = 0.7661]
the byte repetition statistic = 0.54142 [P = 0.4618]
the 2-byte AND statistic = 7.55244 [P = 0.2728]
the 4-byte AND statistic = 2.29755 [P = 0.3170]
the 4-byte AND-OR statistic = 0.77068 [P = 0.6802]
the 2-byte up/down statistic = 1.76852 [P = 0.4130]
the 4-byte up/down statistic = 5.47047 [P = 0.6027]
the rect. distance statistic = 3.91695 [P = 0.6879]
the 4-byte collision statistic = 0.92141 [P = 0.3371]
the 6-byte collision statistic = 0.03675 [P = 0.8480]
the 8-byte collision statistic = 0.13106 [P = 0.7173]
the 12-byte collision statistic = 0.42721 [P = 0.5134]
the 16-byte collision statistic = 0.72974 [P = 0.3930]
the 24-byte collision statistic = 0.48487 [P = 0.4862]
the 32-byte collision statistic = 1.66227 [P = 0.1973]
the 1-byte offset XOR statistic = 264.58594 [P = 0.3268]
the 2-byte offset XOR statistic = 246.44141 [P = 0.6382]
the 6-byte offset XOR statistic = 270.93457 [P = 0.2355]
the 24-byte offset XOR stat. = 231.43848 [P = 0.8526]
the 120-byte offset XOR stat. = 288.39746 [P = 0.0738]*
the 720-byte offset XOR stat. = 273.25781 [P = 0.2063]
the 5040-byte offset XOR stat. = 273.25293 [P = 0.2064]
the 40320-byte offset XOR stat. = 210.17969 [P = 0.9814]^
the 362880-byte off. XOR stat. = 289.05176 [P = 0.0701]*
the mod 3 statistic = 0.25772 [P = 0.8791]
the mod 5 statistic = 5.32286 [P = 0.2557]
the mod 7 statistic = 6.73563 [P = 0.3460]
the mod 11 statistic = 7.51404 [P = 0.6762]
the mod 13 statistic = 14.08170 [P = 0.2955]
the mod 17 statistic = 10.21892 [P = 0.8549]
the mod 19 statistic = 19.83270 [P = 0.3423]
the mod 23 statistic = 20.18278 [P = 0.5716]
------------------------------------------------------------------------------
the bit runs statistic = 5.50454 [P = 0.8550]
the alt. 1 bit runs statistic = 13.27752 [P = 0.2086]
the alt. 2 bit runs statistic = 11.80450 [P = 0.2984]
the alt. 3 bit runs statistic = 8.26894 [P = 0.6026]
the alt. 4 bit runs statistic = 18.91678 [P = 0.0413]*
the alt. 5 bit runs statistic = 6.21333 [P = 0.7970]
the block bit freq. statistic = 239.19385 [P = 0.7673]
the bit frequency statistic = 0.27542 [P = 0.5997]
the tidbit frequency statistic = 5.53846 [P = 0.1364]
the nibble frequency statistic = 26.36621 [P = 0.0343]*
the byte frequency statistic = 245.66064 [P = 0.6514]
the bit 0 statistic = 6.79865 [P = 0.0091]**
the bit 1 statistic = 0.01154 [P = 0.9145]^
the bit 2 statistic = 4.98371 [P = 0.0256]*
the bit 3 statistic = 1.14975 [P = 0.2836]
the bit 4 statistic = 0.08698 [P = 0.7681]
the bit 5 statistic = 3.69360 [P = 0.0546]*
the bit 6 statistic = 0.10895 [P = 0.7413]
the bit 7 statistic = 3.48639 [P = 0.0619]*
the overall bit statistic = 20.31957 [P = 0.0092]**
the 8-bit-sum statistic = 3.96140 [P = 0.8606]
the 16-bit-sum statistic = 0.30772 [P = 0.8574]
the 32-bit-sum statistic = 1.77396 [P = 0.4119]
the odd/even-bit-sum statistic = 69.54945 [P = 0.2665]
the 64-bit matrix statistic = 319.12256 [P = 0.0039]**
the 128-bit matrix statistic = 238.24512 [P = 0.7670]
the 256-bit matrix statistic = 288.52686 [P = 0.0731]*
the 512-bit matrix statistic = 277.21191 [P = 0.1621]
the 1024-bit matrix statistic = 283.47656 [P = 0.1064]
the 2048-bit matrix statistic = 273.28662 [P = 0.2060]
the bit prediction A statistic = 1.15152 [P = 0.2832]
the bit prediction B statistic = 0.41153 [P = 0.5212]
the bit prediction C statistic = 1.24524 [P = 0.2645]
the bit prediction D statistic = 0.35267 [P = 0.5526]
the bit prediction E statistic = 0.00526 [P = 0.9422]^
the byte prediction A statistic = 2.02966 [P = 0.1543]
the byte prediction B statistic = 0.51863 [P = 0.4714]
the byte prediction C statistic = 2.40221 [P = 0.1212]
the byte prediction D statistic = 1.30613 [P = 0.2531]
the byte repetition statistic = 0.45319 [P = 0.5008]
the 2-byte AND statistic = 8.46326 [P = 0.2061]
the 4-byte AND statistic = 0.28434 [P = 0.8675]
the 4-byte AND-OR statistic = 0.96773 [P = 0.6164]
the 2-byte up/down statistic = 2.90012 [P = 0.2346]
the 4-byte up/down statistic = 9.73065 [P = 0.2044]
the rect. distance statistic = 12.28262 [P = 0.0560]*
the 4-byte collision statistic = 0.49111 [P = 0.4834]
the 6-byte collision statistic = 0.30460 [P = 0.5810]
the 8-byte collision statistic = 0.00195 [P = 0.9648]^
the 12-byte collision statistic = 2.29021 [P = 0.1302]
the 16-byte collision statistic = 0.01835 [P = 0.8922]
the 24-byte collision statistic = 0.10380 [P = 0.7473]
the 32-byte collision statistic = 0.56012 [P = 0.4542]
the 1-byte offset XOR statistic = 289.30566 [P = 0.0688]*
the 2-byte offset XOR statistic = 242.54590 [P = 0.7023]
the 6-byte offset XOR statistic = 226.23633 [P = 0.9024]^
the 24-byte offset XOR stat. = 278.18066 [P = 0.1524]
the 120-byte offset XOR stat. = 312.69727 [P = 0.0079]**
the 720-byte offset XOR stat. = 288.51758 [P = 0.0731]*
the 5040-byte offset XOR stat. = 249.60352 [P = 0.5836]
the 40320-byte offset XOR stat. = 275.55957 [P = 0.1797]
the 362880-byte off. XOR stat. = 313.19824 [P = 0.0075]**
the mod 3 statistic = 0.23185 [P = 0.8905]
the mod 5 statistic = 8.45700 [P = 0.0762]*
the mod 7 statistic = 2.98952 [P = 0.8102]
the mod 11 statistic = 9.34211 [P = 0.5000]
the mod 13 statistic = 3.81230 [P = 0.9866]^
the mod 17 statistic = 23.10464 [P = 0.1110]
the mod 19 statistic = 20.89438 [P = 0.2848]
the mod 23 statistic = 12.87915 [P = 0.9365]^
------------------------------------------------------------------------------

 

B

C

the bit runs statistic = 7.79699 [P = 0.6487]
the alt. 1 bit runs statistic = 9.47736 [P = 0.4875]
the alt. 2 bit runs statistic = 5.97983 [P = 0.8170]
the alt. 3 bit runs statistic = 8.97908 [P = 0.5341]
the alt. 4 bit runs statistic = 8.82896 [P = 0.5484]
the alt. 5 bit runs statistic = 6.77680 [P = 0.7463]
the block bit freq. statistic = 275.21899 [P = 0.1954]
the bit frequency statistic = 1.43704 [P = 0.2306]
the tidbit frequency statistic = 4.53295 [P = 0.2094]
the nibble frequency statistic = 19.78632 [P = 0.1803]
the byte frequency statistic = 280.84277 [P = 0.1277]
the bit 0 statistic = 1.12062 [P = 0.2898]
the bit 1 statistic = 4.19770 [P = 0.0405]*
the bit 2 statistic = 1.13722 [P = 0.2862]
the bit 3 statistic = 0.82483 [P = 0.3638]
the bit 4 statistic = 0.36423 [P = 0.5462]
the bit 5 statistic = 0.36896 [P = 0.5436]
the bit 6 statistic = 0.72849 [P = 0.3934]
the bit 7 statistic = 2.92063 [P = 0.0875]*
the overall bit statistic = 11.66268 [P = 0.1669]
the 8-bit-sum statistic = 8.41506 [P = 0.3940]
the 16-bit-sum statistic = 4.47611 [P = 0.1067]
the 32-bit-sum statistic = 4.03280 [P = 0.1331]
the odd/even-bit-sum statistic = 45.14945 [P = 0.9564]^
the 64-bit matrix statistic = 279.03955 [P = 0.1441]
the 128-bit matrix statistic = 264.03760 [P = 0.3354]
the 256-bit matrix statistic = 219.27686 [P = 0.9487]^
the 512-bit matrix statistic = 240.42236 [P = 0.7352]
the 1024-bit matrix statistic = 270.57764 [P = 0.2402]
the 2048-bit matrix statistic = 272.79150 [P = 0.2120]
the bit prediction A statistic = 0.02770 [P = 0.8678]
the bit prediction B statistic = 3.39169 [P = 0.0655]*
the bit prediction C statistic = 0.44589 [P = 0.5043]
the bit prediction D statistic = 0.14163 [P = 0.7067]
the bit prediction E statistic = 0.25900 [P = 0.6108]
the byte prediction A statistic = 0.43235 [P = 0.5108]
the byte prediction B statistic = 0.76863 [P = 0.3806]
the byte prediction C statistic = 2.45098 [P = 0.1175]
the byte prediction D statistic = 0.63750 [P = 0.4246]
the byte repetition statistic = 0.37279 [P = 0.5415]
the 2-byte AND statistic = 4.83071 [P = 0.5657]
the 4-byte AND statistic = 0.93420 [P = 0.6268]
the 4-byte AND-OR statistic = 0.50630 [P = 0.7764]
the 2-byte up/down statistic = 4.05436 [P = 0.1317]
the 4-byte up/down statistic = 11.07762 [P = 0.1353]
the rect. distance statistic = 7.47441 [P = 0.2792]
the 4-byte collision statistic = 0.32632 [P = 0.5678]
the 6-byte collision statistic = 0.58583 [P = 0.4440]
the 8-byte collision statistic = 2.24223 [P = 0.1343]
the 12-byte collision statistic = 2.62525 [P = 0.1052]
the 16-byte collision statistic = 2.49145 [P = 0.1145]
the 24-byte collision statistic = 1.12994 [P = 0.2878]
the 32-byte collision statistic = 0.17840 [P = 0.6727]
the 1-byte offset XOR statistic = 222.81055 [P = 0.9279]^
the 2-byte offset XOR statistic = 231.63965 [P = 0.8504]
the 6-byte offset XOR statistic = 240.17676 [P = 0.7389]
the 24-byte offset XOR stat. = 275.79004 [P = 0.1772]
the 120-byte offset XOR stat. = 213.89160 [P = 0.9712]^
the 720-byte offset XOR stat. = 239.59473 [P = 0.7475]
the 5040-byte offset XOR stat. = 216.12012 [P = 0.9631]^
the 40320-byte offset XOR stat. = 226.90039 [P = 0.8968]
the 362880-byte off. XOR stat. = 230.92871 [P = 0.8581]
the mod 3 statistic = 0.55609 [P = 0.7573]
the mod 5 statistic = 6.30607 [P = 0.1774]
the mod 7 statistic = 11.00113 [P = 0.0883]*
the mod 11 statistic = 14.57153 [P = 0.1485]
the mod 13 statistic = 16.88413 [P = 0.1540]
the mod 17 statistic = 17.55455 [P = 0.3506]
the mod 19 statistic = 21.39930 [P = 0.2597]
the mod 23 statistic = 14.81448 [P = 0.8701]
------------------------------------------------------------------------------
the bit runs statistic = 17.80726 [P = 0.0583]*
the alt. 1 bit runs statistic = 6.81020 [P = 0.7432]
the alt. 2 bit runs statistic = 9.27882 [P = 0.5059]
the alt. 3 bit runs statistic = 11.94879 [P = 0.2885]
the alt. 4 bit runs statistic = 11.12592 [P = 0.3478]
the alt. 5 bit runs statistic = 4.92468 [P = 0.8962]
the block bit freq. statistic = 308.21362 [P = 0.0140]*
the bit frequency statistic = 0.03125 [P = 0.8597]
the tidbit frequency statistic = 2.61225 [P = 0.4553]
the nibble frequency statistic = 16.07097 [P = 0.3774]
the byte frequency statistic = 264.77832 [P = 0.3238]
the bit 0 statistic = 0.06348 [P = 0.8011]
the bit 1 statistic = 0.33649 [P = 0.5619]
the bit 2 statistic = 0.30336 [P = 0.5818]
the bit 3 statistic = 6.46669 [P = 0.0110]*
the bit 4 statistic = 0.35719 [P = 0.5501]
the bit 5 statistic = 4.14981 [P = 0.0416]*
the bit 6 statistic = 0.50266 [P = 0.4783]
the bit 7 statistic = 2.05519 [P = 0.1517]
the overall bit statistic = 14.23488 [P = 0.0758]*
the 8-bit-sum statistic = 8.00358 [P = 0.4331]
the 16-bit-sum statistic = 2.95777 [P = 0.2279]
the 32-bit-sum statistic = 1.50544 [P = 0.4711]
the odd/even-bit-sum statistic = 58.69963 [P = 0.6302]
the 64-bit matrix statistic = 213.46924 [P = 0.9725]^
the 128-bit matrix statistic = 214.63574 [P = 0.9687]^
the 256-bit matrix statistic = 234.51172 [P = 0.8167]
the 512-bit matrix statistic = 263.50732 [P = 0.3438]
the 1024-bit matrix statistic = 223.25439 [P = 0.9249]^
the 2048-bit matrix statistic = 269.76025 [P = 0.2512]
the bit prediction A statistic = 4.32881 [P = 0.0375]*
the bit prediction B statistic = 0.03554 [P = 0.8505]
the bit prediction C statistic = 0.00021 [P = 0.9884]^
the bit prediction D statistic = 0.00588 [P = 0.9389]^
the bit prediction E statistic = 1.57774 [P = 0.2091]
the byte prediction A statistic = 0.19216 [P = 0.6611]
the byte prediction B statistic = 0.05515 [P = 0.8143]
the byte prediction C statistic = 1.30613 [P = 0.2531]
the byte prediction D statistic = 0.01985 [P = 0.8879]
the byte repetition statistic = 0.47451 [P = 0.4909]
the 2-byte AND statistic = 2.78780 [P = 0.8350]
the 4-byte AND statistic = 1.95095 [P = 0.3770]
the 4-byte AND-OR statistic = 0.51192 [P = 0.7742]
the 2-byte up/down statistic = 0.53484 [P = 0.7654]
the 4-byte up/down statistic = 6.79466 [P = 0.4506]
the rect. distance statistic = 8.53545 [P = 0.2014]
the 4-byte collision statistic = 1.70893 [P = 0.1911]
the 6-byte collision statistic = 0.00335 [P = 0.9538]^
the 8-byte collision statistic = 1.75803 [P = 0.1849]
the 12-byte collision statistic = 0.01790 [P = 0.8936]
the 16-byte collision statistic = 0.38552 [P = 0.5347]
the 24-byte collision statistic = 1.13569 [P = 0.2866]
the 32-byte collision statistic = 0.40233 [P = 0.5259]
the 1-byte offset XOR statistic = 257.57227 [P = 0.4431]
the 2-byte offset XOR statistic = 277.58984 [P = 0.1583]
the 6-byte offset XOR statistic = 227.08594 [P = 0.8952]
the 24-byte offset XOR stat. = 233.55762 [P = 0.8284]
the 120-byte offset XOR stat. = 240.54590 [P = 0.7333]
the 720-byte offset XOR stat. = 258.36328 [P = 0.4295]
the 5040-byte offset XOR stat. = 293.56445 [P = 0.0487]*
the 40320-byte offset XOR stat. = 289.87793 [P = 0.0657]*
the 362880-byte off. XOR stat. = 249.60742 [P = 0.5835]
the mod 3 statistic = 1.85251 [P = 0.3960]
the mod 5 statistic = 2.36222 [P = 0.6695]
the mod 7 statistic = 10.73201 [P = 0.0970]*
the mod 11 statistic = 8.56218 [P = 0.5741]
the mod 13 statistic = 10.26279 [P = 0.5929]
the mod 17 statistic = 13.92656 [P = 0.6042]
the mod 19 statistic = 14.92757 [P = 0.6669]
the mod 23 statistic = 24.06245 [P = 0.3440]
------------------------------------------------------------------------------

 

D

IDS

the bit runs statistic = 3.23651 [P = 0.9753]^
the alt. 1 bit runs statistic = 2.40307 [P = 0.9922]^^
the alt. 2 bit runs statistic = 12.11100 [P = 0.2777]
the alt. 3 bit runs statistic = 6.03290 [P = 0.8125]
the alt. 4 bit runs statistic = 2.14133 [P = 0.9951]^^
the alt. 5 bit runs statistic = 4.13804 [P = 0.9409]^
the block bit freq. statistic = 223.15405 [P = 0.9318]^
the bit frequency statistic = 0.20771 [P = 0.6486]
the tidbit frequency statistic = 0.33019 [P = 0.9543]^
the nibble frequency statistic = 3.72997 [P = 0.9985]^^
the byte frequency statistic = 211.58154 [P = 0.9780]^
the bit 0 statistic = 0.34562 [P = 0.5566]
the bit 1 statistic = 1.84790 [P = 0.1740]
the bit 2 statistic = 0.04047 [P = 0.8406]
the bit 3 statistic = 0.20005 [P = 0.6547]
the bit 4 statistic = 1.14139 [P = 0.2854]
the bit 5 statistic = 0.09644 [P = 0.7561]
the bit 6 statistic = 0.47266 [P = 0.4918]
the bit 7 statistic = 1.37787 [P = 0.2405]
the overall bit statistic = 5.52239 [P = 0.7006]
the 8-bit-sum statistic = 2.92743 [P = 0.9388]^
the 16-bit-sum statistic = 0.47174 [P = 0.7899]
the 32-bit-sum statistic = 1.94260 [P = 0.3786]
the odd/even-bit-sum statistic = 56.22564 [P = 0.7145]
the 64-bit matrix statistic = 229.89160 [P = 0.8688]
the 128-bit matrix statistic = 240.55566 [P = 0.7332]
the 256-bit matrix statistic = 298.66357 [P = 0.0313]*
the 512-bit matrix statistic = 280.72998 [P = 0.1287]
the 1024-bit matrix statistic = 277.33252 [P = 0.1609]
the 2048-bit matrix statistic = 234.46191 [P = 0.8174]
the bit prediction A statistic = 0.14477 [P = 0.7036]
the bit prediction B statistic = 0.58540 [P = 0.4442]
the bit prediction C statistic = 0.23767 [P = 0.6259]
the bit prediction D statistic = 0.02266 [P = 0.8803]
the bit prediction E statistic = 1.73409 [P = 0.1879]
the byte prediction A statistic = 1.68848 [P = 0.1938]
the byte prediction B statistic = 1.03554 [P = 0.3089]
the byte prediction C statistic = 0.01201 [P = 0.9127]^
the byte prediction D statistic = 3.07451 [P = 0.0795]*
the byte repetition statistic = 0.14118 [P = 0.7071]
the 2-byte AND statistic = 10.95675 [P = 0.0897]*
the 4-byte AND statistic = 1.53870 [P = 0.4633]
the 4-byte AND-OR statistic = 9.85702 [P = 0.0072]**
the 2-byte up/down statistic = 2.60050 [P = 0.2725]
the 4-byte up/down statistic = 3.12586 [P = 0.8731]
the rect. distance statistic = 12.55167 [P = 0.0507]*
the 4-byte collision statistic = 1.67523 [P = 0.1956]
the 6-byte collision statistic = 0.00430 [P = 0.9477]^
the 8-byte collision statistic = 1.73417 [P = 0.1879]
the 12-byte collision statistic = 0.01034 [P = 0.9190]^
the 16-byte collision statistic = 0.71606 [P = 0.3974]
the 24-byte collision statistic = 0.58924 [P = 0.4427]
the 32-byte collision statistic = 0.10534 [P = 0.7455]
the 1-byte offset XOR statistic = 236.48633 [P = 0.7913]
the 2-byte offset XOR statistic = 262.63965 [P = 0.3578]
the 6-byte offset XOR statistic = 282.58008 [P = 0.1133]
the 24-byte offset XOR stat. = 243.32617 [P = 0.6898]
the 120-byte offset XOR stat. = 255.80566 [P = 0.4740]
the 720-byte offset XOR stat. = 233.79102 [P = 0.8256]
the 5040-byte offset XOR stat. = 231.36035 [P = 0.8534]
the 40320-byte offset XOR stat. = 241.89844 [P = 0.7125]
the 362880-byte off. XOR stat. = 268.90332 [P = 0.2630]
the mod 3 statistic = 0.55387 [P = 0.7581]
the mod 5 statistic = 7.62531 [P = 0.1063]
the mod 7 statistic = 0.95117 [P = 0.9874]^
the mod 11 statistic = 9.39605 [P = 0.4950]
the mod 13 statistic = 9.22845 [P = 0.6833]
the mod 17 statistic = 16.62820 [P = 0.4100]
the mod 19 statistic = 37.21644 [P = 0.0049]**
the mod 23 statistic = 12.59308 [P = 0.9439]^
------------------------------------------------------------------------------
the bit runs statistic = 5.68391 [P = 0.8411]
the alt. 1 bit runs statistic = 12.25425 [P = 0.2684]
the alt. 2 bit runs statistic = 10.40514 [P = 0.4057]
the alt. 3 bit runs statistic = 4.84112 [P = 0.9015]^
the alt. 4 bit runs statistic = 2.24659 [P = 0.9941]^^
the alt. 5 bit runs statistic = 2.33914 [P = 0.9930]^^
the block bit freq. statistic = 273.66895 [P = 0.2139]
the bit frequency statistic = 0.12112 [P = 0.7278]
the tidbit frequency statistic = 1.68490 [P = 0.6403]
the nibble frequency statistic = 16.07684 [P = 0.3770]
the byte frequency statistic = 221.83398 [P = 0.9342]^
the bit 0 statistic = 2.36271 [P = 0.1243]
the bit 1 statistic = 0.48618 [P = 0.4856]
the bit 2 statistic = 5.14191 [P = 0.0234]*
the bit 3 statistic = 0.66333 [P = 0.4154]
the bit 4 statistic = 0.46463 [P = 0.4955]
the bit 5 statistic = 3.80707 [P = 0.0510]*
the bit 6 statistic = 1.52368 [P = 0.2171]
the bit 7 statistic = 0.05678 [P = 0.8117]
the overall bit statistic = 14.50629 [P = 0.0695]*
the 8-bit-sum statistic = 3.42060 [P = 0.9053]^
the 16-bit-sum statistic = 0.20716 [P = 0.9016]^
the 32-bit-sum statistic = 2.40825 [P = 0.3000]
the odd/even-bit-sum statistic = 58.54286 [P = 0.6357]
the 64-bit matrix statistic = 288.51758 [P = 0.0731]*
the 128-bit matrix statistic = 259.90576 [P = 0.4031]
the 256-bit matrix statistic = 276.57520 [P = 0.1688]
the 512-bit matrix statistic = 279.21924 [P = 0.1424]
the 1024-bit matrix statistic = 257.57910 [P = 0.4430]
the 2048-bit matrix statistic = 269.22168 [P = 0.2586]
the bit prediction A statistic = 0.06353 [P = 0.8010]
the bit prediction B statistic = 0.22114 [P = 0.6382]
the bit prediction C statistic = 0.61319 [P = 0.4336]
the bit prediction D statistic = 1.85620 [P = 0.1731]
the bit prediction E statistic = 0.00506 [P = 0.9433]^
the byte prediction A statistic = 0.14118 [P = 0.7071]
the byte prediction B statistic = 0.00882 [P = 0.9252]^
the byte prediction C statistic = 0.28333 [P = 0.5945]
the byte prediction D statistic = 1.20098 [P = 0.2731]
the byte repetition statistic = 0.00613 [P = 0.9376]^
the 2-byte AND statistic = 3.66326 [P = 0.7221]
the 4-byte AND statistic = 0.66204 [P = 0.7182]
the 4-byte AND-OR statistic = 3.26311 [P = 0.1956]
the 2-byte up/down statistic = 0.99284 [P = 0.6087]
the 4-byte up/down statistic = 12.83845 [P = 0.0761]*
the rect. distance statistic = 6.57247 [P = 0.3622]
the 4-byte collision statistic = 3.48481 [P = 0.0619]*
the 6-byte collision statistic = 0.28231 [P = 0.5952]
the 8-byte collision statistic = 3.76996 [P = 0.0522]*
the 12-byte collision statistic = 0.06066 [P = 0.8055]
the 16-byte collision statistic = 0.45863 [P = 0.4983]
the 24-byte collision statistic = 0.00058 [P = 0.9808]^
the 32-byte collision statistic = 0.09503 [P = 0.7579]
the 1-byte offset XOR statistic = 222.86914 [P = 0.9275]^
the 2-byte offset XOR statistic = 249.72949 [P = 0.5814]
the 6-byte offset XOR statistic = 282.03223 [P = 0.1177]
the 24-byte offset XOR stat. = 235.24121 [P = 0.8075]
the 120-byte offset XOR stat. = 262.33789 [P = 0.3627]
the 720-byte offset XOR stat. = 274.75879 [P = 0.1887]
the 5040-byte offset XOR stat. = 218.66016 [P = 0.9518]^
the 40320-byte offset XOR stat. = 234.70508 [P = 0.8143]
the 362880-byte off. XOR stat. = 225.65527 [P = 0.9071]^
the mod 3 statistic = 0.08700 [P = 0.9574]^
the mod 5 statistic = 1.98835 [P = 0.7379]
the mod 7 statistic = 4.84382 [P = 0.5640]
the mod 11 statistic = 8.90116 [P = 0.5415]
the mod 13 statistic = 18.33863 [P = 0.1058]
the mod 17 statistic = 12.75509 [P = 0.6906]
the mod 19 statistic = 13.67917 [P = 0.7498]
the mod 23 statistic = 15.84742 [P = 0.8234]
------------------------------------------------------------------------------

 

K2

K3

the bit runs statistic = 11.86104 [P = 0.2945]
the alt. 1 bit runs statistic = 17.50135 [P = 0.0640]*
the alt. 2 bit runs statistic = 13.99420 [P = 0.1733]
the alt. 3 bit runs statistic = 10.40383 [P = 0.4058]
the alt. 4 bit runs statistic = 11.20613 [P = 0.3417]
the alt. 5 bit runs statistic = 12.15332 [P = 0.2749]
the block bit freq. statistic = 245.29529 [P = 0.6737]
the bit frequency statistic = 2.10886 [P = 0.1464]
the tidbit frequency statistic = 3.82098 [P = 0.2815]
the nibble frequency statistic = 11.30148 [P = 0.7309]
the byte frequency statistic = 249.81445 [P = 0.5799]
the bit 0 statistic = 0.18970 [P = 0.6632]
the bit 1 statistic = 0.22525 [P = 0.6351]
the bit 2 statistic = 4.84516 [P = 0.0277]*
the bit 3 statistic = 0.51660 [P = 0.4723]
the bit 4 statistic = 0.03664 [P = 0.8482]
the bit 5 statistic = 1.94472 [P = 0.1632]
the bit 6 statistic = 1.01963 [P = 0.3126]
the bit 7 statistic = 1.29657 [P = 0.2548]
the overall bit statistic = 10.07427 [P = 0.2599]
the 8-bit-sum statistic = 8.01784 [P = 0.4317]
the 16-bit-sum statistic = 2.08202 [P = 0.3531]
the 32-bit-sum statistic = 5.87358 [P = 0.0530]*
the odd/even-bit-sum statistic = 52.30330 [P = 0.8296]
the 64-bit matrix statistic = 237.47363 [P = 0.7778]
the 128-bit matrix statistic = 230.35254 [P = 0.8641]
the 256-bit matrix statistic = 272.58789 [P = 0.2145]
the 512-bit matrix statistic = 301.27393 [P = 0.0247]*
the 1024-bit matrix statistic = 245.12451 [P = 0.6604]
the 2048-bit matrix statistic = 185.47412 [P = 0.9996]^^^
the bit prediction A statistic = 0.67866 [P = 0.4100]
the bit prediction B statistic = 0.01346 [P = 0.9076]^
the bit prediction C statistic = 0.10444 [P = 0.7466]
the bit prediction D statistic = 1.82808 [P = 0.1764]
the bit prediction E statistic = 0.21341 [P = 0.6441]
the byte prediction A statistic = 2.02966 [P = 0.1543]
the byte prediction B statistic = 0.20613 [P = 0.6498]
the byte prediction C statistic = 0.82451 [P = 0.3639]
the byte prediction D statistic = 0.35392 [P = 0.5519]
the byte repetition statistic = 3.76863 [P = 0.0522]*
the 2-byte AND statistic = 4.29863 [P = 0.6363]
the 4-byte AND statistic = 0.81388 [P = 0.6657]
the 4-byte AND-OR statistic = 2.37301 [P = 0.3053]
the 2-byte up/down statistic = 4.34323 [P = 0.1140]
the 4-byte up/down statistic = 4.08104 [P = 0.7704]
the rect. distance statistic = 6.05680 [P = 0.4169]
the 4-byte collision statistic = 2.61853 [P = 0.1056]
the 6-byte collision statistic = 2.69016 [P = 0.1010]
the 8-byte collision statistic = 5.21072 [P = 0.0224]*
the 12-byte collision statistic = 1.94682 [P = 0.1629]
the 16-byte collision statistic = 3.31178 [P = 0.0688]*
the 24-byte collision statistic = 0.82848 [P = 0.3627]
the 32-byte collision statistic = 0.36557 [P = 0.5454]
the 1-byte offset XOR statistic = 254.82031 [P = 0.4914]
the 2-byte offset XOR statistic = 282.02637 [P = 0.1178]
the 6-byte offset XOR statistic = 282.17480 [P = 0.1166]
the 24-byte offset XOR stat. = 230.40137 [P = 0.8636]
the 120-byte offset XOR stat. = 219.81348 [P = 0.9459]^
the 720-byte offset XOR stat. = 260.64062 [P = 0.3907]
the 5040-byte offset XOR stat. = 290.58398 [P = 0.0621]*
the 40320-byte offset XOR stat. = 256.34570 [P = 0.4645]
the 362880-byte off. XOR stat. = 254.31348 [P = 0.5004]
the mod 3 statistic = 1.48364 [P = 0.4762]
the mod 5 statistic = 0.48299 [P = 0.9751]^
the mod 7 statistic = 1.60842 [P = 0.9520]^
the mod 11 statistic = 13.93409 [P = 0.1760]
the mod 13 statistic = 11.32979 [P = 0.5009]
the mod 17 statistic = 8.89736 [P = 0.9176]^
the mod 19 statistic = 21.54541 [P = 0.2528]
the mod 23 statistic = 23.65006 [P = 0.3658]
------------------------------------------------------------------------------		 .
the bit runs statistic = 5.41881 [P = 0.8615]
the alt. 1 bit runs statistic = 6.78501 [P = 0.7456]
the alt. 2 bit runs statistic = 3.51346 [P = 0.9666]^
the alt. 3 bit runs statistic = 4.70147 [P = 0.9102]^
the alt. 4 bit runs statistic = 5.77836 [P = 0.8335]
the alt. 5 bit runs statistic = 5.46811 [P = 0.8578]
the block bit freq. statistic = 303.05566 [P = 0.0231]*
the bit frequency statistic = 6.57031 [P = 0.0104]*
the tidbit frequency statistic = 6.62681 [P = 0.0848]*
the nibble frequency statistic = 12.35707 [P = 0.6518]
the byte frequency statistic = 236.48047 [P = 0.7913]
the bit 0 statistic = 2.28529 [P = 0.1306]
the bit 1 statistic = 2.37473 [P = 0.1233]
the bit 2 statistic = 2.91396 [P = 0.0878]*
the bit 3 statistic = 0.59218 [P = 0.4416]
the bit 4 statistic = 0.96899 [P = 0.3249]
the bit 5 statistic = 0.00138 [P = 0.9704]^
the bit 6 statistic = 1.51405 [P = 0.2185]
the bit 7 statistic = 2.06641 [P = 0.1506]
the overall bit statistic = 12.71699 [P = 0.1220]
the 8-bit-sum statistic = 9.71741 [P = 0.2854]
the 16-bit-sum statistic = 7.50582 [P = 0.0234]*
the 32-bit-sum statistic = 7.90096 [P = 0.0192]*
the odd/even-bit-sum statistic = 60.64689 [P = 0.5607]
the 64-bit matrix statistic = 303.75928 [P = 0.0195]*
the 128-bit matrix statistic = 270.42725 [P = 0.2422]
the 256-bit matrix statistic = 289.70410 [P = 0.0666]*
the 512-bit matrix statistic = 244.78857 [P = 0.6659]
the 1024-bit matrix statistic = 275.87842 [P = 0.1763]
the 2048-bit matrix statistic = 250.92676 [P = 0.5603]
the bit prediction A statistic = 6.34222 [P = 0.0118]*
the bit prediction B statistic = 0.00000 [P = 0.9983]^^
the bit prediction C statistic = 0.04913 [P = 0.8246]
the bit prediction D statistic = 0.01346 [P = 0.9076]^
the bit prediction E statistic = 0.09106 [P = 0.7628]
the byte prediction A statistic = 1.60809 [P = 0.2048]
the byte prediction B statistic = 0.47451 [P = 0.4909]
the byte prediction C statistic = 0.00392 [P = 0.9501]^
the byte prediction D statistic = 0.74142 [P = 0.3892]
the byte repetition statistic = 0.15319 [P = 0.6955]
the 2-byte AND statistic = 5.69903 [P = 0.4577]
the 4-byte AND statistic = 1.06772 [P = 0.5863]
the 4-byte AND-OR statistic = 6.68942 [P = 0.0353]*
the 2-byte up/down statistic = 3.36984 [P = 0.1855]
the 4-byte up/down statistic = 20.36571 [P = 0.0048]**
the rect. distance statistic = 0.52364 [P = 0.9975]^^
the 4-byte collision statistic = 0.00845 [P = 0.9268]^
the 6-byte collision statistic = 0.61777 [P = 0.4319]
the 8-byte collision statistic = 0.82936 [P = 0.3625]
the 12-byte collision statistic = 1.38850 [P = 0.2387]
the 16-byte collision statistic = 0.29207 [P = 0.5889]
the 24-byte collision statistic = 0.83341 [P = 0.3613]
the 32-byte collision statistic = 2.66220 [P = 0.1028]
the 1-byte offset XOR statistic = 260.37207 [P = 0.3952]
the 2-byte offset XOR statistic = 222.79199 [P = 0.9280]^
the 6-byte offset XOR statistic = 275.35938 [P = 0.1820]
the 24-byte offset XOR stat. = 283.08496 [P = 0.1094]
the 120-byte offset XOR stat. = 247.03418 [P = 0.6281]
the 720-byte offset XOR stat. = 277.78223 [P = 0.1564]
the 5040-byte offset XOR stat. = 243.00586 [P = 0.6950]
the 40320-byte offset XOR stat. = 261.87891 [P = 0.3702]
the 362880-byte off. XOR stat. = 253.05469 [P = 0.5227]
the mod 3 statistic = 2.69352 [P = 0.2601]
the mod 5 statistic = 3.05977 [P = 0.5479]
the mod 7 statistic = 12.40590 [P = 0.0535]*
the mod 11 statistic = 4.19289 [P = 0.9382]^
the mod 13 statistic = 14.86717 [P = 0.2488]
the mod 17 statistic = 18.30175 [P = 0.3065]
the mod 19 statistic = 19.53018 [P = 0.3599]
the mod 23 statistic = 24.72563 [P = 0.3104]
------------------------------------------------------------------------------

 

MIXBITS

MIXBITS (zi&zi+1)
the bit runs statistic = 8.41227 [P = 0.5886]
the alt. 1 bit runs statistic = 9.47094 [P = 0.4881]
the alt. 2 bit runs statistic = 7.56601 [P = 0.6711]
the alt. 3 bit runs statistic = 2.80016 [P = 0.9857]^
the alt. 4 bit runs statistic = 3.80694 [P = 0.9556]^
the alt. 5 bit runs statistic = 4.71935 [P = 0.9091]^
the block bit freq. statistic = 255.37695 [P = 0.4992]
the bit frequency statistic = 0.50588 [P = 0.4769]
the tidbit frequency statistic = 1.19841 [P = 0.7534]
the nibble frequency statistic = 12.00906 [P = 0.6783]
the byte frequency statistic = 219.60498 [P = 0.9470]^
the bit 0 statistic = 2.07203 [P = 0.1500]
the bit 1 statistic = 0.15720 [P = 0.6917]
the bit 2 statistic = 0.39552 [P = 0.5294]
the bit 3 statistic = 0.36659 [P = 0.5449]
the bit 4 statistic = 0.10011 [P = 0.7517]
the bit 5 statistic = 3.08304 [P = 0.0791]*
the bit 6 statistic = 2.64698 [P = 0.1037]
the bit 7 statistic = 0.34792 [P = 0.5553]
the overall bit statistic = 9.16939 [P = 0.3282]
the 8-bit-sum statistic = 9.86087 [P = 0.2749]
the 16-bit-sum statistic = 0.23730 [P = 0.8881]
the 32-bit-sum statistic = 1.20320 [P = 0.5479]
the odd/even-bit-sum statistic = 54.77289 [P = 0.7603]
the 64-bit matrix statistic = 247.24365 [P = 0.6245]
the 128-bit matrix statistic = 234.87109 [P = 0.8122]
the 256-bit matrix statistic = 222.41846 [P = 0.9305]^
the 512-bit matrix statistic = 224.90771 [P = 0.9129]^
the 1024-bit matrix statistic = 251.40039 [P = 0.5519]
the 2048-bit matrix statistic = 252.08252 [P = 0.5399]
the bit prediction A statistic = 0.11032 [P = 0.7398]
the bit prediction B statistic = 0.35349 [P = 0.5521]
the bit prediction C statistic = 0.01298 [P = 0.9093]^
the bit prediction D statistic = 0.00526 [P = 0.9422]^
the bit prediction E statistic = 0.45236 [P = 0.5012]
the byte prediction A statistic = 0.30025 [P = 0.5837]
the byte prediction B statistic = 0.20613 [P = 0.6498]
the byte prediction C statistic = 0.26691 [P = 0.6054]
the byte prediction D statistic = 0.02451 [P = 0.8756]
the byte repetition statistic = 0.07083 [P = 0.7901]
the 2-byte AND statistic = 9.59928 [P = 0.1426]
the 4-byte AND statistic = 0.49575 [P = 0.7805]
the 4-byte AND-OR statistic = 3.88284 [P = 0.1435]
the 2-byte up/down statistic = 0.96596 [P = 0.6169]
the 4-byte up/down statistic = 4.35953 [P = 0.7376]
the rect. distance statistic = 8.52603 [P = 0.2020]
the 4-byte collision statistic = 1.70893 [P = 0.1911]
the 6-byte collision statistic = 0.53953 [P = 0.4626]
the 8-byte collision statistic = 0.21102 [P = 0.6460]
the 12-byte collision statistic = 0.45178 [P = 0.5015]
the 16-byte collision statistic = 0.04777 [P = 0.8270]
the 24-byte collision statistic = 0.62093 [P = 0.4307]
the 32-byte collision statistic = 0.05908 [P = 0.8080]
the 1-byte offset XOR statistic = 253.89941 [P = 0.5077]
the 2-byte offset XOR statistic = 255.39453 [P = 0.4813]
the 6-byte offset XOR statistic = 252.67773 [P = 0.5293]
the 24-byte offset XOR stat. = 243.50879 [P = 0.6869]
the 120-byte offset XOR stat. = 273.27930 [P = 0.2060]
the 720-byte offset XOR stat. = 282.28613 [P = 0.1157]
the 5040-byte offset XOR stat. = 272.04590 [P = 0.2213]
the 40320-byte offset XOR stat. = 279.03809 [P = 0.1441]
the 362880-byte off. XOR stat. = 259.18164 [P = 0.4154]
the mod 3 statistic = 0.41081 [P = 0.8143]
the mod 5 statistic = 0.87914 [P = 0.9275]^
the mod 7 statistic = 2.50250 [P = 0.8682]
the mod 11 statistic = 10.54454 [P = 0.3941]
the mod 13 statistic = 13.38666 [P = 0.3416]
the mod 17 statistic = 21.09791 [P = 0.1748]
the mod 19 statistic = 10.81073 [P = 0.9022]^
the mod 23 statistic = 15.45672 [P = 0.8419]
------------------------------------------------------------------------------
the bit runs statistic = 8.87745 [P = 0.5438]
the alt. 1 bit runs statistic = 16.35386 [P = 0.0899]*
the alt. 2 bit runs statistic = 9.57846 [P = 0.4782]
the alt. 3 bit runs statistic = 7.58637 [P = 0.6692]
the alt. 4 bit runs statistic = 10.86509 [P = 0.3681]
the alt. 5 bit runs statistic = 6.87834 [P = 0.7369]
the block bit freq. statistic = 287.59729 [P = 0.0850]*
the bit frequency statistic = 3.04013 [P = 0.0812]*
the tidbit frequency statistic = 7.97648 [P = 0.0465]*
the nibble frequency statistic = 16.87556 [P = 0.3264]
the byte frequency statistic = 266.82764 [P = 0.2928]
the bit 0 statistic = 0.21067 [P = 0.6462]
the bit 1 statistic = 1.73807 [P = 0.1874]
the bit 2 statistic = 0.34562 [P = 0.5566]
the bit 3 statistic = 0.96132 [P = 0.3269]
the bit 4 statistic = 0.51380 [P = 0.4735]
the bit 5 statistic = 1.71242 [P = 0.1907]
the bit 6 statistic = 0.35953 [P = 0.5488]
the bit 7 statistic = 1.11237 [P = 0.2916]
the overall bit statistic = 6.95378 [P = 0.5416]
the 8-bit-sum statistic = 8.40722 [P = 0.3947]
the 16-bit-sum statistic = 3.93700 [P = 0.1397]
the 32-bit-sum statistic = 7.86048 [P = 0.0196]*
the odd/even-bit-sum statistic = 51.49670 [P = 0.8495]
the 64-bit matrix statistic = 249.91846 [P = 0.5781]
the 128-bit matrix statistic = 228.18213 [P = 0.8853]
the 256-bit matrix statistic = 235.45117 [P = 0.8049]
the 512-bit matrix statistic = 249.99707 [P = 0.5767]
the 1024-bit matrix statistic = 305.27783 [P = 0.0168]*
the 2048-bit matrix statistic = 293.57275 [P = 0.0487]*
the bit prediction A statistic = 1.01225 [P = 0.3144]
the bit prediction B statistic = 0.90283 [P = 0.3420]
the bit prediction C statistic = 1.08580 [P = 0.2974]
the bit prediction D statistic = 1.96887 [P = 0.1606]
the bit prediction E statistic = 2.61320 [P = 0.1060]
the byte prediction A statistic = 0.49632 [P = 0.4811]
the byte prediction B statistic = 0.23554 [P = 0.6274]
the byte prediction C statistic = 0.47451 [P = 0.4909]
the byte prediction D statistic = 0.58848 [P = 0.4430]
the byte repetition statistic = 0.14118 [P = 0.7071]
the 2-byte AND statistic = 14.35977 [P = 0.0259]*
the 4-byte AND statistic = 4.84373 [P = 0.0888]*
the 4-byte AND-OR statistic = 1.70058 [P = 0.4273]
the 2-byte up/down statistic = 0.12598 [P = 0.9390]^
the 4-byte up/down statistic = 4.22835 [P = 0.7531]
the rect. distance statistic = 12.05520 [P = 0.0607]*
the 4-byte collision statistic = 1.02358 [P = 0.3117]
the 6-byte collision statistic = 0.26086 [P = 0.6095]
the 8-byte collision statistic = 0.00412 [P = 0.9488]^
the 12-byte collision statistic = 0.22738 [P = 0.6335]
the 16-byte collision statistic = 0.04663 [P = 0.8290]
the 24-byte collision statistic = 0.92898 [P = 0.3351]
the 32-byte collision statistic = 0.07599 [P = 0.7828]
the 1-byte offset XOR statistic = 244.79395 [P = 0.6658]
the 2-byte offset XOR statistic = 240.89355 [P = 0.7280]
the 6-byte offset XOR statistic = 254.38965 [P = 0.4990]
the 24-byte offset XOR stat. = 242.98438 [P = 0.6953]
the 120-byte offset XOR stat. = 267.34961 [P = 0.2851]
the 720-byte offset XOR stat. = 253.36035 [P = 0.5172]
the 5040-byte offset XOR stat. = 243.45996 [P = 0.6877]
the 40320-byte offset XOR stat. = 280.25391 [P = 0.1329]
the 362880-byte off. XOR stat. = 236.48730 [P = 0.7913]
the mod 3 statistic = 0.82434 [P = 0.6622]
the mod 5 statistic = 3.61676 [P = 0.4603]
the mod 7 statistic = 3.96069 [P = 0.6820]
the mod 11 statistic = 14.82106 [P = 0.1387]
the mod 13 statistic = 10.39581 [P = 0.5813]
the mod 17 statistic = 14.65813 [P = 0.5498]
the mod 19 statistic = 12.91182 [P = 0.7968]
the mod 23 statistic = 24.56542 [P = 0.3183]
------------------------------------------------------------------------------

 

eMT (Zi & Zi+1)

IDS (zi & Zi+1)

the bit runs statistic = 8.54008 [P = 0.5762]
the alt. 1 bit runs statistic = 7.59005 [P = 0.6688]
the alt. 2 bit runs statistic = 8.32103 [P = 0.5975]
the alt. 3 bit runs statistic = 7.33930 [P = 0.6931]
the alt. 4 bit runs statistic = 4.49229 [P = 0.9224]^
the alt. 5 bit runs statistic = 5.97361 [P = 0.8175]
the block bit freq. statistic = 213.21838 [P = 0.9760]^
the bit frequency statistic = 0.20708 [P = 0.6491]
the tidbit frequency statistic = 2.39809 [P = 0.4940]
the nibble frequency statistic = 13.87936 [P = 0.5347]
the byte frequency statistic = 282.30518 [P = 0.1155]
the bit 0 statistic = 0.35022 [P = 0.5540]
the bit 1 statistic = 1.06348 [P = 0.3024]
the bit 2 statistic = 0.61341 [P = 0.4335]
the bit 3 statistic = 2.89399 [P = 0.0889]*
the bit 4 statistic = 1.38706 [P = 0.2389]
the bit 5 statistic = 1.40089 [P = 0.2366]
the bit 6 statistic = 1.72266 [P = 0.1894]
the bit 7 statistic = 0.45404 [P = 0.5004]
the overall bit statistic = 9.88575 [P = 0.2731]
the 8-bit-sum statistic = 6.53115 [P = 0.5880]
the 16-bit-sum statistic = 0.01183 [P = 0.9941]^^
the 32-bit-sum statistic = 1.24043 [P = 0.5378]
the odd/even-bit-sum statistic = 52.72088 [P = 0.8187]
the 64-bit matrix statistic = 272.16748 [P = 0.2197]
the 128-bit matrix statistic = 241.35889 [P = 0.7209]
the 256-bit matrix statistic = 267.02930 [P = 0.2898]
the 512-bit matrix statistic = 258.26172 [P = 0.4312]
the 1024-bit matrix statistic = 261.13037 [P = 0.3826]
the 2048-bit matrix statistic = 249.16650 [P = 0.5912]
the bit prediction A statistic = 0.05037 [P = 0.8224]
the bit prediction B statistic = 0.05742 [P = 0.8106]
the bit prediction C statistic = 2.54665 [P = 0.1105]
the bit prediction D statistic = 0.56653 [P = 0.4516]
the bit prediction E statistic = 1.09734 [P = 0.2949]
the byte prediction A statistic = 0.35392 [P = 0.5519]
the byte prediction B statistic = 3.52941 [P = 0.0603]*
the byte prediction C statistic = 0.54142 [P = 0.4618]
the byte prediction D statistic = 0.07941 [P = 0.7781]
the byte repetition statistic = 4.80392 [P = 0.0284]*
the 2-byte AND statistic = 8.45515 [P = 0.2066]
the 4-byte AND statistic = 0.93345 [P = 0.6271]
the 4-byte AND-OR statistic = 2.17138 [P = 0.3377]
the 2-byte up/down statistic = 0.49288 [P = 0.7816]
the 4-byte up/down statistic = 3.40972 [P = 0.8447]
the rect. distance statistic = 2.60725 [P = 0.8563]
the 4-byte collision statistic = 0.03246 [P = 0.8570]
the 6-byte collision statistic = 1.71831 [P = 0.1899]
the 8-byte collision statistic = 2.96896 [P = 0.0849]*
the 12-byte collision statistic = 2.24922 [P = 0.1337]
the 16-byte collision statistic = 1.78767 [P = 0.1812]
the 24-byte collision statistic = 1.81755 [P = 0.1776]
the 32-byte collision statistic = 0.72105 [P = 0.3958]
the 1-byte offset XOR statistic = 261.62988 [P = 0.3743]
the 2-byte offset XOR statistic = 227.21973 [P = 0.8940]
the 6-byte offset XOR statistic = 258.42188 [P = 0.4284]
the 24-byte offset XOR stat. = 251.57129 [P = 0.5489]
the 120-byte offset XOR stat. = 241.81836 [P = 0.7138]
the 720-byte offset XOR stat. = 250.94141 [P = 0.5601]
the 5040-byte offset XOR stat. = 259.72754 [P = 0.4061]
the 40320-byte offset XOR stat. = 262.78516 [P = 0.3554]
the 362880-byte off. XOR stat. = 220.81445 [P = 0.9403]^
the mod 3 statistic = 0.50978 [P = 0.7750]
the mod 5 statistic = 3.44937 [P = 0.4856]
the mod 7 statistic = 11.57746 [P = 0.0721]*
the mod 11 statistic = 22.68954 [P = 0.0120]*
the mod 13 statistic = 13.39416 [P = 0.3411]
the mod 17 statistic = 28.96587 [P = 0.0242]*
the mod 19 statistic = 18.53727 [P = 0.4208]
the mod 23 statistic = 24.04529 [P = 0.3449]
------------------------------------------------------------------------------
the bit runs statistic = 7.85278 [P = 0.6432]
the alt. 1 bit runs statistic = 12.74801 [P = 0.2381]
the alt. 2 bit runs statistic = 16.18138 [P = 0.0946]*
the alt. 3 bit runs statistic = 11.96288 [P = 0.2875]
the alt. 4 bit runs statistic = 10.30668 [P = 0.4140]
the alt. 5 bit runs statistic = 10.83367 [P = 0.3706]
the block bit freq. statistic = 290.09387 [P = 0.0703]*
the bit frequency statistic = 0.09785 [P = 0.7544]
the tidbit frequency statistic = 5.80970 [P = 0.1212]
the nibble frequency statistic = 15.06821 [P = 0.4465]
the byte frequency statistic = 256.34766 [P = 0.4645]
the bit 0 statistic = 0.22525 [P = 0.6351]
the bit 1 statistic = 0.13771 [P = 0.7106]
the bit 2 statistic = 0.55375 [P = 0.4568]
the bit 3 statistic = 0.00110 [P = 0.9735]^
the bit 4 statistic = 0.05312 [P = 0.8177]
the bit 5 statistic = 0.86432 [P = 0.3525]
the bit 6 statistic = 0.53644 [P = 0.4639]
the bit 7 statistic = 0.05960 [P = 0.8071]
the overall bit statistic = 2.43129 [P = 0.9649]^
the 8-bit-sum statistic = 4.31156 [P = 0.8280]
the 16-bit-sum statistic = 0.04429 [P = 0.9781]^
the 32-bit-sum statistic = 0.43982 [P = 0.8026]
the odd/even-bit-sum statistic = 57.36044 [P = 0.6766]
the 64-bit matrix statistic = 226.47070 [P = 0.9004]^
the 128-bit matrix statistic = 224.88086 [P = 0.9131]^
the 256-bit matrix statistic = 250.34473 [P = 0.5706]
the 512-bit matrix statistic = 252.75098 [P = 0.5280]
the 1024-bit matrix statistic = 246.88867 [P = 0.6306]
the 2048-bit matrix statistic = 299.59082 [P = 0.0288]*
the bit prediction A statistic = 0.31750 [P = 0.5731]
the bit prediction B statistic = 0.37601 [P = 0.5397]
the bit prediction C statistic = 0.10849 [P = 0.7419]
the bit prediction D statistic = 2.74887 [P = 0.0973]*
the bit prediction E statistic = 0.38111 [P = 0.5370]
the byte prediction A statistic = 0.68848 [P = 0.4067]
the byte prediction B statistic = 0.00613 [P = 0.9376]^
the byte prediction C statistic = 0.30025 [P = 0.5837]
the byte prediction D statistic = 1.45319 [P = 0.2280]
the byte repetition statistic = 0.00098 [P = 0.9750]^
the 2-byte AND statistic = 1.52576 [P = 0.9578]^
the 4-byte AND statistic = 0.20824 [P = 0.9011]^
the 4-byte AND-OR statistic = 2.02832 [P = 0.3627]
the 2-byte up/down statistic = 2.27399 [P = 0.3208]
the 4-byte up/down statistic = 10.47101 [P = 0.1634]
the rect. distance statistic = 4.72252 [P = 0.5799]
the 4-byte collision statistic = 0.86781 [P = 0.3516]
the 6-byte collision statistic = 0.00020 [P = 0.9887]^
the 8-byte collision statistic = 0.68800 [P = 0.4068]
the 12-byte collision statistic = 0.08207 [P = 0.7745]
the 16-byte collision statistic = 0.03474 [P = 0.8521]
the 24-byte collision statistic = 0.00223 [P = 0.9624]^
the 32-byte collision statistic = 0.53598 [P = 0.4641]
the 1-byte offset XOR statistic = 227.86133 [P = 0.8883]
the 2-byte offset XOR statistic = 275.10156 [P = 0.1848]
the 6-byte offset XOR statistic = 264.21094 [P = 0.3327]
the 24-byte offset XOR stat. = 252.29688 [P = 0.5361]
the 120-byte offset XOR stat. = 295.49512 [P = 0.0413]*
the 720-byte offset XOR stat. = 236.13477 [P = 0.7959]
the 5040-byte offset XOR stat. = 246.70215 [P = 0.6338]
the 40320-byte offset XOR stat. = 281.41895 [P = 0.1228]
the 362880-byte off. XOR stat. = 260.84082 [P = 0.3874]
the mod 3 statistic = 4.88177 [P = 0.0871]*
the mod 5 statistic = 13.29216 [P = 0.0099]**
the mod 7 statistic = 6.29151 [P = 0.3913]
the mod 11 statistic = 9.38626 [P = 0.4959]
the mod 13 statistic = 19.25748 [P = 0.0825]*
the mod 17 statistic = 9.54349 [P = 0.8894]
the mod 19 statistic = 8.48937 [P = 0.9704]^
the mod 23 statistic = 16.62989 [P = 0.7834]
------------------------------------------------------------------------------

 

Avalanche Effect

Avalanche Effect for 8192 bit flips: