• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Chi2 10b
 

Chi2 10b

on

  • 304 views

 

Statistics

Views

Total Views
304
Views on SlideShare
304
Embed Views
0

Actions

Likes
0
Downloads
0
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Chi2 10b Chi2 10b Document Transcript

    •  
    •    
    •   
    •  DEKART Random Run’s Tests    
    •  
    •    
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999K
    •  Dekart S.R.L, Tel. +3732 24-14-30, 24-55-80   Fax. +3732 24-25-08    E-mail: valera@dekart.com D-2012, http://www.dekart.com!    
    •  "#  
    • $ %Dekart S.R.L.»    , 
    •  E-mail: petrova@dekart.com)     
    •  E-mail: owl@dekart.com)   
    •     
    •  
    • 
    •     
    •     
    •      
    •     
    •   
    •     !   
    •  _______________________ 2Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999       !"  # ! !  !    $!% #  2.  #   " %&" #$"   ()*+, +-./01 +2.34 ,5464   " 7# _______________________ 3Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999
    • 1 &()*(+ ,-( ..............................................................................52 &()*(+ . (!(-+)(/ 0+)0& .............................................6 2.1  ......................................................................... 6 2.2   ........................................................................................ 6 2.3   ............................................................................... 6 2.4 8 ................................................................................................ 6 2.5 9 :#  ......................................................................... 7 2.6   ........................................................................... 7 2.7    ...................................................................... 7 2.8 9 ;:< 7 => ........................................................................... 7 2.9 9  0?5@A-BBC.D 1862BA5 6546E ............................................. 73 (*0+!!+01(2 !+,34500&.......................................................84    DEKART RANDOM RUN’S TESTS ........................9 4.1 F@5G25.HI J    !E ........................ 9 4.2 45@C-A J  H............................................................................. 9 4.3 D-B J   .................................................................... 10 4.4 B0K5@ J  J   :LE ........................................ 10 4.5 02B0. J  :#  ........................................................ 11 4.6 B5@1265 J   .......................................................... 11 4.7 B5@1 J ! ML #  .................... 12 4.8 @2.4 J    .......................................................... 12 4.9 1-NC121 J  O:< 7 =P ...................................................... 13 4.10 162BA5 J   ............................................................. 13 4.11 QRS J ! # ............................................................. 14 4.12 .QRS J ! #& %  !  :  :< TU .............................................................................................. 14 4.13 D-11- J ! 7!# %M V8ML ................ 15 4.14 5@F J ! 7!# % # .............................. 15 W XT H0115.6 J L# 7 #  Y 216 W XZ B[?-A25 J ! # Bs #  :#  16 W X 46C@] J ! ! ^% %   .............................. 17 W X= F-H6 J ! M .............................................................. 175 
    • 
    •     
    •   
    • 
    • DEKART RANDOM RUN’S TESTS ..............................................................19
    • 
    • ...............................................................................................23_______________________ 4Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 19991
    •    !    !" ! 77 !  #     ! ^!# #   !  !&7 " :  ###  2 [1, 2].
    • 7#  # ! !"   7#   # !%  #  %!%    M  2   1 s  k (Ys  n  ps ) 2 n  ps%  Ys - ! &    %Y s; ps - # %& ! 7 #    %Y s; k - ! %_ n – :$ !   7!Y 2  !  :   = k – 1 !## p -# # :#&     7 %7 `  n  : & !: # Y: ps 7  .  ps:  < T a p    7 U JX b  cc J XUU b& 7 :Y#   ! ! a p    cc  cTb    T  X b&  7 !Y# ; 7>_ 7!#" p, 7Y!"   cT  cU b  XU  T b& 7 ;% 7> [1]. (    6$   !"7 0 – 1 %, 99 – 100 % d  1 – 5 %, 95 – 99 %  7 5 – 10 %, 90 – 95 % ^%  7 10 – 90 % e    " % DEKART Random Run’s Tests 7 !  #  ! !  
    • L 7 #  $Y # 2  #L  %!   _______________________ 5Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 19992
    •   2.1   
    •   ^! !    :     U  d–1 (d = 256  M M  $Y!" & d = 10 8 %  #Y# #! LM)  ##  !#  7      !  ##    k=d  ## ps =1 / d.2.2   $   #  !  7   Y$" % 7 % n !" ! # % !# !   <#   ##    k= dn  ## ps = 1 / dn.2.3        ##     ##7!&  $"  7  7 [, f # % ## !   U& X& ]& &XT   ! :<  15) ! 7!# ::Y# H $Y#   KgXZhX  ##" B0=p, p1=p(1-p), p2=p(1-p)2,...,p16=p(1-p)16 .2.4 8 i! 8  n % 7 #  Y$" %7 % !" !    %  #  !  Y$"! ` %    T T 7" J  7_ W 7" J   _ j 7" J    j  %  _ ] 7" J  :  W  %  _  7" J #  %      !# ! %&  " # T8W8j8]8U7" !  7 ##  2. d#  ML#  7Y!#   Y$    7 m%  Y$" % 7 % !" !" !  ## ! Y$"  J   &   & &   ! k_______________________ 6Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999 !#&  %    % U8X8]8j8WE&  !% ##  2.2.5 0  #     "    !" !  #Y#  n " %& :" " # %& !: : ;:> L" !  U  d8X  %  !  7  #  %  #   2.6      l" #   #  n %  T       % 7 % T  %# !  !#  7    &  !% ##    k=5 ## p=1/5!2.7   
    •    7 m  7  " :Y$"    "    !" !2.8 0 %# 7 " 9 l" #   !" ! #  % 7 = Y$" % 7 % !    % ### :<  k  !#  7    7!  ##  22.9 0 6$ :overlapping m-tuple test)   ###   ML    l" #   !" ! #  %  j   %  7   7 "  <": " "  V2)  " " ( V3) % fjn  7# ! ME  ::  %Y#   7 "  V2)  "  ojE #!" LM _______________________ 7Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 19993 ! "#$   
    •   e  7 # % 7!& ! ! !        U  ]TT  # !  E   U  XU  #   #!" LME  7 #   $ a      7&  % & !E  Y$" % 7 % !"!  "    7 %  %      #YE     l7  % 7 %  & !  #     ## !! Uj ,  $ 7  7 [, [ (  Uj < ),!#  !& Y$ 7  # 8 e  7 %  7!& !! ## 7!" :L !"  Y$" % 7 %!    7&   &     EY ## 0  #       8 #7  :  &       !  & !  % 7  :#  & !  #  % !  &:" # # : ;% :> !#  !&Y$ #      a     7&        # " !   !#   !   
    •    7 l7  % 7 %   & !  7 % 7# !   Y 7  ## 0 %# 7 " 9 e  7 %  & !    ! 7 =  Y$" % 7 %  !   !#  #Yp = 1/i8. 0 6$ a #    7 7 V3-V2    2  d3-d2E # : E ( Y! E  Y$" % 7 % !" !7     _______________________ 8Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 19994           7   #   ML  ML 7  #7 C .    7 BorlandC 3.02. pL    L  MS DOS.    ML& 7Y$ !  % ML&  7! # ! !%# i   ##    !" !&!" 7 M& 7 %  :  < X q 7 #    :L 7!  2 , #  "   ##      M  7 # 7#  7!# # 7##   yy[9]%:# #E a   %8:  ##& ! " #7  " (c 1 & ")&   7< :     Y$ :$ Name of test (not enough statistics).
    •  ML  #   # :: #7 C.4.1 frequency ;   
    •   :   <pL# void frequency(FILE *stream)  frequency.c
    • 
    • $#   !   # %  !#  7 #   7 7"      ! M  LM J    #!" LME k !##    "   stream.7$ 7!    yy[i] %:# #E
    • %!# d4.2 serial ;   =$pL# void serial(FILE *stream)  serial.c_______________________ 9Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999
    •  #   7   ! !  E  !  # #!  E  Y$" % 7 % !" ! !  
    •  ## !     7 :L 7 "#Y#   pcount,  7#  -&  %  !# :$ !         npairsE&  !% ##    "   stream.7$ 7!    yy[i] %:# #E
    • %!# d4.3 gap ;    pL# void gap(FILE *stream)  gap.c
    •  ##     # ! ! Uj ,  $ 7  7 [, [ :   Uj < .  "  count[0]...count[15] "## ! ##  %   U  XT&   X8  J ! & :<" XT  ##    "   stream.7$ 7! 9   yy[i] %:# #E
    • %!# d4.4 poker ;  ;  :  
    • #>$<pL# void poker(void)  poker.c
    •  i  ! 7  U dn  %# :: J 7 ##  W  "  a, b, c, d._______________________ 10Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999  !# !  Y$"     !  Y$" % 7 % ! c $Y   pcount, !%  ML  % serial,  ##  ! :L " ##  5N65@. /02rA5 s2D5 BH02.6 fZTTjZtn  # !  !#E_ 5N65@. /02rA5 s2D5 BH02.6 fXUUUUn  # #!  !#E_ extern double npairs;  #" ML serial.7$ 7! `   yy[i] %:# #E
    • %!#   ML 7 :7  % 7# ML serial.4.5 ?@A?B ;   #   pL# void coupon(FILE *stream)  coupon.c
    • 
    •  #  %   !" !& :" " # %& !: : P :P L" !  U  /&  ! ! ##  % %&  7#  Y$   count, 7 9hX   ! 9gWU_   count[T] c  ! %&  "  < 9E  ##   # ps #    !# !#Y#  $Y % p_value). "   stream.7$ 7! #   yy[i] %:# #E
    • %!# d4.6 permute ;     pL# void permute(FILE *stream)_______________________ 11Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999  permute.c
    •  l" #   !" ! 7 ##  %  T      !#&  7 !#      !  %  7 7#  $Y #  . "   stream.7$ 7! u   yy[i] %:# #E
    • %!# d! 9:  % int perm(int a, int b, int c, int d, int e)4.7 perm ; 6 C>      pL# int perm(int a, int b, int c, int d, int e)  permute.c
    •  !# ! :" "  # # !#    !" ! a, b, c, d, e  LY MLY F& # "7   :7     % fXn .. V 7 # & !# 7 int a, int b, int c, int d, int e.7$ 7! k! ML&   :7 "7Y$ #   # !  %
    • %!# d 4.8 runs ;   
    •    7pL# void runs(FILE *stream)  runs.c_______________________ 12Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999
    •  7Y#  " :Y$"    !  "     $Y #  . "   stream.7$ 7! ^    yy[i] %:# #E
    • %!# d4.9 maximum ;  “# 7 " ”pL# void maximum(FILE *stream)  maximum.c
    •  l" #   !" ! 7:#    = ! k 7Y#  7!#   "   #" . "   stream.7$ 7!    yy[i] %:# #E
    • %!# d4.10 mtuple ;   6$pL# void mtuple(FILE *stream)  mtuple.c
    •  l" #   !" ! 7:#  %  j  k 7Y#  :  E   "  <" : " "  " "   !  !#E :   "  " #  #$" LM  #!#  !#E ^  LY MY#   triples  # ;>E  B-C@4  # O PE&  " ### ! #   :L O P  OP      # :_______________________ 13Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999 OP ! Hvvrvv- rvv-E1& %  a, b, c – ! 7  E ! 7  Y#  $Y #   "   stream.7$ 7! #   yy[i] %:# #E
    • %!# d4.11 CHI ; 6   pL# double CHI(double x, int n)  chi.c
    •  !# # $#  2  7 " #" :   `  :  n   2 – x.7$ 7! # :#
    • %!# d! 7 ML  $#  7%   : - double CHI(double x, int n)  double chi(double x, int n)4.12 nCHI ; 6     D  $  # 6 # 7 EpL# double nCHI(double x, int n)  chi.c1 || -  L_______________________ 14Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999
    •  !# # $#  2 , %  !  :  :< TU # ML# ### : # CHI. `  :  n   2 - x.7$ 7! # :# a  "  # % %:# # ier   1, nCHI 7$  7!
    • %!# d4.13 gamma ; 6 "  DC
    •  
    • 8C>pL# double gamma(double arg)  chi.c
    •  !# 7! %MV8ML  7 % %  k! % arg.7$ 7! %M V8ML
    • %!# d! pL# 7 :  % static double pos (double arg), static double asym (double arg), static double neg(double arg) .4.14 erf ; 6 " D   pL# double erf(double x)  chi.c
    •  !# 7! % # ML <:E c $Y  L [5]. k! "%   % # 7$ 7! k! % #
    • %!# d_______________________ 15Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999!  ! # 7#   %:  ier # 7! X 4.15 comment ; > "7    F 2pL# void comment(void)  comment.c
    •  7 7 # !       X    :$ 7Y  ! # 7#   ier=1, yy[i]<0  IIfCnwX E  # :$  O(@@0@ 0F 6546P Result of test is :A. Frequency Test - SatisfactoryB. Serial Test - SatisfactoryC. Gap Test - SatisfactoryD. Poker Test - Faintly suspiciousE. Coupon Test - SatisfactoryF. Permutation Test - SatisfactoryG. Runs Up Test - SatisfactoryH. Maxi-of-8 Test - SatisfactoryI. Lapped M-Tuple Test - Satisfactory k!# # H:: extern double yy[9].7$ 7! d
    • %!# d4.16 p_value ; 6    ps    #   pL# void p_value(void)  p_value.c
    •  % p_value (#  : :7  MLYE !#  7!# # ps #  :#  ( # %& !#   < d, # ps  YE !  #    M ZE fX& 7  j j ]]._______________________ 16Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999  7 B[?-A25 :"  7 M! 7!#  9  /   7L 9gWU_ /g= # !   : /gXU J # #!E a p_value :  :7  MLY&  T  d :"      ! .7$ 7! 7 !  #   & :  :   M
    • %!# d! pL# 7 :  % float stir2 (int, int), double fact(int).4.17 stir2 ; 6  )D   D  pL# float p_value(int n, int k)  p_value.c
    •  !# ! ^% %    M [4]:  n, k   1 k  1)  kj  k  j n! j  0 ( j   n  !  7Y# L ! n  k.7$ 7! ` ^% %  
    • %!# d! pL# 7 :Y  % double fact(int).4.18 fact ; 6 C pL# double fact(int n)  p_value.c
    •  !# M  % ! n. d ! n.7$ 7! p n!._______________________ 17Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999
    • %!# d_______________________ 18Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 19995  ! "#$%&    #() * !! DEKART Random Run’s Testsd  ML&  "    " %DEKART Random Run’s Tests : 7: % # #!"     ! – main2.exeE  #!" LM (main10.exe) #  : L  %#7 bat8M CHI_TEST.BAT:@echo offREM 1 - number system (2 or 10)REM 2 - input_file_nameREM 3 - output_file_name (NULL==CON)if %1 ==/? goto er1if %1 .==. goto er1if %2 .==. goto er1if %1 == 2 goto m2if %1 == 10 goto m10goto err:m2if %3 .==. goto m22main2 %1 %2 >%3goto exit:m22main2 %1 %2goto exit:m10if %3 .==. goto m12main10 %1 %2 >%3goto exit:m12main10 %1 %2goto exit:errecho Number system must be decimal (10) or binary (2)goto exit:er1echo*****************************************************************echo * Tests for randomness on characters of a file*echo * Copyright (c) Dekart SRL*echo **echo **_______________________ 19Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999echo * Usage:*echo * 1. CHI_TEST number_system input_file_name*echo * 2. CHI_TEST number_system input_file_name output_file_name*echo **echo **echo * File should contain at least 1 Mbyte of random data*echo*****************************************************************:exit 6   D
    • 6 k % Hhi_test $ # :<path> chi_test.bat n_s <path> input_file_name (a)<path> chi_test.bat n_s <path> input_file_name <path> output_file_name (b)
    • ! 7Y!#   :    7#     EE     M (b)). G 6  6G 6 6  ! " " "7Y#   !# n_s    !" !& 7#  M input_file_name, 7 %  :  < X q   ! " # # :  ! 7 # 7##  :Lx  d7  # ! `  :#   2 :  :L  # L# 7 7   7!Y # #  %     (    6$   !"7 0 – 1 %, 99 – 100 % d  1 – 5 %, 95 – 99 %  7 5 – 10 %, 90 – 95 % ^%  7 10 – 90 % e  & 7 #  & 7  M b1: 1000000 characters in file: b1A. Frequency Test CHI = 0.659510 x2 = 263.715328 n = 255_______________________ 20Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999B. Serial Test CHI = 0.367744 x2 = 65412.102144 n = 65535C. Gap Test CHI = 0.571380 x2 = 16.352818 n = 16D. Poker Test CHI = 0.073851 x2 = 0.888890 n = 4E. Coupon Test CHI = 0.284641 x2 = 27.051418 n = 32F. Permutations Test CHI = 0.351198 x2 = 112.558610 n = 119G. Runs Up Test CHI = 0.288077 x2 = 2.922561 n = 5H. Max-of-8 Test CHI = 0.534920 x2 = 55.252936 n = 55I. Lapped M-Tuple Test CHI = 0.695418 x2 = 462.797214 n = 448 Result of test is :A. Frequency Test - SatisfactoryB. Serial Test - SatisfactoryC. Gap Test - SatisfactoryD. Poker Test - Faintly suspiciousE. Coupon Test - SatisfactoryF. Permutation Test - SatisfactoryG. Runs Up Test - SatisfactoryH. Maxi-of-8 Test - SatisfactoryI. Lapped M-Tuple Test - Satisfactory! CHI J  ! # _ n J !  : _ x2 J 7!  2. a   %8:  7< 7#   Y&  CHI # U   #:$ : “Error of test”. < # ML#  7< : % #     7  E  7E 7#  M output_file_name. ) #H 7" F a  7 % chi_test : 7 # " % M input_file_name, :  !#&   : 7 Y! /? -     #:$ Tests for randomness on characters of a file Copyright (c) Dekart SRL Usage: 1. CHI_TEST number_system input_file_name 2. CHI_TEST number_system input_file_name output_file_name File should contain at least 1 Mbyte of random data !% % 7< Y : a  ! " % : 7 # $Y$% M& ### :$ ***: no such file or directory_______________________ 21Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999  % 7!# a   %8:  ##& ! " #7  ",   7< :     Y$ :$ Name of test (not enough statistics)._______________________ 22Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999+  1. i  l %# # my 9 ] ! % 8  & Xc 8 ]  2.    9 & d!  p & d! d p !  < < 8  < u & Xc=W 8 T]  3. Wegentkittl S. Empirical testing of pseudorandom number generator/ Master’s thesis, University of Salzburg, Austria, 1995.4. ! L !  y V   " z  J  ^ L #& Xc== J =W  5. #   ^!  %  %  #7 : # " m ^! 8  d& Xc=c J ]WU  _______________________ 23Copyright © DEKART S.R.L.
    • Data Security Section of Smart Card Technology, DEKART S.R.L.Moldova, Kishinev February 8, 1999_______________________ 24Copyright © DEKART S.R.L.