.
, . .
, , . , n! m! {\displaystyle n!m!} , n {\displaystyle n} m {\displaystyle m} [8].
:
: -
: -
: (3, 1, 4, 2)
: (3, 2, 4, 1, 5)
:
. . ( ). , + ܻ, + ܻ, + ܻ. .
( )
(), . , :
;
, , , , . .
.
, n , ., , 4 , 6 , : : . n = 23, t, , : t = {1, 7, 13, 19, 2, 8, 14, 20, 3, 9, 15, 21, 4, 10, 16, 22, 5, 11,17, 23, 6, 12, 18}.
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(. Verrnam Cipher) , 1917 AT&T [1].
. Ȼ. [2]. [3].
AT&T , 1917 , 1919 .
Ȼ , . XOR ( ) [4].
, , . , . , .
, , . [5].
, , ( ). , , (1 1 0 0 0). 1 , 0 . [5].
Ȼ . , , (1 1 1 0 1) (1 1 0 0 0) (0 0 1 0 1): {\displaystyle (11000)\oplus (11101)=(00101)} , (1 1 1 0 1), : {\displaystyle (00101)\oplus (11101)=(11000)} [2]:
1. : {\displaystyle P_{k}(k)=1/2^{N}} , k , N ;
2. ;
3. .
m, , Zm. , m = 2[2].
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, m = 26 (A=0,B=1,, Z=25):
: EVTIQWXQVVOPMCXREPYZ : ALLSWELLTHATENDSWELL (All's well that ends well): EGEAMAIBOCOIQPAJATJK. , , . . () ( ), () , , , .[6].
[ | -]
1945 ( 1949 . ), . . , [2]. , , , . , , [5].
(). , , , , . , (, , , , ). , - MD5[9].
. . - , . -. -, . - - . , , -, [8].
, . , , . , () , .
. , : . (, DES), , DES. , , , , . [8].
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. , . , , 40- , , . , 1940- . 40 Venona, .
, , . , , . Oops
, : ! -, . - , -, . . .
- . , , , , . , , ( 1945 ). : , , , .
, , , . , , , : . , , , - ? , , , , ? , ? ?
, . . , . , , (. VENONA). , , .
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, . , . , .
. (straddling checkerboard). - , zip, rar .., . , =1, =2 ., - - . ,
: . . AT ONE SIR ( . ) .. , , . , 8, 9 0, , ( ) , . , , , ( =3), , , , =81, ?=07:
1 2 3 4 5 6 7 8 9 0 8 9 0 .,?-- ( , ..). , :
, , : 80. , : 7. . :
80781 48386 18239 11000 . , .. . , .
! , . , . ! , ( , )! , , . , , :
80781 48386 18239 11000+ 14358 89753 24133 40169 26799= 14358 69434 62419 58398 37799:
14358 69434 62419 58398 37799, , . , , , . . 8, , , 0 , ., . . , : .
, ( ): . , ! : , . , , , 1 , , .. . d10, , !
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, , , , :
11 = 0 21 = 6 31 = 2 41 = 8 51 = 4 12 = 1 22 = 7 32 = 3 42 = 9 52 = 5 13 = 2 23 = 8 33 = 4 43 = 0 53 = 6 14 = 3 24 = 9 34 = 5 44 = 1 54 = 7 15 = 4 25 = 0 35 = 6 45 = 2 55 = 8 16 = 5 26 = 1 36 = 7 46 = 3 56 = 9, 0 9. , , , .
, , , , .
! , , , . , , . - - ,
*
All specialists unanimously agreed that a reading [of the Enigma] is impossible.
Admiral Kurt Fricke, Chief of Naval War Command
, . , , , , . , -, .
20 . ( ) 26 . . . , . 26 . , , 26 .
, . , . 26n, n .
:
( ), , ( ) 4 : A, B, C, D. : A-C; B-A; C-B; D-D. A-B; B-C; C-A; D-D A-A; B-C; C-B; D-D .
B , , . B C. :
. .
.
-, . , .
-, , , . , . , . , , . .
, (A-B; C-D) . B C. , . B D.
, D, , D B. .
, , - . .
. . . , .
26 , 263=17476 . , 3! . .. 6*17576=105456. , . : . .
, B A. A A-B, B.
. D D-D-D-D-C-B-A-B. B A.
. . . , .
. , .
, 3 , I, II, III :
Entry = ABCDEFGHIJKLMNOPQRSTUVWXYZ
I = EKMFLGDQVZNTOWYHXUSPAIBRCJ
II = AJDKSIRUXBLHWTMCQGZNPYFVOE
III = BDFHJLCPRTXVZNYEIWGAKMUSQO
, 6 .
26 . ..
6*263=105456 .
n! /((n-2m)! m! 2m), n , m .
26 10 150738274937250=247 .
:
150738274937250*105456=15,896,255,521,782,636,000≈264.
.
.
264 .
. , , 105456 .
- . , P C, .
P = WETTERVORHERSAGEBISKAYA
C = RWIVTYRESXBFOGKUHQBAISE
:
w | e | t | t | e | r | v | o | r | h | e | r | s | a | g | e | b | i | s | k | a | y | a |
r | w | i | v | t | y | r | e | s | x | b | f | o | g | k | u | h | q | b | a | i | s | e |
, 14, 15 20 . 14 A G. , , K 15 . K A 20 , A-G-K-A. . : 1) 2) .
, . . . , . :
Ei = S-1R-1TRS,
S S-1, ;
R R-1 ;
T .
Pi:
Pi = R-1TR
:
Ei = S-1PiS
14, 15 20 .
S-1P14S(A) = G P14S(A) = S(G).
P15S(G) = S(K)
P20S(K) = S(A)
S(K) :
P20P15P14S(A) = S(A) (1), S(A) , A .
. (1). S, A S. .
, 1/26 , .
, . , . , . .. .
P.S.