PERFIL E IDENTIDAD DOCENTE OBJETIVOS:

The discovery of the rotor led to the implementation of several electromechanical crypto- graphic systems, which were patented (Table 6.1). Hebern’s rotor machine (Fig. 6.5) used a typewriter (2) to input plaintext consisting of the lettersA,B,. . .,Z. Ouput was signaled by lamps (37) located just above the keys (4). The rotors, five in Figure 6.5 (75a – e), have window (7), which allow their positions to be viewed.

Edward Hebern, born in 1869, spent his adult life trying to use cryptography to better himself financially. He was not discouraged at all when a solution to his magazine adver- tisement of anunbreakablecipher in 1921 was provided by a naval cryptanalyst. Hebern was at the right place at the right time as the U.S. Navy was seeking a quality crypto- graphic system. Hebern set off for Washington D.C. to seek his fortune selling his Electric Code Machine. Anticipating success from his Washington outing, the Hebern Electric

Figure 6.4 An encipherment path in a straight-through rotor system.

Code Company was established in Oakland, California. He advertised his cipher machine using the ode:

Marvelous invention comes out of the West Triumph of patience, long years without rest Solved problem of ages, deeper than thought A code of perfection, a wonder is wrought.

As part of the review process, Hebern submitted ten examples of ciphertext to the Navy for analysis. While they were cryptanalyzed by William Friedman, Hebern wasnottold about the results nor were the weaknesses in his design explained to him. Even though Hebern’s TABLE 6.1 Patented Electromechanical Cryptographic Systems

Patent no. Year Country Patenter Description 52,279 1919 Sweden Arvid G. Damm

1,484,477 1924 United States Apparatus for enc/deciphering code expressions

1,502,889 1924 United States Production of Ciphers 1,540,107 1925 United States Apparatus for the production of

cipher documents 10,700 1919 Holland Hugo A. Koch Geheimsschrijtmachine 1,533,252 1925 United States Printing telegraph system 1,657,411 1928 United States Arthur Scherbius Ciphering machine 1,510,441 1924 United States Edward H. Hebern Electric code machine 1,861,857 1932 United States Cryptographic machine

concepts were later used by the U.S. Government, they never gave Hebern the order he expected. Only 12 machines were purchased, the Hebern Electric Code Company went bankrupt and Hebern was found guilty of violating California’s Corporate Securities Act.

6.4

A CHARACTERISTIC PROPERTY OF CONJUGACY

The substitutionC₂iuCiis aconjugateofu, a term from group theory. Conjugacy enjoys an

interesting and important property illustrated in the substitution table (Table 6.2) in which

. The leftmost entry in theith row gives the rotational displacementi, and

. The next 26 columns in theith row list the ciphertext letters (C₂iuCi)(t) correspond-

ing to the plaintext lettertwith 0t,26.

We begin with the following observation:u(t)¼sif and only ifu(t2iþi)2i¼s2i, from which it follows that

TABLE 6.2 Table of Rotor Conjugates

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 0 f Q t g x a n w c j o i v z p h y b d r k u s l e m 1 p s f w z m v b i n h u y o g x a c q j t r k d l e 2 r e v y l u a h m g t x n f w z b p i s q j c k d o 3 d u x k t z g l f s w m e v y a o h r p i b j c n q 4 t w j s y f k e r v l d u x z n g q o h a i b m p c 5 v i r x e j d q u k c t w y m f p n g z h a l o b s 6 h q w d i c p t j b s v x l e o m f y g z k n a r u 7 p v c h b o s i a r u w k d n l e x f y j m z q t g 8 u b g a n r h z q t v j c m k d w e x i l y p s f o 9 a f z m q g y p s u i b l j c v d w h k x o r e n t 10 e y l p f x o r t h a k i b u c v g i w n q d m s z 11 x k o e w n q s g z j h a t b u f i v m p c l r y d 12 j n d v m p r f y i g z s a t e h u l o b k q x c w 13 m c u l o q e x h f y r z s d g t k n a j p w b v i 14 b t k n p d w g e x q y r c f s j m z i o v a u h l 15 s j m o c v f d w p x q b e r i l y h n u z t g k a 16 i l n b u e c v o w p a d q h k x g m t y s f j z r 17 k m a t d b u n v o z c p g j w f l s x r e i y q h 18 l z s c a t m u n y b o f i v e k r w q d h x p g j 19 y r b z s l t m x a n e h u d j q v p c g w o f i k 20 q a y r k s l w z m d g t c i p u o b f v n e h j x 21 z x q j r k v y l c f s b h o t n a e u m d g i w p 22 w p i q j u x k b e r a g n s m z d t l c f h v o y 23 o h p i t w j a d q z f m r l y c s k b e g u n x v 24 g o h s v i z c p y e l q k x b r j a d f t m w u n 25 n g r u h y b o x d k p j w a q i z c e s l v t m f 6.4 A CHARACTERISTIC PROPERTY OF CONJUGACY 155

. IfE(4) is enciphered tox(23) with the rotor in positioni¼0 u(4þ0)0¼23;

. Then D(3)¼C₂1E is enciphered to C21x¼w(22) when the rotor is in

position i¼1

u(3þ1)1¼u(4)1¼231¼22:

The property (C₂iuCi)(t)¼s if and only if (C2(iþ1)uCiþ1)(t21)¼s21 shows that

the letters in Table 6.2 traverse the alphabet in the standard ordera,b,. . .,zon upward diagonals; the letters on the diagonal starting in row 2, column A are underlined.

6.5 ANALYSIS OF A 1-ROTOR SYSTEM: