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Chapter 2
CONVENTIONAL ENCRYPTION:
CLASSICAL TECHNIQUES
Yeuan-Kuen LeeSeptember
Ch 2 Conventional Encryption: Classical Techniques 2
Outline
9Conventional Encryption Model
9 Steganography
9 Classical Encryption Techniques
Ch 2 Conventional Encryption: Classical Techniques 3
2.1 Conventional Encryption Model
Figure 2.1 Simplified Model of Conventional Encryption
Ch 2 Conventional Encryption: Classical Techniques 4
2.1 Conventional Encryption Model
9 Plaintext9 Original intelligible message
9Ciphertext9 Apparently random nonsense message
9 Encryption process
9 An algorithm - produce a different output dependingon the specific key being used at the time.
9 A key a value independent of plaintext, shared bysender and recipient.
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Ch 2 Conventional Encryption: Classical Techniques 5
2.1 Conventional Encryption Model
9 The ciphertext can be transformed back to the original
plaintext by using a decryption algorithm and the samekey that was used for encryption.
9 The security of conventional encryption depends on the
secrecy of the key, not the secrecy of the algorithm.
9 It is impractical to decrypt a message based on the
ciphertext plus knowledge of the encryption/decryption
algorithm.
9 The principal security problem is maintaining the secrecyof the key.
Ch 2 Conventional Encryption: Classical Techniques 6
2.1 Conventional Encryption Model
Encryption
Algorithm
Encryption
Algorithm
Decryption
Algorithm
Decryption
Algorithm
CryptanalystX
K
DestinationMessage
source
Key
source
Secure channel
X Y X
PlaintextX = [X1, X2, , XM]
KeyK = [K1, K2, , KJ]
K
CiphertextY = [Y1, Y2, , YN]
Encryption algorithm ( E )Y = EK(X)
Decryption algorithm ( D )
X = DK(Y)
Figure 2.2 Model of Conventional Cryptosystem
Ch 2 Conventional Encryption: Classical Techniques 7
2.1 Conventional Encryption Model
9 An opponent
9 Observing Y, but not having access to K and X, may
attempt to recover X or K, or both X and K.9 Assumed that the opponent knows E and D
9 If only the message is interested, then an estimated
plaintext is generated.
9 If future messages are interested, then an estimated
key is generated.
X
K
Ch 2 Conventional Encryption: Classical Techniques 8
2.1 Conventional Encryption Model
9 Cryptography - the art of secret writing.9 Classified along three independent dimensions:
1. The type of operations used for transforming
plaintext to ciphertext. Substitution
Transposition
2. The number of keys used. Symmetric, single-key, secret-key encryption
Asymmetric, two-key, public-key encryption
3. The way in which the plaintext is processed. Block cipher
Stream cipher
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Ch 2 Conventional Encryption: Classical Techniques 9
2.1 Conventional Encryption Model
9 Cryptanalysis
9 The process of attempting to discover X or K or both.
9 Table 2.1 summarizes the various types ofcryptanalytic attacks based on the amount ofinformation known to the cryptanalyst.
9 Ciphertext only attack -
9 Known to cryptography
1. Encryption algorithm
2. Ciphertext to be decoded
9 Brute-force approach of trying all possible keys
9 Statistical tests: type of plaintext
Ch 2 Conventional Encryption: Classical Techniques 10
2.1 Conventional Encryption Model
9 Cryptanalysis (Conti.)
9 Known plaintext attack
9 Known to cryptography
1. Encryption algorithm
2. Ciphertext to be decoded
3. One or more plaintext-ciphertext pairs formed with thesecret key
9 Probable-word attack may have little knowledge ofwhat is in the message
9 Accounting file: placement of certain key words
9 Copyright statement in some standardized position
Ch 2 Conventional Encryption: Classical Techniques 11
2.1 Conventional Encryption Model
9 Cryptanalysis (Conti.)
9 Chosen-plaintext attack
9 Known to cryptography
1. Encryption algorithm
2. Ciphertext to be decoded
3. Plaintext message chosen by cryptanalyst, together withits corresponding ciphertext generated with the secretkey
9 Example: password file
9 Differential cryptanalysis (explored Ch3)
Ch 2 Conventional Encryption: Classical Techniques 12
2.1 Conventional Encryption Model
9 Cryptanalysis (Conti.)
9 Chosen-ciphertext attack
9 Known to cryptography
1. Encryption algorithm
2. Ciphertext to be decoded
3. Purported ciphertext chosen by cryptanalyst, togetherwith its corresponding decrypted plaintext generatedwith the secret key
9 Chosen-text attack chosen-plaintext or chosen-ciphertext attack
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Ch 2 Conventional Encryption: Classical Techniques 13
2.1 Conventional Encryption Model
9 Cryptanalysis (Conti.)
9 Only relative weak algorithms fail to withstand aciphertext-only attack.
9 Generally, an encryption algorithm is designed towithstand a know-plaintext attack.
Ch 2 Conventional Encryption: Classical Techniques 14
2.1 Conventional Encryption Model
9 Unconditionally secure9 If the ciphertext generated by an encryption scheme does not
contain enough information to determine uniquely thecorresponding plaintext, no matter how much ciphertext isavailable and how much time an opponent has.
9 No encryption algorithm is unconditionally secure, except theone-time pad scheme
9 Conditionally secure1. The cost of breaking the cipher exceeds the value of the
encrypted information
2. The time required to break the cipher exceeds the usefullifetime of the information
Ch 2 Conventional Encryption: Classical Techniques 15
2.1 Conventional Encryption Model
Key Size (bits) Number ofalternative keys
Time required at1 encryption/us
Time required at106 encryption/us
32 232 = 4.3*109 231 us = 35.8 min 2.15 ms
56 256 = 7.2*1016 255 us = 1142 years 10.01 hrs
128 2128 = 3.4*1038 2127 us = 5.4*1024 years 5.4*1018 years
26 char perm. 26! = 4*1026 2*1026 us = 6.4*1012years 6.4*106 years
Table 2.2 Average Time Required for Exhaustive Key Search
Ch 2 Conventional Encryption: Classical Techniques 16
2.2 Steganography
9 Cryptography9 crypto graphy : secret writing
9 Conceal the meaning of message
9 Steganography9 stegano graphy : covered writing
9 Conceal the existence of message
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Ch 2 Conventional Encryption: Classical Techniques 17
2.2 Steganography
9 Stegosaur (Roof Lizard)
Ch 2 Conventional Encryption: Classical Techniques 18
2.2 Steganography
Dear George,
Greetings to all at Oxford. Many thanks for yourLetter and for the summer examination package.All Entry Forms and Fees Forms should be readyfor final despatch to the syndicate by Friday20th or at the very latest, Im told, by the 21st.
Admin has improved here, though theres roomfor improvement still; just give us all two or three
more years and well really show you! Pleasedont let these wretched 16 + proposals destroy
your basic O and A pattern. Certainly thissort of change, if implemented immediately,would bring chaos.
Sincerely yours,
Ch 2 Conventional Encryption: Classical Techniques 19
2.2 Steganography
9 Historical steganographic techniques
9 Character marking
9Invisible ink
9 Pin punctures
9 Typewriter correction ribbon
Ch 2 Conventional Encryption: Classical Techniques 20
2.2 Steganography
Conceal the existence of message
Steganography
CryptographyConceal the meaning of message
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Ch 2 Conventional Encryption: Classical Techniques 21
2.2 Steganography
9 General Steganographic Model
image,textaudio,video
CompressingCompressing
EncryptingEncrypting
EmbeddingEmbedding
Message
DecompressingDecompressing
DecryptingDecrypting
ExtractingExtracting
Message
Stego-media
Cover-media
Stego-key Stego-key
Warden
Sender
(Blindness)
Receiver
Ch 2 Conventional Encryption: Classical Techniques 22
2.2 Steganography
9 Requirements of a Steganographic System
9 Imperceptible (image fidelity)
9 Undetectable (Steganalysis)
9 Security
9 Payload
9 Limited Robustness
Ch 2 Conventional Encryption: Classical Techniques 23
2.2 Steganography
9 Steganalysis
9 The art of detecting any hidden message onthe communication channel.
9 If the existence of the hidden message isrevealed, the goal of steganography isdefeated.
9 Two types of steganalytic techniques
9 Visual attack
9 Statistical attack
Ch 2 Conventional Encryption: Classical Techniques 24
2.2 Steganography
luminance-ordered palette in stego-image
palette in cover-image
Result of the Airfield image embedded in the8-bit Renoir with S-Tools. (the cover imagewas reduced from 248 to 32 unique colors)
9 Specific Pattern of S-Tools
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Ch 2 Conventional Encryption: Classical Techniques 25
2.3 Classical Encryption Techniques
9 Two basic building blocks
9 Substitution techniques - the letters of plaintextare replaced by other letters or by numbers of symbols
- Caeser cipher
- Monoalphabetic cipher
- Playfair cipher
- Hill cipher
9Transposition techniques - performing some sortof permutation on the plaintext letters
9 Rotor machines - multiple stages of encryption
Ch 2 Conventional Encryption: Classical Techniques 26
2.3 Classical Encryption Techniques
9 Caesar cipher
9 Replacing each letter of the alphabet with the letterstanding three places further down the alphabet
9 Transformation
Cipher: P H H W P H D I W H U W K H W R J D S D U W B
Plain: 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
Cipher: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
Plain: m e e t m e a f t e r t h e t o g a p a r t y
Ch 2 Conventional Encryption: Classical Techniques 27
2.3 Classical Encryption Techniques
9 Caesar cipher (Conti.)
9 If we assign a numerical equivalent to each letter(a=0, b=1, c=2etc), then for each plaintext letter p,
substitute the ciphertext letter C :C = E(p) = (p + 3) mod 26
9 General Caesar algorithm
C = E(p) = (p + k) mod 26
where 1 k 25
9 Decryption algorithm
p = D(C) = (C - k) mod 26
Ch 2 Conventional Encryption: Classical Techniques 28
2.3 Classical Encryption Techniques
9 Caesar cipher (Conti.)9 Brute-force cryptanalysis
9 Why? Three important characteristics:
1. The encryption and decryption algorithms are known.
2. There are only 25 keys to try.
3. The language of the plaintext is known and easilyrecognizable.
< Fig.2.5 >Using ZIP algorithm to Compress the plaintext before encryption
Fig.2.4
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Ch 2 Conventional Encryption: Classical Techniques 29
2.3 Classical Encryption Techniques
9 Monoalphabetic cipher
9 An arbitrary substitution is used
9 26! ( 41026 ) possible keys:to eliminate brute-force attack (table 2.2)
9 If the cryptanalyst knows the nature of theplaintext (e.g., noncompressed English text), thenthe analyst can exploit the regularities of thelanguage.
9 < Fig.2.6 >Relative frequency of letters in English text
Ch 2 Conventional Encryption: Classical Techniques 30
2.3 Classical Encryption Techniques
Fig. 2.6 Relative frequency of letters in English text
Ch 2 Conventional Encryption: Classical Techniques 31
2.3 Classical Encryption Techniques
9 Monoalphabetic cipher (Conti.)9 Digram two-letter combination
9 Frequency of diagrams is a powerful regularity.
9 The most common digram is th. (ZW)
9 Trigram three-letter combination
9 The most frequent trigram is the. (ZWP)
9 Homophone
9 Provide multiple substitutes for a single letter
9 Multiple-letter patterns (e.g., digram frequencies)still survive in the ciphertext
Ch 2 Conventional Encryption: Classical Techniques 32
2.3 Classical Encryption Techniques
9 Playfair cipher
9 The best-known multiple-letter encryption cipher
9Treat digrams in the plaintext as single units andtranslates these units into ciphertext digrams.
9 5*5 matrix of letters
constructed using a keyword.
MM RROO NN AA
CC DDHH YY BB
EE KKFF GG I/JI/J
LL TTPP QQ SS
UU ZZVV WW XX
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Ch 2 Conventional Encryption: Classical Techniques 33
2.3 Classical Encryption Techniques
9 Playfair cipher (Conti.)
9 Plaintext is encrypted two letters at a time, according tothe following rules:
1. Repeating plaintext letter that would fall in the same pairare separated with a filler letter (such as x)
[ balloon ] [ ba lx lo on ]
2. Plaintext letters that fall in thesame row of the matrix are
replaced by the letter to theright in a circular fashion
[ ar ] [ RM ]
MM RROO NN AA
CC DDHH YY BB
EE KKFF GG I/JI/J
LL TTPP QQ SS
UU ZZVV WW XX
Ch 2 Conventional Encryption: Classical Techniques 34
2.3 Classical Encryption Techniques
9 Playfair cipher (Conti.)
3. Plaintext letters that fall in the same column of thematrix are replaced by the letter beneath, with the topelement of the column circularity following the last.
[ mu ] [ CM ]
4. Otherwise, each plaintext letteris replaced by the letter that liesin its own row and the columnoccupied by the other plaintext
letter.[ hs ] [ BP ],[ ea ] [ IM ] ( or [ JM ] )
MM RROO NN AA
CC DDHH YY BB
EE KKFF GG I/JI/J
LL TTPP QQ SS
UU ZZVV WW XX
Ch 2 Conventional Encryption: Classical Techniques 35
2.3 Classical Encryption Techniques
9 Playfair cipher (Conti.)9 There are 26*26=676 digrams, so that identification of
individual digrams is more difficult.
9The relative frequencies of individual letters exhibit amuch greater range than that of diagrams, makingfrequency analysis much more difficult.
9 Standard field system by the British Army in WWI
9 Considerable use by the U.S. Army and other alliedforces during WWII.
9 However, it still leaves much of the structure of theplaintext language intact.
Ch 2 Conventional Encryption: Classical Techniques 36
2.3 Classical Encryption Techniques
Fig.2.7 Relative Frequency of Occurrence of Letters.
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Ch 2 Conventional Encryption: Classical Techniques 37
2.3 Classical Encryption Techniques
9 Hill cipher
9 Lester Hill, 19299 Take m successive plaintext letters and substitutes for
them m ciphertext letters
9 The substitution is determined by m lineartransformation.
9 For m = 3,C1 = (k11p1+k12p2+k13p3) mod 26C
2
= (k21
p2
+k22
p2
+k23
p3
) mod 26C3 = (k31p3+k32p2+k33p3) mod 26
Ch 2 Conventional Encryption: Classical Techniques 38
2.3 Classical Encryption Techniques
9 Hill cipher (Conti.)
9 Matrix-vector form
C = KPwhere C and P are column vectors of length 3,representing the plaintext and ciphertext, and K is a
3*3 matrix, representing the encryption key.Operation are performed mod 26.
=
3
2
1
333231
232221
131211
3
2
1
p
p
p
kkk
kkk
kkk
c
c
c
Ch 2 Conventional Encryption: Classical Techniques 39
2.3 Classical Encryption Techniques
9 Hill cipher (Conti.)9 Example:
9 Plaintext paymoremoney
9 Key
9 The first three letters is pay = (15, 0, 24) t
9 C = KP mod 26 = (375, 819, 486) t mod 26= (11, 13, 18) t = LNS
9 Ciphertext LNSHDLEWMTRW
1922
211821
51717
K
=
Ch 2 Conventional Encryption: Classical Techniques 40
2.3 Classical Encryption Techniques
9 Hill cipher (Conti.)9 Decryption requires using K-1, the inverse of the
matrix K,
9 KK-1 = K-1K=I
9 General Expressions
C = EK(P) = KP
P = DK(C) = K-1C = K-1KP = P
17024
61715
1594
K1-
=
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Ch 2 Conventional Encryption: Classical Techniques 41
2.3 Classical Encryption Techniques
9 Hill cipher (Conti.)
9 As with Playfair, the strength of the Hill cipher is thatit completely hides single-letter frequencies.
9 A 3*3 Hill cipher hides not only single-letter but two-letter frequency information.
9 Use a larger matrix hides more frequency information
9 Strong against a ciphertext-only attack
9 Easily broken with a known plaintext attack.
Ch 2 Conventional Encryption: Classical Techniques 42
2.3 Classical Encryption Techniques
9 Hill cipher (Conti.)
9 For an m*m Hill cipher,suppose we have m plaintext-ciphertext pairs,each of length m.
9 Pj = ( p1j, p2j, p3j, p4j . . ., pmj )
9 Cj = ( c1j, c2j, c3j, c4j . . ., cmj )
9 Cj = KPj for 1 j m and for some unknown keymatrix K.
9 Define X = (pij) , Y = (cij). Y = XK
9 If X has an inverse, K =X-1Y
Ch 2 Conventional Encryption: Classical Techniques 43
2.3 Classical Encryption Techniques
9 Polyalphabetic ciphers9 Use different monoalphabetic substitutions as one
proceeds through the plaintext message
1. A set of related monoalphabetic substitution rules isused.
2. A key determines which particular rule is chosen for agiven transformation.
9 Vigenere cipher9 26 Caesar ciphers are used, with shifts of 0 through 25
9 Each cipher is denoted by a key letter (from a to z)
Ch 2 Conventional Encryption: Classical Techniques 44
2.3 Classical Encryption Techniques
Table 2.4 The Modern Vigenere Tablean
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Ch 2 Conventional Encryption: Classical Techniques 45
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)
9 Given a key letter xand a plaintext letter y, theciphertext letter is at the intersection of the rowlabeled xand the column labeled y
9 The strength is that there are multiple ciphertext
letters for each plaintext letter, one for each uniqueletter of the keyword.
key: d e c e p t i v e d e c e p t i v e d e c e p t i v e
plaintext: w e a r e d i s c o v e r e d s a v e y o u r s e l f
ciphertext: Z I C V T W Q N G R Z G V T W A V Z H C Q Y G L M G J
Ch 2 Conventional Encryption: Classical Techniques 46
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)
9 Not all knowledge of the plaintext structure is lost.Example: Fig. 2.7.
9 Attack:
1. Either monoalphabetic substitution or a Vigenerecipher?
If a monoalphabetic substitution is used, then thestatistical properties of the ciphertext should be thesame as that of the language of the plaintext.
Referring to Fig. 2.6
Ch 2 Conventional Encryption: Classical Techniques 47
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)9 Attack (Conti.)
2. How to determine the keyword length?
9 If two identical sequences of plaintext letters occur ata distance that is an integer multiple of the keywordlength, they will generate identical ciphertext sequences
9 An analyst looking at only the ciphertext can detect therepeated sequences, e.g., VTW at a displacement of 9.Assume that the keyword either 3 or 9 in length
9 By looking for common factors in the displacements ofthe various sequences, the analyst will make a good guessof the keyword length.
Ch 2 Conventional Encryption: Classical Techniques 48
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)9 Attack (Conti.)
3. If the keyword length is N, then the cipher consists
of N monoalphabetic substitution ciphers.9 The letters at positions 1, N+1, 2N+1, and so on will be
encrypted with the same monoalphabetic ciphers.
4. Each monoalphabetic ciphers can be attacked usingfrequency characteristics
9 Using a non-repeating keyword can eliminate theperiodic nature
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Ch 2 Conventional Encryption: Classical Techniques 49
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)
9 Autokey system a keyword is concatenated with theplaintext itself to provide a running key
9 Statistical techniques can be applied to cryptanalysissince the key and the plaintext share the same
frequency distribution of lettersExample: e enciphered by e can be expeated to occurwith a frequency of (0.1275)2=0.0163
key: d e c e p t i v e w e a r e d i s c o v e r e d s a v
plaintext: w e a r e d i s c o v e r e d s a v e y o u r s e l f
ciphertext: Z I C V T W Q N G K Z E I I G A S X S T S L V V W L A
Ch 2 Conventional Encryption: Classical Techniques 50
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)
9 Ultimate defense - To choose a keyword that is aslong as the plaintext and has no statisticalrelationship to it
9 Vernam cipher: 1918, AT&T engineer, Gilbert Vernam9 binary data
9 Ci = pi kipi = ith binary digit of plaintext
ki = ith binary digit of key
Ci = ith binary digit of ciphertext = exclusive-or (XOR) operation
9 pi = Ci ki
Ch 2 Conventional Encryption: Classical Techniques 51
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)9 Vernam cipher (Conti.)
9 The essence of this technique is the mean of
construction of the key.9 Use a running loop of tape as keyword : a very long but
repeating keyword
9 Can be broken with sufficient ciphertext, the use ofknown or probable plaintext sequences, or both.
Ch 2 Conventional Encryption: Classical Techniques 52
2.3 Classical Encryption Techniques
9 Vigenere cipher (Conti.)9 One-time pad
9 Army Signal Corp officer, Joseph Mauborgne
9 Using a random key that was truly as long as the message9 Unbreakable
9 Produce random output that bears no statisticalrelationship to the plaintext
9 The practical difficult sender and receiver must bein possession of, and protect, the random key.
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Ch 2 Conventional Encryption: Classical Techniques 53
2.3 Classical Encryption Techniques
9 Transposition Techniques
9 Performs some sort of permutation on the plaintextletters
9 Rail fence technique
9 The plaintext is written down as a sequence of diagonalsand then read off as a sequence of rows
9 Plaintext meet me after the toga party
9 m e m a t r h t g p r y
e t e f e t e o a a t9 Ciphertext MEMATRHTGPRYETEFETEOAAT
Ch 2 Conventional Encryption: Classical Techniques 54
2.3 Classical Encryption Techniques
9 Transposition Techniques (Conti.)
9 A more complex scheme9 to write the message in a rectangle, row by row, and
read the message off, column by column, but permutethe order of the columns.
9 The order of the columns then becomes the key.
9 Plaintext attack postponed until two am xyz
Key: 4 3 1 2 5 6 7plaintext: a t t a c k p
o s t p o n ed u n t i l tw o a m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
Ch 2 Conventional Encryption: Classical Techniques 55
2.3 Classical Encryption Techniques
9 Transposition Techniques (Conti.)9 Perform more than one stage of transposition
9 Key: 4 3 1 2 5 6 7
plaintext: t t n a a p tm t s u o a od w c o i x kn l y p e t z
Ciphertext: NSCYAUOPTTWLTMDNAOIEPAXTTOKZ
Ch 2 Conventional Encryption: Classical Techniques 56
2.3 Classical Encryption Techniques
9 Transposition Techniques (Conti.)9 Perform more than one stage of transposition (Conti.)
9 The original sequence of letters is01 02 03 04 05 06 07 08 09 10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25 26 27 28
9 After the first transposition:03 10 17 24 04 11 18 25 02 09 16 23 01 0815 22 05 12 19 26 06 13 20 27 07 14 21 28
9 After the second transposition:17 09 05 27 24 16 12 07 10 02 22 20 03 2515 13 04 23 19 14 11 01 26 21 18 08 06 28
9 This is a much less structured permutation and is muchmore difficult to cryptanalysis.
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Ch 2 Conventional Encryption: Classical Techniques 57
2.3 Classical Encryption Techniques
9 Rotor machines
Edward Heberns Electric Code Machine, 1921U.S. Patent 1683072.
Rotors are 75a-e.
Ch 2 Conventional Encryption: Classical Techniques 58
2.3 Classical Encryption Techniques
9 Rotor machines (Conti.)
9 Consists of a set of independently rotating cylinders
9 A single cylinder defines a monoalphabeticsubstitution
9 After each input key is depressed, the cylinder rotatesone position, so that the internal connections areshifted accordingly. Thus, a different monoalphabeticsubstitution cipher is defined.
9A polyalphabetic substitution algorithm with a periodof 26.
Ch 2 Conventional Encryption: Classical Techniques 59
2.3 Classical Encryption Techniques
9 Rotor machines (Conti.)9 Multiple cylinders
9 The output pins of one cylinder are connected to theinput pins of the next
9 The cylinder farthest from the operator inputrotates one pin position with each keystroke
9 For every complete rotation of the outer cylinder, themiddle cylinder rotates one pin position
9 For every complete rotation of the middle cylinder,the inner cylinder rotates one pin position
9 26*26*26=17576 different substitution algorithms
9 Point to the way to DES
Ch 2 Conventional Encryption: Classical Techniques 60
2.3 Classical Encryption Techniques
Fig. 2.8 Three-Rotor Machine with wiring represented by numbered contacts.