Lecture 6: Classical Encryption Part 2 (polyalphabetic substitution ciphers, Vigenere cipher, other polyalphabetic ciphers, Hill cipher)

Question 1

Define polyalphabetic substitution

Answer 1

• Using multiple mappings from plaintext to ciphertext
• Given d ciphertext alphabets C0, C1, … Cd-1, let fi: A→ Ci be a mapping from plaintext alphabet A to ith ciphertext alphabet Ci for 0 <= i <= d - 1

Question 2

What is the point of using multiple alphabets in polyalphabetic substitution

Answer 2

smooths frequency distribution → direct frequency analysis not effective

Question 3

What are typical polyalphabetic ciphers?

Answer 3

periodic substitution ciphers based on period d

Question 4

What is the encryption process for polyalphabetic ciphers?

Answer 4

Plaintext message M = M0 … Md-1Md … M2d-1Md …

encrypted to

E(K,M) = f0(M0)…fd-1(Md-1)f0(Md)…fd-1(M2d-1)f0(M2d)…,

where d ≡ 0 mod d

Question 5

In terms of polyalphabetic ciphers’ encryption process, what is the special case?

Answer 5

When d = 1
Monoalphabetic cipher (simple substitution cipher)

Question 6

Briefly outline the key generation process for a random polyalphabetic substitution cipher

Answer 6

1) select block length d

2) generate d random simple substitution tables

Question 7

Briefly outline the encryption process for a random polyalphabetic substitution cipher

Answer 7

encrypt ith char using substitution table number j s.t. i ≡ j (mod d)

Question 8

Briefly outline the decryption process for a random polyalphabetic substitution cipher

Answer 8

using same substitution table as in encryption to reverse simple substitution

Question 9

Explain the example of the polyalphabetic substitution encryption in slide 8 of set 6.

Answer 9

TODO

let X be number of value
then X mod 3 ≡ Y

Cy is the value it corresponds to

Question 10

What is the Vigenere Ciphers based on?

Answer 10

shifted alphabets

Question 11

What is the key K in the Vigenere Cipher?

Answer 11

seq of chars

Question 12

How do you compute the amount of shift in the ith alphabet in the Vigenere Cipher?

Answer 12

For 0 <= i <= d-1, K gives amount of shift in ith alphabet, i.e. fi(M) = (M+Ki) mod n

Question 13

Explain the example of the Vigenere Cipher on slide 10, set 6

Answer 13

Use a word as the period and repeat for each section of the message M.

Use the word’s char’s corresponding number as the shift amount for each ith char

Question 14

How you can identify the period length during cryptanalysis of the Vigenere Cipher?

Answer 14

1) Kasiski method

2) CrypTool uses autocorrection to estimate period

Question 15

How you can attack separately d substitution tables during cryptanalysis of the Vigenere Cipher?

Answer 15

Each substitution is a shift (Caesar cipher) → if there is sufficient ciphertext then straightforward

Question 16

What do you determine from cryptanalysis for Vigenere Cipher?

Answer 16

1) Identify period length

2) Attack separately d substitution tables

Question 17

What is the purpose of identifying the period using autocorrelation?

Answer 17

Method used to find period length d of any periodic polyalphabetic cipher

Question 18

Explain what identifying the period using autocorrelation is

Answer 18

Given ciphertext C, computing correlation between C and its shift Ci for all vals i of period

Plotting results on histogram and identifying period

Question 19

When do we see peaks in value Ci when doing period identification using autocorrelation for a periodic polyalphabetic cipher?

Answer 19

when i is multiple of period

Question 20

Explain the Kasiski method used in identifying period length d

Answer 20

1) note which sequences of letters appear multiple times
2. guage the number of chars that separate these pairs of strings
3. check common divsors of these numbers –> period is likely one of these common divisors

Question 21

Explain the crytanalysis example for polyalphabetic cipher on slides 13-15 in set 6

Answer 21

TODO - note sure about part 2

Question 22

Briefly outline the beaufort cipher

Answer 22

polyalphabetic cipher similar to Vignere cipher but using substitution fi(M) = (Ki - M) mod n

Question 23

Briefly outline the autokey cipher

Answer 23

polyalphabetic cipher starting off as Vigenere cipher but using plaintext to define subsequent alphabets once the alphabets defined by the key have been used → not periodic cipher as change key

Question 24

Briefly outline the running key cipher

Answer 24

polyalphabetic cipher using (practically) infinite set of alphabets from shared key → in practice, shared key is extract from book (book cipher)

Question 25

Briefly outline rotor machines’ purpose

Answer 25

electromechanical machines developed for encryption using rotors as moving alphabets

Question 26

What type of cipher is Hill cipher?

Answer 26

Polygram cipher (aka polygraphic cipher) → simple substitution cipher on extended alphabet consisting of multiple characters

Question 27

What is the major weakness of the Hill cipher?

Answer 27

linearity so known plaintext attacks are easy

Question 28

Briefly outline the encryption in the Hill cipher

Answer 28

Encryption involves multiply d x d matrix K by block of plaintext M → C = KM

linear transformation of d plaintext chars to get d ciphertext chars

Question 29

Briefly outline the decryption in the Hill cipher

Answer 29

Decryption involves multiplying matrix K^(-1) by block of ciphertext C → M = K^(-1)*C

linear transformation of d ciphertext chars to get d plaintext chars

Question 30

How are plaintext pairs represented in the Hill cipher?

Answer 30

Plaintext pairs written as col vector, letters encoded as numbers

Question 31

What do we do if there are insufficicent numbers to fill block?

Answer 31

Pad

Question 32

What is n in Hill cipher?

Answer 32

27 –> mod 27

Question 33

What should K*(K^(-1)) give for the Hill cipher?

Answer 33

identity matrix

Question 34

How is the size of a matrix written? What must be satisfied when multiplying matrices?

Answer 34

cols * # rows

inner values same

Question 35

Do the encryption and decryption example for the Hill cipher on slide 22 of set 6

Answer 35

TODO

Question 36

What attack is possible on Hill cipher?

Answer 36

Known plaintext attacks possible given d plaintext-ciphertext matching blocks → since linear function and need enough elements to solve eqn and get K

Question 37

How can you perform a known plaintext attack on the Hill cipher?

Answer 37

Given blocks (col vectors) Mi and Ci for 0 <= i <= d-1

C = [C0C1…Cd-1]
M = [M0M1…Md-1]
Solving C = KM for K
M = K-1C

Question 38

Explain the cryptanalysis example of the Hill cipher on slides 24-27 of set 6

Answer 38

TODO

Question 39

What attack follows from the known plaintext attack on Hill cipher?

Answer 39

ciphertext only attack

Question 40

What else needs to be done to do a ciphertext only attack on the Hill cipher, knowing that known plaintext attacks are possible?

Answer 40

extra task of finding probable blocks of matching plaintext-ciphertext