Lecture 5: Classical Encryption Part 1 (introduction, transposition ciphers, simple substitution ciphers, Caesar cipher, random simple substitution cipher)

Question 1

What are the two facets of cryptology?

Answer 1

1. cryptography

2. cryptanalysis

Question 2

What is cryptography?

Answer 2

study of designing cryptosystems

science of secret writing

transformations of data depending on a secret (key)

Question 3

What is cryptanalysis?

Answer 3

study of breaking cryptosystems

Question 4

What is cryptography used to provide?

Answer 4

1. confidentiality

2. authentication (or integrity)

Question 5

What is confidentiality in terms of cryptography?

Answer 5

key is needed to read mesage

Question 6

What is authentication in terms of cryptography?

Answer 6

key is needed to write message (with digital signature)

Question 7

What does a cryptosystem consist of?

Answer 7

1. Set of plaintexts (holding original message)
2. Set of ciphertexts (holding encrypted message)
3. Set of keys
4. Function → encryption/encipherment → transforms plaintext into ciphertext
5. Inverse function → decryption/decipherment → transforms ciphertext back into plaintext

Question 8

What is another name for ciphertext?

Answer 8

cryptogram

Question 9

What are the main characteristics of a symmetric key cipher?

Answer 9

• Encryption and decryption keys knowing ONLY to sender & receiver
• Secure channel for transmission of keys

Question 10

What are main characteristics of an asymmetric key cipher?

Answer 10

• Each participant has public key & private key

* Possibly working for both encryption of messages and creation of digital signatures

Question 11

What is another name for a symmetric key cipher?

Answer 11

secret key cipher

Question 12

What is another name of an asymmetric key cipher?

Answer 12

public key cipher

Question 13

What is the notation for an encryption function for a symmetric encryption algorithm?

Answer 13

E

Question 14

What is the notation for an decryption function for a symmetric encryption algorithm?

Answer 14

D

Question 15

What is the notation for a message/plaintext for a symmetric encryption algorithm?

Answer 15

M

Question 16

What is the notation for a cryptogram/ciphertext for a symmetric encryption algorithm?

Answer 16

C

Question 17

What is the notation for a shared secret key for a symmetric encryption algorithm?

Answer 17

K

Question 18

How is encryption denoted as for a symmetric encryption algorithm?

Answer 18

C = E(M,K)

Question 19

How is decryption denoted as for a symmetric encryption algorithm?

Answer 19

M = D(C,K)

Question 20

What are some resources available to an adversary?

Answer 20

• computational capability

* system inputs/outputs

Question 21

What may the adversary’s goal be?

Answer 21

• retrieving whole secret key
• distinguishing two messages (e.g. YES and NO) → may want to send message rather than control system and this may be enough info

Question 22

What is exhaustive key search?

Answer 22

Try all possible keys

Question 23

Can you prevent exhaustive key search?

Answer 23

No, so all cryptosystems must have enough keys to make search too difficult computationally

Question 24

Is it possible that an adversary finds key without trying exhaustive key search?

Answer 24

Yes

Question 25

Is it possible that an adversary breaks cryptosystem without finding key?

Answer 25

Yes, e.g. ciphertext may leak info about key

Question 26

What is a minimum standard for a cryptosystem?

Answer 26

Prevention of exhaustive search

Question 27

What is the ciphertext only attack?

Answer 27

attacker has access to ONLY intercepted ciphertexts

Question 28

What is the known plaintext attack?

Answer 28

attacker knows a small amount of plaintexts and their corresponding ciphertexts

Question 29

What is the chosen plaintext attack?

Answer 29

attacker can obtain ciphertext from some plaintext that it has selected (attack has “insider encryptor” available who helps trigger attack)

Question 30

What is the chosen ciphertext attack?

Answer 30

attacker can obtain plaintext from some ciphertext that is has selected (attack has “inside decryptor” available who decrypts attacker’s chosen ciphertext)

Question 31

When is a cryptosystem seen as highly insecure?

Answer 31

if it can be practically attacked using only intercepted ciphertexts

Question 32

What attacks should a cryptosystem be secure against?

Answer 32

chosen plaintext and chosen ciphertext attacks

Question 33

What sort of attack is practical for an attacker?

Answer 33

ciphertext attacks

Question 34

What is Kerckhoffs’ Principle?

Answer 34

attacker has complete knowledge of ciphertext i.e. decryption key is only item unknown to attacker

Question 35

What is using a secret, non-standard algorithm an example of?

Answer 35

security through obscurity => severe problems

Question 36

What do statistical attacks depend on?

Answer 36

using redundancy of alphabet

Question 37

What info helps in a statistical attack?

Answer 37

distribution of single letters, diagrams (double letters) and trigrams (triple letters)

Question 38

What are the most frequent letters (including space) in English (top 3)?

Answer 38

space E N

Question 39

What are the most frequent digrams in English?

Answer 39

E + space | space + A

Question 40

In terms of transposition ciphers, what two operations do historical ciphers combine?

Answer 40

transposition | substitution

Question 41

Define the transposition operation

Answer 41

characters in plaintext mixed up with each other (permuted) → limited to plaintext’s alphabet

Question 42

Define the substitution operation

Answer 42

each character (resp. set of characters) replaced by different character

Question 43

Explain how transposition ciphers work

Answer 43

* Permuting characters in fixed period d and permutation f * Plaintext seen as a matrix of rows of length d * Permuting rows/cols and outputting in row/col order * E.g. permutation of rows and outputting in column order * Number off cols in random order → x cols have x! possible keys https://www.youtube.com/watch?v=sHsnH1u03e4

Question 44

Explain simple transposition cipher

Answer 44

* Key → (d,f) * Each block of d characters is re-ordered using permutation f * d! permutations of length d → d x (d - 1) x (d-2) x … x 2 x 1 → take ball without replacement i.e. one less permutation choice

Question 45

How can we identify a transposition cipher?

Answer 45

Frequency distribution of ciphertext = frequency distribution of plaintext characters

Question 46

Can we solve transposition ciphers by hand if d is small? If so, how?

Answer 46

Yes, using anagramming

Question 47

What is anagramming?

Answer 47

restoring disarranged characters to original position

Question 48

How can you optimize the trials for attempting to solve a transposition cipher?

Answer 48

Knowledge of plaintext language diagrams and trigrams

Question 49

How can we speed up the process of solving a transposition cipher?

Answer 49

automate the process

Question 50

Compare the permutation done in a transposition and substitution cipher

Answer 50

Transposition ciphers permutes PLAINTEXT chars while substitution ciphers permute ALPHABET chars

Question 51

What is the general idea of a simple substitution cipher?

Answer 51

each char in plaintext alphabet replaced b character in ciphertext alphabet following substitution table

Question 52

What is a simple substitution cipher also called?

Answer 52

monoalphabetic substitution cipher

Question 53

Explain the Caesar cipher

Answer 53

Moving ith letter of alphabet to (i+j)th letter s.t.c key is j → every char moved by j positions to right

Question 54

What is the encryption function for the caesar cipher?

Answer 54

Ci = (Mi + j) mod n

Question 55

What is the decryption function for the caesar cipher?

Answer 55

Mi = (Ci - j) mod n

Question 56

What is n in the caesar cipher?

Answer 56

Either n = 26 or n = 27 (includes space) → size of alphabet

Question 57

How do you perform cryptanalysis on caesar cipher?

Answer 57

Finding where one of the most frequent chars is shifted to --> count freqs --> trial mapping

Question 58

Explain how the random simple substitution cipher works

Answer 58

Assigning random char of alphabet to another char in alphabet

Question 59

How are encryption and decryption defined as for random substitution cipher?

Answer 59

defined by substitution table that randomly permutes alphabet

Question 60

How many keys if random substitution cipher alphabet has 26 chars?

Answer 60

26! keys | if say A=C, then can’t assign A again → selection without replacement

Question 61

What is caesar cipher a special case of?

Answer 61

substitution cipher

Question 62

Can you do frequency analysis for random substitution cipher?

Answer 62

Yes, but solving by hand is tedious → many trials and errors