Hill cipher, stream ciphers and the One Time Pad

Question 2

What is the hill cipher?

Answer 2

Polygram cipher (polygraphic cipher)

Perform a linear transformation on d number of plaintext characters, to get d ciphertext characters.

Enc:
Multiply a d x d matrix K by the block of plaintext P
C = KP

Dec:
Multiply the matrix K⁻1 by the block of the ciphertext C
P = K⁻1C

Question 3

What is a weakness of the Hill cipher?

Answer 3

It is linear, known plaintext attacks are easy

Question 4

Do a cryptanalysis of the Hill cipher

Answer 4

Known plaintext are possible given d number of plaintext ciphertext matching blocks.

We are given d blocks of matching P and C,
Then we are able to C = KP for K

And use K to get rest of plaintext:
P = K⁻1*C

Question 5

What are stream filters?

Answer 5

Characterised by the generation of a keystream of any required length.

Each element of the keystream encrypts one or more ciphertext characters

Usually symmetric ciphers

Keystream must have good randomness properties

Question 6

What is a synchronous stream cipher?

Answer 6

Keystream generated independently of the P

Question 7

How does enc and dec in synchronous stream ciphers work?

Answer 7

Enc: c(t) = p(t) XOR s(t)

Dec: p(t) = c(t) XOR s(t)

Question 8

What is the one time pad?

Answer 8

Key: truly random sequence of characters, independently generated

Each character in key is used one time only

non-periodic binary synchronous stream cipher

Provides perfect secrecy

Question 9

Define perfect secrecy

Answer 9

Message set: {M1, M2, …, Mk}
Ciphertext set: {C1, C2, …, CK}

P(Mi|Cj): Probability of Mi was encrypted given that Cj was observed

Perfect secrecy:
P(Mi|Cj) = P(Mi)

Question 10

How does enc and dec work in the one time pad?

Answer 10

Enc:
ci = (pi + ki) mod 26

Dec:
pi = (ci -ki) mod 26

mod 26 when using roman alphabeth

Question 11

With P = HELLO
K = EZABD

What is C?

Answer 11

LDLMR

Given C, note that P can be any 5-letter message

Question 12

How does enc and dec work in binary one time pad?

Answer 12

Enc:
ci = pi XOR ki

Dec:
pi = ci XOR ki

Question 13

What are some properties of perfect secrecy, in regards to the number of keys?

Answer 13

Any cipher with perfect secrecy, myst have as many keys as there are messages.

This makes one-time pad the only unbreakable cipher.

Question 14

What is the main problem with one time pad?

Answer 14

Key distribution and random keys

Dealing with keys are difficult when these are so large

Question 15

What is visual cryptography?

Answer 15

Application of one time pad

Split image into two shares

Dec: Overlaying the twoshares

Each pixel is shared in a random way

Each share reveals no information about the image

Question 16

How does encryption work in visual cryptography?

Answer 16

Generate a one time pad P (random string of bits) with length equals to number of pixels in the image

Generate an image share by replacing each bit using these sub-pixels patterns:
0 bit: black-white
1 bit: white-black

Generate the other share as follows:
- The same as the first share for all the white pixels of the image
- The opposite of the first share for all black pixels of the image

Question 17

How do we decrypt in visul cryptography?

Answer 17

Overlay the two shares