7CCSMCIS Cryptography and Information Security

Caesar Cipher: Exercise

Use the following relative frequencies in an English text of 1000 letters:

to decide the most likely shift used to obtain:

K DKVO DYVN LI KX SNSYD, PEVV YP CYEXN KXN PEBI, CSQXSPISXQ XYDRSXQ.

Don’t just brute force but proceed strategically. Tally the frequencies of letters in the ciphertext.

As X appears in the ciphertext 7 times and E is the most frequent letter in the given table, it is reasonable to assume that X = E. If X = E, we have a shift of $ -19 \bmod 26 $ . This would result in our cipher -> plaintext looking like this:

Which gives this plaintext for the ciphertext:

R KRCV KFCU SP RE ZUZFK, WLCC FW JFLEU REU WLIP, JZXEZWPZEX EFKYZEX.

which, doesn’t make any sense. Systematically you can then apply X = ? where ? is the next most frequent letter from the given table. This gives X = T and finally X = N $ -10 \bmod 26 $ where you’ll find:

Which gives this plaintext for the ciphertext:

A TALE TOLD BY AN IDIOT, FULL OF SOUND AND FURY, SIGNIFYING NOTHING.

The Playfair Cipher: Exercise

Use the keyword “CHARLES” to encrypt the plaintext

MEET ME AT HAMMERSMITH BRIDGE TONIGHT

First we construct our $ 5 \times 5 $ matrix with the keyword CHARLES:

We can then split the plaintext into pairs with Xs to fill repeated characters when necessary:

ME ET ME AT HA MX ME RS MI TH BR ID GE TO NI GH TX

We can then cipher this to get:

GD DO GD RQ AR KY GD HD NK PR DA MS OG UP GK IC QY

And decrypt to get:

ME ET ME AT HA MX ME RS M(I/J) TH BR (I/J)D GE TO N(I/J) GH TX
MEET ME AT HAMXMERSM(I/J)TH BR(I/J)DGE TON(I/J)GHTX
MEET ME AT HAMMERSMITH BRIDGE TONIGHT

Viginère Cipher: Exercise

Use the tableu and keyword RELATIONS to encrypt TO BE OR NOT TO BE THAT IS THE QUESTION.

Steps:

1. Find $ x $ value for each character in key by using it’s index in the alphabet. i.e. R = 17, E = 4
2. Perform Caesar cipher for each character in plaintext with each $ x $ value, repeating key when necessary.

Encrypting TO BE OR NOT BE THAT IS THE QUESTION gives:

Key:            RE LA TI ONS RE LA TION SR ELA TIONSREL
Plain-text:     TO BE OR NOT TO BE THAT IS THE QUESTION
Cipher-text:    KS ME HZ BBL KS ME MPOG AJ XSE JCSFLZSY

To decrypt:

Cipher-text:    KS ME HZ BBL KS ME MPOG AJ XSE JCSFLZSY
Key:            RE LA TI ONS RE LA TION SR ELA TIONSREL
Plain-text:     TO BE OR NOT TO BE THAT IS THE QUESTION

The Viginère cipher presents an improvement over the Caesar cipher as it places a positional dependency on the cipher-text. It is isn’t immune to frequency attacks as you can see it is possible to guess the length of the key where there are reptitions in the cipher-text (there is ME encrypted for LA twice).

The Churchyard Cipher (Simplified): Exercise

What kind of cipher is it?

This is a mono-alphabetic cipher as each letter is mapped to one symbol/character in the ciphertext alphabet.

Why is it so difficult to break? (Especially without the hint!)

It is really difficult to break as it uses a ciphertext alphabet that we are not as familiar with.

What is the plaintext message?

So, after reading about the pigpen cipher and the tic-tac-toe hint; it’s clear that we can place our alphabet inside 3 tic-tac-toe grids and use the surrounding borders as an identifier for each letter; like so:

We can guess that the dots refer to which grid to use, but which one? We can easily find out by writing down each combination (there are only 3!):

I E D E D B E T   D E A B H
R N M N M K N R   M N J K Q
_ W V W V T W _   V W S T _

From here, there is only one sensical phrase: REMEMBER DEATH.

What is the key?

From the above, this makes our key:

One-time pad: Exercise

Given two distinct cipher-texts that have used the same one-time pad, what technique could an attacker use to break them?

The attacker could perform the same pad operation on the cipher-texts to obtain some information about the key. Ideally he’d need to intercept more cipher-texts with the same one-time pad. See coursework from QMUL (using XORs).