Recap
Definition (Encryption: Caesar Cipher)
+3=⇥
mod 26
Definition (Encryption: Shift Cipher)
+d =⇥
mod 26, d a number
Definition (Decryption: Caeser Cipher)
+ 23 = ⇥
mod 26
Definition (Decryption: Shift Cipher)
⇥ + d mod 26 =
, d is the additive inverse of d
Code Summary: Caesar Cipher
We will talk about several di↵erent types of codes during the next
few weeks and it will be good to keep a summary for each.
• Encryption/Decryption Key
• Key Secrecy is the idea of how secret the decryption key must
be. There are codes where anyone can have access to the key!
• Letter Frequency, or how much a cipher changes the nature of
how often letters appear, will become increasingly important.
Cipher
Caesar
Shift
Encrypt
Key(s)
3
d
Decrypt
Key(s)
23
d
Key
Secrecy
Private
Private
Letter
Frequency
Normal
Normal
Encryption Method: Vigenère Cipher
Definition
An English Language Vigenère Cipher uses a di↵erent shift for
each letter, depending on the position of the letter in the message.
Encryption uses the rule
1
+d1 mod 26 = ⇥1
2
+d2 mod 26 = ⇥2
3
+d3 mod 26 = ⇥3
..
.
where 1 is the first plaintext letter and d1 is the first shift,
the second plaintext letter and d2 is the second shift, etc...
2
is
Example
Example
Suppose you use a Vigenère Cipher with the following shifts.
d1 = 4, d2 = 15, d3 = 7.
Encrypt the plaintext “ATE”.
Encrypt the plaintext “TEA”.
Encrypt these two words using the Caeser Cipher and compare
the encrypted words to the ones you got above.
Related Idea: Keyword
Definition
We use a Keyword to represent all of the di↵erent shifts (and the
order) to be used with a Vigenère Cipher.
Example
The keyword ENEMY gives the following shifts:
d1 = 5
d2 = 14
d3 = 5
d4 = 13
d5 = 25
So the first letter in our message will get shifted 5 places to the
right, the second letter will get shifted 14 places to the right, and
so on.
One more example!
Example
Encode the word DUMPLING using the keyword ARENA.
A=1
R=18
E=5
N=14
DUMPLING 7! EMRDMJFL
What is we used the keyword GOB?
G=7
O=15
B=2
DUMPLING 7! KJOWAKUV
A=1
Decryption Method: Vigenère Cipher
Definition
A Vigenère Cipher can be decrypted as follows:
(i) Identify d1 ,d2 , d3 , etc . . . corresponding to the letters of the
Keyword.
(ii) Find the additive inverse d 1 to d1 . Next find the
additive inverse d 2 to d2 . Continue for all values dk .
Together, the numbers d 1 , d 2 , d 3 , . . . are called the Decryption
Sequence.
To decrypt a Vigenère Cipher, we use the rule
⇥k + d k mod 26 =
k.
Example
Example ( Example )
The enemy agent starts using a new keyword. You MUST break
this new code! You figure out the shifts being used are
d1 = 1, d2 = 16, d3 = 16 d4 = 12, d5 = 5.
What Keyword is being used for this Vigenère Cipher?
What is the decryption sequence?
Decrypt the ciphertext message “FDUYD”.