1. Cryptography (Traditional Ciphers)
Week-7

2. Substitution Ciphers Monoalphabetic Substitution Ciphers
An improvement over the Caesar cipher
Change/replace one symbol with another
Obscures the meaning of a symbol (confusion)
P : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
C : Z X Y W U V T R S Q O P N L M K I J H F G E C D B A
Each symbol in the plain alphabet P maps onto some other symbol in the cipher alphabet C

3. Substitution Ciphers Monoalphabetic Substitution Ciphers
Effectively, we are using a 26-character key (26-letter string) corresponding to the alphabet
In how many ways can all the 26-character be rearranged (permutation)?
Brute force attack
Not feasible: 26! (4 x 1026 ) – Enormous the key space
At 1 nsec (billionth of a second) per solution, a computer would take ~10 billion years (1010) to try all the keys

4. Substitution Ciphers
4 x 1026 Incomprehensible!

5. Substitution Ciphers Cryptanalysis Attack
Basic attack takes advantage of statistical properties of English:
In English, e (most common letter) followed by
t, o, a, n, i, etc.
Common two-letter combinations (digrams):
th, in, er, re, an
Common three-letter combinations (trigrams):
the, ing, and, ion

6. Substitution Ciphers Cryptanalysis Attack
First, count relative frequencies of all letters in the ciphertext
Second, tentatively assign most common letter to e, next common one to t and so on
Third, find common trigrams of the form [t ? e], strongly suggesting that ? is h
Fourth, check if [t h ? t] occurs frequently, suggesting that ? stands for a

7. Substitution Ciphers
English Letter Frequencies

8. Substitution Ciphers Multiple Substitution
Two or more substitution ciphers used in series
Letters 1, 3, 5 .. encrypted under cipher (or key) 1;
Letter 2, 4, 6 encrypted cipher (or key) 2 etc.

9. Substitution Ciphers Multiple Substitution - Exampleq r s t u v w x y z 13 14 15 16 17 18 19 20 21 22 23 24 25
I THINK THAT I SHALL NEVER SEE
Under cipher 1: I H N T A I H L N V R E
Under cipher 2: T I K H T S A L E E S E
Cipher 1 = n + 3; cipher 2 = n + 5
Ciphertext 1 : L K Q W D L K O Q Y U H
Ciphertext 2 : Y N P M Y X F Q J J X J
Result: LYKNQPWMDYLXKFOQQJYJUXHJ

10. Transposition Ciphers
Various Types
Plaintext symbols are simply reordered and not replaced like substitution cipher (diffusion)
Each letter represents itself keeping the frequency distribution intact
Simple Example
Plaintext : CAT
Possible Ciphertext: { CTA, ACT, ATC, TCA, TAC }

11. Transposition Ciphers
Columnar Transposition Simple Example
Plaintext written in fixed-length rows, read off by columns
Example: SAM
PLE
becomes SPALME
Other more complex Examples
Use of a key to number the columns. “we lost the war”
W E L O
S T T H
E W A R
Result:
Lta ohr etw wse

12. One-Time Pad The only unbreakable cipher (Theoretically) Example:
First, convert the plaintext message into a bit string (ASCII) e.g. “ I love you.”
Second, choose random bit string key (key pad) with same length as the plaintext
Third, compute XOR (eXclusive OR) of the two strings, bit by bit
plaintext: …
key pad: …
Ciphertext: …

13. Book Cipher Similar to one-time pad
Uses book (poem, piece of music, newspaper) to which both sender and receiver have access
Starting at a predetermined place in the shared object, use the element of the object as random numbers for a on-time pad
Weaknesses due to predictability in written objects, possible availability of shared objects to third party

14. Book Cipher
Example
uaopm kmkvt unhbl jmed because row M column i is u, row A column a is a, and so on.

15. Hardware Implementation
Transposition
P-Box (Permutation Box or P-Box) device
Substitution
S-Box (Substitution Box or S-Box) device
Product Cipher
Combines P-Boxes and S-Boxes

16. Thank You !