2. Digital Communications

3. Secure Communication
CRYPTOGRAPHY

4. How does mathematics help in establishing secure communication?
PROBLEM QUESTION
How does mathematics help in establishing secure communication?

5. The REAL WORLD Problem

6. Solving the Problem

7. Solving the Problem

8. Goal of a Cryptosystem
Relay an information from one place to another without anyone else being able to know it.

9. Continue reading the contents of this slide.
LEARN MORE
Continue reading the contents of this slide.

10. Encryption and Decryption
Encryption is the process of using an algorithm to transform information into a format that cannot be read.
Decryption is the process of using another algorithm to transform encrypted information back into a readable format.

11. Plain text and Cipher text
The original information is referred to as the plain text while the encrypted version is the cipher text.

12. Objectives of Encryption

13. Confidentiality
The sender (let us call her Alice) and receiver (let us call him Bob) can be assured that no third party can read the message.

14. Integrity
Alice and Bob can be sure that no third party can make changes in the message.

15. Authenticity
Bob can be sure that it is Alice who sent the message.

16. Non-repudiation
Bob can prove to any third party that Alice sent the message

17. Simple Ciphers

18. Pigpen Cipher

19. Caesar’s Cipher
If he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others. “— Suetonius, Life of Julius Caesar 56

20. Caesar’s Cipher
Encipher the word SECRET.

21. YOU ARE RIGHT IF YOU WROTE …
VHFUHW

22. Caesar’s Cipher
Decipher the word NLQJ.

23. YOU ARE RIGHT IF YOU WROTE …
KING

24. Vigenère Cipher
The Vigenère encryption was the creation of the French diplomat, Blaise de Vigenere, He viewed the cipher as a substitution cipher where a different alphabet was used for the next letter of the message, with the alphabets repeating periodically --- according to some key.

25. Vigenère Cipher Suppose the message to be sent is RUNNOW.
Using the alphabet A B … Z → 0 1 … 25 and keyword HUSH, we proceed as follows.

26. Vigenère Cipher
To decrypt, we reverse the process, i.e. do subtractions.

27. Which is more difficult to decrypt
Which is more difficult to decrypt? A monoalphabetic cryptosystem or a polyalphabetic cryptosystem?

28. Testing Your Understanding