Introduction to cryptography. Using Caesar cipher ,Vigenere cipher to help Phineas and Ferb hide their plan from Candace . And finally ,RSA encryption technique explained.

2. Cryptography
What and Why?

3. History
Hieroglyph
The Oldest Cryptographic Technique
Steganography

4. Evolution

5. Goals of a Cryptography

6. Cryptosystems

7. FERB PHINEAS CANDACE

8. LETS GET AN ICECREAM

9. CAESAR CIPHER
p is the plaintext and 𝑝𝑖 is the i th character in p
and k is the secret key
Each letter 𝑐𝑖of the cipher text c is calculated as:

10. LETS GET AN ICECREAM
WV JHW DQ LFHFUHDPO H
CAESARCIPHER

12. VIGENERE CIPHER
Each letter 𝑐𝑖of the cipher text c is calculated as:
p is the plaintext and 𝑝𝑖 is the i th character in p
and 𝑘𝑗 is the j th letter of the secret key.

13. VIGENERE CIPHER
KEY : PERRY
LETS GET AN
ICECREAMPERR YPE RR
YPERRYPE
AIKJ ETX RE

14. RSA
(RIVEST-SHAMIR-ADLEMAN)

15. RSA
(RIVEST-SHAMIR-ADLEMAN)
• Generation of a pair of keys
• Encryption of the message at sender end
• Decryption of the message at receiver’s end

16. Generation of RSA key pairs
• Choose two prime numbers, p and q
p = 7 and q = 13
• Calculate RSA modulus (n)
n = pq
n = 91
• Find a number e such that 1<e<m and
gcd(e,m) = 1 where m = (p-1)(q-1)
let e = 5

17. • Public key is of the form (n,e).
Thus the pair (91,5) form our public key.
• Private key (d)
ed = 1 mod m
5d = 1 mod 72
• Extended Euclidean Algorithm
ax + by = gcd(a,b)
5x + 72y = 1
5x = 1 – 72y
5x = 1 mod 72

18. x y d k
1 0 5
0 1 72

19. x y d k
1 0 5
0 1 72 0

20. x y d k
1 0 5
0 1 72 0
1 0 5 14

21. x y d k
1 0 5
0 1 72 0
1 0 5 14
-14 1 2 2

22. x y d k
1 0 5
0 1 72 0
1 0 5 14
-14 1 2 2
29 -2 1 2

23. • Private key is the pair (91,29)
• Message , p is “CS”
c = 𝒑 𝒆
𝒎𝒐𝒅 𝒏
c1 = 58
c2 = 83
Cipher text c = 58 83

24. • To Decrypt the message
p = 𝒄 𝒅
mod n
p1 = 58 ^ 29 (mod 91)
p1 = 67 i.e C
p2 = 83 ^ 29 (mod 91)
p2 = 83
So the message is “CS”