Cryptography
- 3. History Hieroglyph The Oldest Cryptographic Technique Steganography
- 4. Evolution
- 5. Goals of a Cryptography
- 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
- 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”
Editor's Notes
- #5: The growing understandability of number theory and algebra led to the advancement in ciphers or algorithms, it was adopted by govt, military business organizations to secure their secrets.Cryptography has decided wars and now is at the heart of communication
- #12: FREQUENCY ANALYSIS AND BRUTE FORCE ATTACKS
- #17: Pick 2 prime numbers.in practice this no are too big so that its harder to crack.p and q recommended to be 1024 bits i.e each no over 300 decimal digits.