Upcoming SlideShare
×

# Cryptography : From Demaratus to RSA

786 views
506 views

Published on

From Demaratus in ancient Sparta using wax covered tablets to the German Enigma to Diffie-Helman and RSA cryptography has always been at the cutting edge.

Published in: Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
786
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
11
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Cryptography : From Demaratus to RSA

1. 1. Cryptography 101
2. 2. What is Cryptography? Encryption is the process of: 1.Transforming data (x) 2.Using an algorithm (e) 3.To make it unreadable to anyone (y) 4.except those possessing the key. (k) K={k1,…,kn} The Quick Brown Fox Me (mod N) where M=The Quick Brown Fox Uif Rvjdl Cspxo Gpy Kerchhoffs’ principle: A cryptosystem should be secure even if the Attacker knows all the details about the system, with the exception of The key.
3. 3. We shall extend the empire of Persia such that its boundaries will be God's own sky, so the sun will not look down upon any land beyond the boundaries of what is our own -Xerxes (Ahasuerus) ~450 B.C.
4. 4. (Spartan) Scytale Rail Fence Cipher Route Cipher Transposition Ciphers
5. 5. The Quick Brown Fox GSV JFRXP YILDM ULC Substitution Ciphers The Quick Brown Fox ZIT JXOEA WKGVF YGB Shift Cipher (Caesar) The Quick Brown Fox SGD PTHBJ AQNVM ENW At-Bash
6. 6. Modular ciphers a = r mod m 42 = 9*4 + 6 r = a – m*q 42 = 6 mod 9 42 = q*9 + 6 6 = 42 – q*9 q = 0, r = 42 q = 1, r = 33 q = 2, r = 24 q = 3, r = 15 q = 4, r = 6 (0<q<m-1) q = 5, r = -3 q = 6, r = -12 12 + 7 = 19 => 1 mod 9 14 – 2 = 12 => 3 mod 9 11 * 8 = 88 => 7 mod 9 15/5 = 3 !=> 3 mod 9 If the multiplicative inverse exists for a number then we can divide by that number 5*2=10 => 1 mod 9 2 is the multiplicative inverse of 5 (and vice versa) 15*2 = 30 => 3 mod 9 If x is coprime with modulus then it has an inverse.
7. 7. Caesar Cipher Encryption: ek (x) = x + k mod 26 Decryption: ek (y) = y – k mod 26 The quick brown fox k=3 t=20, 20 + 3 = 23 mod 26 h=8, 8 + 3 = 11 mod 26 e=5, 5 + 3 = 8 mod 26 Affine Cipher k=(a,b) Encryption: ek (x) = a*x + b mod 26 Decryption: ek (y) = a-1 * (y – b) mod 26 The quick brown fox k=(5, 3) t=20, 5*20 + 3 = 103 = 25 mod 26 h=8, 5*8 + 3 = 43 = 17 mod 26 e=5, 5*5 + 3 = 28 = 2 mod 26 21 * 5 = 105 = 1 mod 26 21 * 25-3 = 462 = 20 mod 26 21 * 17-3 = 294 = 8 mod 26 21 * 2-3 = -21 = 5 mod 26
8. 8. Brute-Force Attacks Given: y = SGD PTHBJ AQNVM ENW Keyspace = {1,…,25} Decryption : ki(y) =? x
9. 9. Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī 850 C.E. Cryptanalysis Letter Frequency Short word and letter combinations the be to of and that have for not http://www.richkni.co.uk/php/crypta/
10. 10. Normal English letter frequency Ciphertext letter frequency
11. 11. Vigenère cipher A polyalphabetic cipher Key = KING The sun and the man in the moon Dpr yev ntn buk wia ox buk wwbt 4 possible ways to spell the word “the” K – DPR I - BUK N – GNO G - ZRM http://www.simonsingh.net/The_Black_Chamber/vigenere_cracking_tool.html http://sharkysoft.com/vigenere/