1. Brief Incursion into Cryptography 1 20 th May 2008 Brief Incursion into Cryptography 20 th May 2008

2. Brief Incursion into Cryptography 2 20 th May 2008 Introduction ● Define terminology ● Evolution of cryptology – Simple methods – The Enigma Machine – Asymmetric Encryption ● Evolution of cryptanalysis ● Future

3. Brief Incursion into Cryptography 3 20 th May 2008 Terminology ● Cryptography or Cryptology (gr. krýpto – “hidden” + gráfo – “to write” or legein – “to speak”) is the practice and study of hiding information. ● Cryptanalysis (gr. krýpto – “hidden” and the verb analýein – “to loosen” or “to untie”) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so.

4. Brief Incursion into Cryptography 4 20 th May 2008 Back to Basics ● Transposition of the message's letters ● Very secure ● Impracticable ● Need to define some patterns to limit the number of possible combinations For example, consider this short sentence cow cwo ocw owcwco woc 3 letters » 3! combinations... 35 letters » 35! combinations » over 50 000 000 000 000 000 000 000 000 000 000 combinations

5. Brief Incursion into Cryptography 5 20 th May 2008 Spartan Scytale ● First cryptographic military device (5 th century BC) ● Strand of leather or parchment wrapped around a wooden crane

6. Brief Incursion into Cryptography 6 20 th May 2008 ● States that women should study 64 arts ● 45 th on the list was mlecchita-vikalpa ● Simple principle: – group letters in the alphabet in randomly chosen pairs – replace the letters with their pair Kama – Sutra A D H I K M O R S U W Y Z ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ ↕ V X B G J C Q L N E F P T meet at midnight cuuz vz cgxsgibz

7. Brief Incursion into Cryptography 7 20 th May 2008 Caesar's Cypher (1) ● First historically certified use of this type of cypher ● Each letter is replaced by the one found on the 3 rd position counting from the letter's index 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 D E F G H I J K L M N O P Q R S T U V W X Y Z A B C veni, vidi, vici yhgl, ylgl, ylfl

8. Brief Incursion into Cryptography 8 20 th May 2008 Caesar's Cypher (2) ● More general: replace each letter shifting its position by 1 to 25 in the alphabet ● Still not very secure – only 25 keys to be checked if someone suspects the algorithm used to encrypt the message

9. Brief Incursion into Cryptography 9 20 th May 2008 Caesar's Cypher (3) ● Most general: allow each letter in the alphabet to be paired up with any other letter ● Very secure ● Practical Over 400 000 000 000 000 000 000 combinations – an interceptor (checking 1 combination / second) would need almost a billion times the life of the universe to crack it Alice and Bob establish a key phrase like JULIUS CAESAR Remove white spaces and letters that repeat in the key phrase: JULISCAER 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 J U L I S C A E R T U V W X Y Z B D F G H J K M P Q

10. Brief Incursion into Cryptography 10 20 th May 2008 Cryptanalysis (1) ● The most general Caesar Cypher was considered very secure until the Arabs invented cryptanalysis ● They developed methods for finding the original message without knowing the key ● First writing of this method is in a book written by Abu Yusuf Ya'qub ibn Is-haq ibn as-Sabba ibn 'omran ibn Ismail al-Kindi

11. Brief Incursion into Cryptography 11 20 th May 2008 Cryptanalysis (2) ● Method consists of 2 steps – Examine a relative long plain text and count the number of appearances of each letters; do the same for the encrypted text – Match the most frequent letters in the plain text with the most frequent in the encrypted one and, with little ingeniousness, discover the message ● This kind of cryptanalysis led to the beheading of Queen Mary of Scotland in 1857

12. Brief Incursion into Cryptography 12 20 th May 2008 Taking advantage of technology ● Arthur Scherbius – wanted to replace code created by means of paper and pencil ● The most dreadful encrypting machine – The Enigma (1918)

13. Brief Incursion into Cryptography 13 20 th May 2008 The Enigma (1) ● Three components: keyboard, rotor, display ● The rotor played the most important role

14. Brief Incursion into Cryptography 14 20 th May 2008 The Enigma (2) ● Later, there were added two more components: the reflector and the plugboard

15. Brief Incursion into Cryptography 15 20 th May 2008 The Enigma (3) ● The plugboard had the role to swap certain letters, increasing the number of possible combinations

16. Brief Incursion into Cryptography 16 20 th May 2008 The Enigma (4) ● Rotor orientation – 3 rotors with 26 orientations each ● 26x26x26= 17 576 ● Rotors' display – 3 rotors can be arranged in ● 3!= 6 ● Plugboard – assume we inverse 6 pairs of leter ● = 100 391 791 500 ≈ 10 000 000 000 000 000 000

17. Brief Incursion into Cryptography 17 20 th May 2008 The Enigma (5) ● At first sight, it was the ultimate encryption machine ● Little flaws in the encryption process, flaws in the usage of the machine, capture of keys notebooks permitted the Allies to crack the system ● Alan Turing was the one to create the machine which, by the end of war, was multiplied in 200 copies ● Successful cryptanalysis of the Enigma machine meant winning the war for the Allies

18. Brief Incursion into Cryptography 18 20 th May 2008 Distributing keys ● Big problem, from both practical and security point of view ● It was tackled by many cryptologists ● In 1976, Whitfield Diffie made the breakthrough, at least in theory

19. Brief Incursion into Cryptography 19 20 th May 2008 Asymmetric key (1)

20. Brief Incursion into Cryptography 20 20 th May 2008 Asymmetric key (2) ● Postal analogy: – Bob makes a padlock and a key – Bob multiplies the padlock in 1000 copies and sends each one to a postal office in the country – Anyone can put a message in a box and lock it using the padlock (you don't need the key to seal the padlock) – Now, only Bob can use his unique key to open the box and read the message

21. Brief Incursion into Cryptography 21 20 th May 2008 Asymmetric key (3) ● Resolves the problem of distributing keys, the biggest issue of cryptography ● Finding a mathematical function which emulates this behavior is not an easy task ● 1977 – Ron Rivest, Adi Shamir and Leonard Adleman came with the mathematical function and completely changed cryptography

22. Brief Incursion into Cryptography 22 20 th May 2008 Asymmetric key (4) ● The algorithm, known as RSA, is a pseudo one-way mathematical function, hard to reverse ● The keys: – Private: two large prime numbers – Public: the multiplication of those two numbers ● Under present conditions of technical and mathematics, to reverse the function it would take all our world's computer power and the age of universe in time

23. Brief Incursion into Cryptography 23 20 th May 2008 Asymmetric key (5) 1. 2.

24. Brief Incursion into Cryptography 24 20 th May 2008 Where are we heading ● Any code, as history taught us, is breakable sooner or later ● Unfortunately for cryptography, tests are being made regarding the build of a quantum computer – making possible to crack asymmetric algorithms in a matter of seconds ● Fortunately, there are already algorithms which are 100% safe and can not be broken – in practice, but also in principle

25. Brief Incursion into Cryptography 25 20 th May 2008 Q & A ● Please feel free to contact me for additional information on any of these topics at alexandru_palade@iqexpert.ro