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Brief Incursion into Cryptography

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

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Brief Incursion into Cryptography

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  1. Brief Incursion into Cryptography 20th May 2008

  2. Introduction • Define terminology • Evolution of cryptology • Simple methods • The Enigma Machine • Asymmetric Encryption • Evolution of cryptanalysis • Future

  3. 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. Back to Basics • Transposition of the message's letters • Very secure • Impracticable • Need to define some patterns to limit the number of possible combinations cow cow ocw woc cwo owc wco 3 letters » 3! combinations For example, consider this short sentence ... 35 letters » 35! combinations » over 50 000 000 000 000 000 000 000 000 000 000combinations

  5. Spartan Scytale • First cryptographic military device (5th century BC)‏ • Strand of leather or parchment wrapped around a wooden crane

  6. Kama – Sutra • States that women should study 64 arts • 45th on the list was mlecchita-vikalpa • Simple principle: • group letters in the alphabet in randomly chosen pairs • replace the letters with their pair meet at midnight 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 cuuz vz cgxsgibz

  7. Caesar's Cypher (1)‏ • First historically certified use of this type of cypher • Each letter is replaced by the one found on the 3rd 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 yhgl, ylgl, ylfl veni, vidi, vici

  8. 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. 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. 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. 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. 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. The Enigma (1)‏ • Three components: keyboard, rotor, display • The rotor played the most important role

  14. The Enigma (2)‏ • Later, there were added two more components: the reflector and the plugboard

  15. The Enigma (3)‏ • The plugboard had the role to swap certain letters, increasing the number of possible combinations

  16. 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. 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. 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. Asymmetric key (1)‏

  20. 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. 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. 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. Asymmetric key (5)‏ 2. 1.

  24. 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. Q & A • Please feel free to contact me for additional information on any of these topics at alexandru_palade@iqexpert.ro

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