brief incursion into cryptography 1 20 th may 2008 brief incursion into cryptography 20 th may 2008
TRANSCRIPT
Brief Incursion into Cryptography
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20th May 2008
Brief Incursion into Cryptography
20th May 2008
Brief Incursion into Cryptography
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20th May 2008
Introduction
Define terminology Evolution of cryptology
Simple methods The Enigma Machine Asymmetric Encryption
Evolution of cryptanalysis Future
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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.
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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
cow cwo ocw owc wco woc
3 letters » 3! combinations
...
35 letters » 35! combinations » over 50 000 000
000 000 000 000 000 000 000 000 combinations
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Spartan Scytale
First cryptographic military device (5th century BC)
Strand of leather or parchment wrapped around a wooden crane
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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
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
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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 zD 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
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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
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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 zJ 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
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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
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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
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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)
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The Enigma (1)
Three components: keyboard, rotor, display The rotor played the most important role
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The Enigma (2)
Later, there were added two more components: the reflector and the plugboard
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The Enigma (3) The plugboard
had the role to swap certain letters, increasing the number of possible combinations
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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
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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
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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
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Asymmetric key (1)
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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
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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
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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
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Asymmetric key (5)
1. 2.
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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
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Q & A
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