CRYPTOGRAPHY v/s CRYPTANALYSIS By Raghuveer Mohan Hardik Barot Neethi Varun Neethi Sekar

Topics Covered Introduction Short History Transposition Substitution Frequency Analysis Vigenere Cipher Enigma Machine Conclusion

INTRODUCTION Motivation – Threat of enemy interception – Nations have operated code-making departments Ongoing Battle – Code Makers - Make stronger Codes – Code Breakers - Invented more powerful methods for attacking them – In this war, both side have used diverse range of disciplines and technologies From mathematics to linguistics, From information theory to quantum theory. – In return, code makers and code breakers have enriched these subjects, and their work has accelerated technological development, most notably in the case of the modern computer.

SHORT HISTORY AD – Arab Scholars were enjoying vigorous period of Intellectual Achievement – Europe was at nascent stage struggling with cryptography. – Only European Monasteries were ahead where monks studied bible in search of hidden messages. – Medieval monks were intrigued by the fact that Old Testaments used Hebrew Cipher where letter replacement happened as follows. – a=>z b=>y and so on AD 1300 – First known European book - Included 7 methods to keep messages secret written by English Franciscan Monk and Polymath Roger Bacon.

Contin… AD 1400 – Use of Cryptography became extremely wide spread with alchemists and scientists using it to keep their discoveries secret. – Famous works include Geffrey Chaucer. He replaced plaintext with symbols e.g b with delta sign. But level of security is the same as letter for letter substitution. AD – European Cryptography was burgeoning industry – Science of cryptanalysis was beginning in the west. The First great cryptanalyst was SORO appointed as Venetion cipher secretary. – Towards the end of sixteenth century French consolidated their code breaking prowess with the arrival of Francois Viete. – Spain was much more naive compared to their rivals elsewhere in Europe. Their cryptgraphers were stunned to know that their messages were transparent to French. – Period of transition where crytanalysts had started using frequency analysis whereas Cryptogaphers relied on monoalphabetic substitution ignorant of the extent to which cryptnalysts like SORO and VIETE were able to read their messages.

Transposition – In transposition the letters of the message are simply re-arranged effectively giving an anagram. Transposition offers high security for the large sentences but if the sender and the receiver do not agree upon a protocol it is going to be difficult even for the receiver to unscramble the message. – Example 1 - Rail-Fence Algorithm Plaintext THY SECRET IS THY PRISONER; IF THOU LET IT GO, THOU ART A PRISONER TO IT Rail-fence Algorithm T Y E R T S H P I O E I T O L T T O H U R A R S N R O T H S C E I T Y R S N R F H U E I G T O A T P I O E T I Ciphertext T Y E R T S H P I O E I T O L T T O H U R A R S N R O T H S C E I T Y R S N R F H U E I G T O A T P I O E T I The receiver can recover the message by simply reversing the process.

Substitution The next form of cipher is the substitution cipher in which we pair letters of the alphabets at random and than substitute each letter in the originals with it partner. Example 1 - Randomly assigned partners – Letters : A D H I K M R S U W Y Z – Partners : V X B G J C Q L N E F P T – Text : MEET AT MIDNIGHT – Cipher : CUUZ VZ CGXSGYBZ

Caesar Cipher Example 2 - Caesar’s Cipher – Caesar used a shift by 3 cipher in which every plain text letter is shifted by 3 letters deep in the alphabet sequence after it. It is possible to substitute by any places in the alphabet sequence. – Plaintext : veni vidi vici – Cipher text : yhql ylgl ylfl

Cryptographic Process The above figure has three components : Plaintext : Normal readable message Key : Used to convert Plaintext to cipher text and vice versa Cipher text : Message obtained after applying the key to Plaintext

Frequency Analysis So what is Frequency analysis and how it works? Here the variation in the frequencies of letters were exploited to break ciphers. Study text to establish the frequency of each letter in the alphabets. Next we examine the cipher text and workout the frequency of each letter. In English e is the most common letter followed by t than a, and so on given in the table. If the most common letter in the cipher text is J than it is likely that the substitute for this is e and so on

VIGENERE CIPHER Example: – Key :K I N G K I N G K I N G K I N G K I N G K I N G – Plain text : T H E S U N A N D T H E M A N I N T H E M O O N – Cipher text : Z P D X V P A Z H S L Z B H L W Z B K M Z N M T Vigenere Square

Breaking Vigenere Charles Babbage, the person who came up with a blue print of computer was able to come up with a method to crack the Vigenere cipher. His Observation – Key :K I N G K I N G K I N G K I N G K I N G K I N G – Plain text : T H E S U N A N D T H E M A N I N T H E M O O N – Cipher text : B P R Y E V N T N B U K W I A O X B U K W W B T

ENIGMA Most fearsome encryption machine Components – Input Keyboard – Scrambler – Output Lamp board – Reflector – Plug board

Enigma Encryption

Contin…

Cracking the ENIGMA 1 st 2 nd 3 rd 4 th 5 th 6 th 1 st MessageL O K R G M 2 nd MessageM V T X Z E 3 rd MessageJ K T M P E 4 th MessageD V Y P Z X 1 st LETTERA 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 4 TH LETTER P M R X 1 st LETTERA 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 4 TH LETTER F Q H P L W O G B M V R X U Y C Z I T N J E A S D K

Contin… A => F => W => A3 Links B => Q => Z => K => V => E => L => R => I => B9 Links C => H => G => O => Y => D => P => C7 Links J => M => X => S => T => N => U => J7 Links

Conclusion Throughout history there has been rivalry between code makers and code breakers. Whenever code makers come up with a new form of encryption the code breakers come up with the methods to crack it. The emergence of RSA has shifted the tide on the favor of Cryptographers. Whether Cryptanalysts will be able to break this code remain to be seen.

Bibliograpgy Simon Singh : The Code Book wikipedia.org cpsc420.clemson.edu

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