Expert System for Analyzing Simple Ciphers: Properties of Cipher Texts Carolyn Rucci Advisor: Ralph Morelli 1 year project.

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Presentation transcript:

Expert System for Analyzing Simple Ciphers: Properties of Cipher Texts Carolyn Rucci Advisor: Ralph Morelli 1 year project

Overview What are letter frequencies and index of coincidence. What are letter frequencies and index of coincidence. What index of coincidence and patterns of letter frequencies does each cipher follow? What index of coincidence and patterns of letter frequencies does each cipher follow? Transposition Transposition Caesar Caesar Affine Affine Vigenère Vigenère Playfair Playfair Summary Summary What next? What next?

Review of Letter Frequencies and Index of Coincidence Letter Frequencies Letter Frequencies 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 monographic frequency distribution of normal alphabet Index of Coincidence Index of Coincidence thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessagesthi 5matches / 44letters ~ 11%

Transposition Cipher Simply rearranges the letters  same letters present in cipher text as plain text Reverse text: there once was a cat named fred derf deman tac a saw ecno ereht Conclusion: Frequency distribution will be the same.

Caesar Each cipher letter corresponds to the plain text letter three after it. Each cipher letter corresponds to the plain text letter three after it. Plain Alphabet: 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 Plain Alphabet: 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 Caesar Alphabet: 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 Caesar Alphabet: 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 Conclusion: Frequency distribution will match when shifted three spots. Conclusion: Frequency distribution will match when shifted three spots. the quick fox jumped over the lazy dog wkh txlfn ira mxpshg ryhu wkh odcb grj Shift 3

Affine Each cipher letter corresponds to exactly one plain text letter. Each cipher letter corresponds to exactly one plain text letter. Conclusion: Same frequencies will be present but in a random order. Conclusion: Same frequencies will be present but in a random order.  Ex: a=4 and b=5:  A = (4*1 + 5) mod 26 = 9  I C = (aP + b) mod 26 PlainremainderCipher B13M C17Q D21U E25Y F3C

Vigenère Many cipher alphabets created based on keyword. Many cipher alphabets created based on keyword. A B C D E F … X Y Z B C D E F G … Y Z A C D E F GH … Z A B : Y Z A B C D... V W X Z A B C D E … W X Y CIPHERCIPHER KEYWORDKEYWORD A B C D E F … X Y Z K L M N O P … H I J E F G H I J K … B C D Y Z A B C D … V W X W X Y Z A B … U V W O P Q R S T … L M N R S T U V W … O P Q D E F G H I … A B C  Conclusion: No pattern to letter frequencies.  Find identical sequences of letters.  the frog jumping the fence…  dlc bffj tyklwej dlc bsefo…  Calculate interval bt/w sequences  If interval between two occurrences has common factor  length of keyword

Playfair Mixed alphabetic sequence of 25 letters is written into a 5x5 square (J normally omitted). Mixed alphabetic sequence of 25 letters is written into a 5x5 square (J normally omitted). DBMWI COXGE QYRFS ZAKTP LUHMV Case1: 2corners  replace w/other corners Case2: same row  replace w/letters to right Case3: same column  replace w/letters below Conclusion: No pattern of letter frequencies. Conclusion: No pattern of letter frequencies.

Summary of Findings Index of Coincidence Frequency Distribution (compared to normal) Transposition~6.6%Same Caesar~6.6% Will match if shifted 3 to right Affine~6.6% Same frequencies present but in different orders Vigenère~3.8% Flat distribution Playfair~3.8%

Review of Letter Frequencies and Index of Coincidence Letter Frequencies Letter Frequencies 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 monographic frequency distribution of normal alphabet Index of Coincidence Index of Coincidence thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessagesthi 5matches / 44letters ~ 11%

What Next? Finalize criteria for distinguishing between Vigenère and Playfair ciphers. Finalize criteria for distinguishing between Vigenère and Playfair ciphers. Create a Java program that: Create a Java program that: 1) Examines index of coincidence and patterns of frequencies 2) Uses this information to determine which cipher was used