Properties of Cipher Texts

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 index of coincidence and patterns of letter frequencies does each cipher follow? Transposition Caesar

Affine Vigenre Playfair Summary What next? Review of Letter Frequencies and Index of Coincidence Letter Frequencies abcdefghijklmnopqrstuvwxyz monographic frequency distribution of normal alphabet Index of Coincidence thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessagest hi 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. 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 the quick fox jumped over the lazy dog Shift 3

wkh txlfn ira mxpshg ryhu wkh odcb grj Conclusion: Frequency distribution will match when shifted three Affine Each cipher letter corresponds to exactly one plain text letter. C = (aP + b) mod 26 Ex: a=4 and b=5: A = (4*1 + 5) mod 26 = 9 I Conclusion: Plain remainder Cipher

B 13 M C 17 Q D 21 U E 25 Y F 3 C

Same frequencies will be present but in a random Vigenre Many cipher alphabets created based on keyword. 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 C I

P H E R ABCDEFXY Z ABCDEFXY Z BCDEFGYZ A C D E F GH Z A B A :B C D E F X Y Z ... H VIJ K KY LZ MANBOCPD XH I J K B C D E EW FG Y YZ ZA AB BC CD D EVW

WX W WXXYY Z A B U V W OOPQRST LMN R RSTUVW OPQ D DEFGH I ABC Playfair Mixed alphabetic sequence of 25 letters is written into a 5x5 square (J normally omitted). D C Q Z L B O Y A U M X R K H

W G F T M Conclusion: I E S P V Case1: 2corners replace w/other corners Case2: same row replace w/letters to right Case3: same column replace w/letters below No pattern of letter Summary of Findings Index of Frequency Distribution Coinciden (compared to normal) ce

~6.6% Same Transpositi on ~6.6% Will match if shifted 3 to Caesar right ~6.6% Same frequencies Affine present but in different orders Vigenre ~3.8% Flat distribution Review of Letter Frequencies and Index of Coincidence Letter Frequencies abcdefghijklmnopqrstuvwxyz monographic frequency distribution of normal alphabet

Index of Coincidence thisisatestoftheindexofcoincidenceinmessages thisisatestoftheindexofcoincidenceinmessagest hi 5matches / 44letters ~ 11% What Next? Finalize criteria for distinguishing between Vigenre and Playfair ciphers. Create a Java program that: 1) 2) Examines index of coincidence and patterns of frequencies Uses this information to determine which cipher was used