【文章內(nèi)容簡介】 I A S S T L R U O H D K French % Italian % Spanish % E E E A A A I I O S O S T N N N L R R R I U T L L S D 20 Classical (secretkey) cryptosystems Cryptanalysis’s Cryptoanalysis of a cryptotext encrypted using the AFINE cryptosystem with an encryption algorithm ea,b(x) = ax + b mod 26 where 0 ? a, b ? 25, gcd(a, 26) = 1. (Number of keys: 12 26 = 312.) Example: Assume that an English plaintext is divided into blocks of 5 letter and encrypted by an AFINE cryptosystem (ignoring space and interpunctions) as follows: How to find the plaintext? IV054 B H J U H N B U L S V U L R U S L Y X H O N U U N B W N U A X U S N L U Y J S S W X R L K G N B O N U U N B W S W X K X H K X D H U Z D L K X B H J U H B N U O N U M H U G S W H U X M B X R W X K X L U X B H J U H C X K X A X K Z S W K X X L K O L J K C X L C M X O N U U B V U L R R W H S H B H J U H N B X M B X R W X K X N O Z L J B X X H B N F U B H J U H L U S W X G L L K Z L J P H U U L S Y X B J K X S W H S S W X K X N B H B H J U H Y X W N U G S W X G L L K 21 Classical (secretkey) cryptosystems Cryptanalysis’s Frequency analysis of plainext and frequency table for English: First guess: E = X, T = U Equations 4a + b = 23 (mod 26) 19a + b = 20 (mod 26) Solutions: a = 5, b = 3 Translation table provides from the above cryptotext the plaintext that starts with KGWTG CKTMO OTMIT DMZEG, what does not make a sense. IV054 % % % E L B T D G A C V O U K N P Q I F X S M J R W Z H Y X 32 J 11 D 2 U 30 O 6 V 2 H 23 R 6 F 1 B 19 G 5 P 1 L 19 M 4 E 0 N 16 Y 4 I 0 K 15 Z 4 Q 0 S 15 C 3 T 0 W 14 A 2 B H J U H N B U L S V U L R U S L Y X H O N U U N B W N U A X U S N L U Y J S S W X R L K G N B O N U U N B W S W X K X H K X D H U Z D L K X B H J U H B N U O N U M H U G S W H U X M B X R W X K X L U X B H J U H C X K X A X K Z S W K X X L K O L J K C X L C M X O N U U B V U L R R W H S H B H J U H N B X M B X R W X K X N O Z L J B X X H B N F U B H J U H L U S W X G L L K Z L J P H U U L S Y X B J K X S W H S S W X K X N B H B H J U H Y X W N U G S W X G L L K crypto A B C D E F G H I J K L M N O P Q R S T U V W X plain P K F A V Q L G B W R M H C X S N I O Y T O J E Y Z Z U 22 Classical (secretkey) cryptosystems Cryptanalysis’s Second guess: E = X, A = H Equations 4a + b = 23 (mod 26) b = 7 (mod 26) Solutions: a = 4 or a = 17 and therefore a=17 This gives the translation table and the following plaintext from the above cryptotext IV054 S A U N A I S N O T K N O W N T O B E A F I N N I S H I N V E N T I O N B U T T H E W O R D I S F I N N I S H T H E R E A R E M A N Y M O R E S A U N A S I N F I N L A N D T H A N E L S E W H E R E O N E S A U N A P E R E V E R Y T H R E E O R F O U R P E O P L E F I N N S K N O W W H A T A S A U N A I S E L S E W H E R E I F Y O U S E E A S I G N S A U N A O N T H E D O O R Y O U C A N N O T B E S U R E T H A T T H E R E I S A S A U N A B E H I N D T H E D O O R crypto A B C D E F G H I J K L M N O P Q R S T U V W X plain V S P M J G D A X U R O L I F C Z W T Q N K H E Y Z B Y 23 Classical (secretkey) cryptosystems Example of monoalphabetic cryptosystem Symbols of the English alphabet will be replaced by squares with or without points and with or without surrounding lines using the following rule: For example the plaintext: WE TALK ABOUT FINNISH SAUNA MANY TIMES LATER results in the cryptotext: Garbage in between method: the message (plaintext or cryptotext) is supplemented by 39。39。garbage letters39。39。. Richelieu cryptosystem used sheets of card board with holes. IV054 24 Classical (secretkey) cryptosystems Polyalphabetic Substitution Cryptosystems Playfair cryptosystem Invented around 1854 by Ch. Wheatstone. Key a Playfair square or a word or text in which repeated letters are then removed and the remaining letters of alphabets are added and divided to form an array. IV054 QKEOTXCLPRWYVMBGNFAHUIZDSEncryption: of a pair of letters x,y ? If x and y are neither in the same row nor in the same column, then the smallest rectangle containing x,y is taken and symbols xy are replaced by the pair of symbols in the remaining corners of the square. ? If x and y are in the same row (column), then they are replaced by the pair of symbols to the right (bellow) them. Example: PLAYFAIR is encrypted as LCMNNFCS Playfair was used in World War I by British army. Playfair square: 25 Classical (secretkey) cryptosystems Polyalphabetic Substitution Cryptosystems VIGENERE and AUTOCLAVE cryptosystems Several polyalphabetic cryptosystems are the following modification of the CAESAR cryptosystem. A 26 26 table is first designed with the first row containing a permutation of all symbols of alphabet and all columns represent CAESAR shifts starting with the\break symbol of the first row. Secondly, for a plaintext w and a key k a word of the same length as w. Encryption: the ith letter of the plaintext wi is replaced by the letter in the wirow and kicolumn of the table. IV054 VIGENERE cryptosystem: a short keyword p is chosen and k = Prefix|w|poo VIGENERE is actually a cyclic version of the CAESAR cryptosystem. AUTOCLAVE cryptosystem: k = Prefix|w|pw. 26 Classical (secretkey) cryptosystems Polyalphabetic Substitution Cryptosystems VIGENERE and AUTOCLAVE cryptosystems Example: Keyword: H A M B U R G Plaintext: I N J E D E M M E N S C H E N G E S I C H T E S T E H T S E I N E G Vigenerekey: H A M B U R G H A M B U R G H A M