第四章 傳統密碼學. outline substitution cipher transportation cipher
TRANSCRIPT
第四章
傳統密碼學
Outline
Substitution Cipher Transportation Cipher
Caesar Cipher
Each plaintext character is replaced by the character three to the right modulo 26
plaintext pi is enciphered as ciphertext letter ci by the
rule ci = E(pi)=pi+3
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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 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 Cipher
Advantages of Caesar Cipher Simple Easy to memorize
Disadvantages of Caesar Cipher interceptor can use a little piece to predict the
entire pattern of the encryption
Cryptanalysis of the Caesar Cipher
Example:T REA TY I MPOSSI BLE WUHDWB LP SRVVLEOH
線索 ss-> vv T, I, and E -> W, L, and H
空白 -> 空白 提示如何分辨一個字 可以改將空白移去 特殊短字： am, is, to, be, he, we, and, are, you, she, ... 試著去找出對應的小字 three-letter word “ too”, “see”, “add”, “odd”, “off” 亦是一特
殊類型
Example
wklv phvvdjh lv qrw wrr kdug wr euhdn t ot too to -ot 可能為 “ cot”, dot”, “got”, “hot”, “not” lv 為 wklv 的字尾， “ so”, “is”, “in” ->”Is” -> k -
> h 常用技巧：
最常出現之開始字元 最常出現之結束字元 前後字元相同：” sleeps”
Monoalphabetic Cipher alphabetic is scrambled （擾亂） each plaintext letter maps to a unique ciphertext letter. A permutation is a recording of the elements of a series. A permutation is a function.
Example of permutation: π1=1,3,5,7,9,10,8,6,4,2 π2=10,9,8,7,6,5,4,3,2,1 π1(3)=5, π2(7)=4
If a1, a2, ..., ak are the letters of the plaintext alphabet, and π is a permutation of the numbers 1,2,...,k, in a monoalphabetic substitution each ci is aπ(pi)
Example of permutation
π(a) might be the function π(a) =25-a Thus , a->z, b-> y, z->a 缺點： E(F)=u, and E(U)=F double correspo
ndence.
monoalphabetic 的變形 keyword mixed alphabet: 利用 KEY 來控制 enciph
ering 若 KEY 為 key 則對應的方式為：
缺點 KEY 一般都很短，移位不多。
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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 K E Y A B C D F G H I J L M N O P Q R S T U V W X Z
Example of monoalphabetic
key 中的字元若有重複： spectacular
缺點：末幾位字元幾乎對應到自己 幸好這些字元一般也比較少用。
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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 S P E C T A U L R B D F G H I J K M N O Q V W X Y Z
Monoalphabetic 再變形 A less regular rearrangement of the letters is desi
rable. One possible is to count by 3s (or 5s or 7s or 9s)
and rearrange the letters in that order.
Example: π(i)=(3*i) mod 26, π(k)=(3*10) mod 26 = 30-26=4
e π(e)=(3*4) mod 26 = 12=m
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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 A D G J M P S V Y B E H K N Q T W Z C F I L O R U X
Ciphers based on multiplications f(a)=ak mod n Example:
If k =9 then Encoding(RENAISSANCE) will generate “XKNAUGGANSK”
Note: If k and n are not relatively prime, several plaintext letters will encipher to the same ciphertext letters.
Example, if n =26 and k =13, f(A)=f(C)=f(R)=...=f(Y)=A f(B)=f(D)=f(F)=...=f(Z)=N
Affine transformation
Addition (shifting) and multiplication cam be combined to give an new method.
f(a)=(ak1 + k0 )mod n, where k and n are relatively prime.
Polynomial transformation of degree t: f(a)=(atkt + at-1kt-1 +...+ ak1 + k0 ) mod n Caesar ciphers are polynomial transformations of
degree 0, while affine transformations are of degree 1.
Churchyard cipher use nonstandard ciphertext alphabets The key to the cipher is given by the “tic-tac-toe” diagrams
Other encoding method: music symbol
Cryptanalysis of Monoalphabetic Ciphers
Use the technique to break the Caesar cipher to break monoalphabetic cipher
Guess-> substantiate -> correct or contradiction
Frequency Distributions: in English, some letters are used more frequently than others.
E, T, and A occur far more frequency than J, Q, and Z for
Example
Solution
Letter Frequency Distribution
Frequency of example
Frequencies of Sample Cipher against Normal Text
Polyalphabetic Substitution
monoalphabetic cipher 的缺點： Their frequency distribution reflects the distribution of th
e underlying alphabet A cipher that is more secure would display a rathe
r flat distribution, which gives no information to a cryptanalyst.
New method: Flatten the distribution, to combine distributions that are
high with ones that are low. E.g. E1(T) =a and E2(T) =b which E1(X) =a and E2(X)=b
Polyalphabetic Substitution
We can combine two distributions by using two separate encryption alphabets, the first for all the characters in odd positions of the plaintext message, the second for all the characters in the even positions.
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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 a d g j m p s v y b e h k n q t w z c f i l o r u x
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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 n s x c h m r w b g l q v a f k p u z e j o t y d i
Example: TREAT YIMPO SSIBL E fumnf dyvtf czysh h
Polyalphabetic Substitution
Two-alphabet encryption letter frequencies
E1(a) =a and E2(a)=25-a
Vigenere Tableaux
polyalphabetic 之缺點 j, q 很少用，但 j -> q
改進法： Select any permutation as π1, and then carefully
choose π1; if π1 maps a high frequency letter such as E to x, the π2 should map a low frequency to x.
Extended the number of permutations.
Vigenere tableau
Vigenere Tableaux
choose keyword: e.g. juliet Assume Plaintext:
Each plaintext letter pi is the converted to the ciphertext letter in row pi, column ki of the tableau.
j u l i e t j u l i e t j u l i e t j U
B U T S O F T W H A T L I G H T T H R O
k o e a s y c q s i
Transposition (permutation) A transportation is an encryption in which the letters of the
message are rearrange. Columnar transportation
The columnar transportation is a rearrangement of the characters of the plaintext into columns.
Example:
c1 c2 c3 c4 c5
c6 c7 c8 c9 c10
c11 c12 c13 c14 c15
The resulting ciphertext is formed by transversing the columns.
c1c6c11c2c7c12c3c8c13c4c9c14c5c10c15
Example of Columnar transportation
Double Transportation Algorithm
The double transportation cipher involves two column transpositions, with different numbers of columns, applied one after the other.
The first transposition displaces adjacent letters, and the second breaks up the adjacency of short series of letters that happened to appear in adjacency columns of the first transposition.
Example of double transposition
Padding letter
A better way of padding is to use letters that would occur frequently anyway, such as a, e, i, n, o, s, so that it would not be possible to identify the padding characters easily.
Fractionated Morse
blocked cipher Morse code is a means of representing
letters as sequences of dots and dashes used with telegraphs, flashing lights, semaphore flags.
Table of Morse codes Encoding: add break or pause between
separate letters.
Example
Morse code
Morse code is really three-symbol coding scheme using the symbols “dash”, “dot” and “separator”.
33=27 =26 + 1 All but one of the possible groups of dashes,
dots, and separators can be associated with the English letter.
Encoding
Step 1: The English plaintext is converted to Morse code, using a separator between letters and an extra separator to represent a space between words.
Step 2: The Morse code message is divided into blocks of three symbols.
Step 3: Finally, each block is encoded as the letter corresponding to that three-symbol pattern.
Example
Example
Cryptanalysis of Transpositions
Most Common Digrams and Trigrams
Frequencies of Digrams in English
Frequencies of Digrams in English
Cryptanalysis of Polyalphabetic Substitutions
Cryptanalysis of Polyalphabetic Substitutions
Cryptanalysis of Polyalphabetic Substitutions
Cryptanalysis of Polyalphabetic Substitutions
Cryptanalysis of affine transformation
Cryptanalysis of affine transformation