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Cryptography Classic Data Encryption 43 views 0 0 RELATED TITLES Cryptography
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Content Page Basic Terminology 33 Introduction 4 Symmetric Cipher 55 Caesar Cipher 77 Base 64 encoding 88 Monoalphabetic Cipher 99 Playfair Cipher 13 Hill Cipher 15 Vigenère Cipher 17 Rail Fence Cipher 18 Row Transposition Cipher 18 Product Cipher 19 Base 64 Encoding Table 20 43 views 0 0 RELATED TITLES Cryptography
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Basic terminology
Plaintext = original message to be encrypted Ciphertext = the encrypted message Enciphering or encryption = the process of converting plaintext into ciphertext Encryption algorithm = The sequence of data processing steps that go into transforming plaintext into ciphertext. - two inputs: a plaintext, secret key Deciphering or decryption = recovering plaintext from ciphertext Decryption algorithm = The sequence of data processing steps that into transforming ciphertext back into plaintext. - two inputs: a ciphertext, secret key Secret key = same key used for encryption and decryption - Also referred as a symmetric key Cryptography = the many schemes available today for encryption and decryption Cryptography system = any single scheme for encryption and decryption Cipher = a cipher means the same thing as a “cryptographic system” Block cipher = a block cipher processes a block of input data at a time and produces a ciphertext block of the same size Stream cipher = a stream cipher encrypts data on the usually one byte at a time Cryptanalysis = means “breaking the code” Brute – force attack = means trying every possible key on a of ciphertext until an intelligible translation into plaintext is obtained Key space = the total number of all possible keys that can be used in a cryptographic system 43 views 0 0 RELATED TITLES Cryptography
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Introduction
Encryption is the conversion of data into a form, called a ciphertext, that cannot be easily understood by unauthorized people. Decryption is the process of converting encrypted data back into its original form, so it can be understood.
The use of encryption/decryption is as old as the art of communication. In wartime, a cipher, often incorrectly called a code, can be employed to keep the enemy from obtaining the contents of transmissions. (Technically, a code is a means of representing a signal without the intent of keeping it secret; examples are Morse code and ASCII.) Simple ciphers include the substitution of letters for numbers, the rotation of letters in the alphabet, and the "scrambling" of voice signals by inverting the sideband frequencies. More complex ciphers work according to sophisticated computer algorithms that rearrange the data bits in digital signals.
In order to easily recover the contents of an encrypted signal, the correct decryption key is required. The key is an algorithm that undoes the work of the encryption algorithm. Alternatively, a computer can be used in an attempt to break the cipher. The more complex the encryption algorithm, the more difficult it becomes to eavesdrop on the communications without access to the key.
Here I would like to introduce some of the classic encryption: 43 views 0 0 RELATED TITLES Cryptography
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Symmetric Cipher A symmetric cipher model
Example (symmetric-key encryption) Let A = {A,B,C,…..,X,Y,Z} be the English Alphabet Let m and c to be the set of all strings (words) of length five over A. To encrypt, an English message is broken up into groups each having five letters (with appropriate padding if the length of the message is not a multiple of five) A permutation(change) e is applied to each letter one at a time. To decrypt, the inverse permutation d = e-1 is applied to each letter of ciphertext. For instance, supposed that the key e is chosen to be the permutation which maps each letter to the one which is three position to its right, as shown: ( ) A message plain text = THIS CIPHER IS CERTAINLY NO SECURE. m = THISC IPHER ISCER TAINL YNOTS ECURE group it into five is encrypted to c = Ee = WKLVF LSKHU LVFHU WDLQO BQRWV HFXUH
Ciphertext = wklvflskhulvfhuwdlqobqrwvhfxuh
Explanation: c = ciphertext E = encryption algorithm d = decryption algorithm 43 views 0 0 RELATED TITLES Cryptography
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- Two requirements for secure use of symmetric encryption: a. a strong encryption algorithm b. a secret key known only to sender / receiver c = Ek (m) m = Dk (c) - Implies a secure channel to distribute key - Cryptography can characterize by: a. type of encryption operations used - substitution / transposition / product b. number of keys used - single – key or private / two – key or public c. way in which plaintext is processed - block / stream
• Mathematically:
Y = EK( X) or Y = E(K, X) X = DK(Y ) or X = D(K, Y )
• X = plaintext • Y = ciphertext • K = secret key • E = encryption algorithm • D = decryption algorithm • Both E and D are known to public
Substitution Ciphers - Replacing each element of the plaintext with another element Shift ciphers Base64 encoding Monoalphabetic ciphers 43 views 0 0 RELATED TITLES Cryptography
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Shift Ciphers : Caesar cipher
- This is the earlier known example of a substitution cipher. - invented by Julius Caesar - First attested use in military affairs - Replacing each letter of the plaintext by a shifted letter in the alphabet used. - If the shift value is (3) then we can define transformation as:
- e.g : plaintext : meet me after toga party ciphertext : PHHW PH DIWHU WKH WRJD SDUWB - If we represent each letter of the alphabet by an integer that corresponds to its position in the alphabet, such as: a, b, c, ..., x, y, z 0, 1, 2, ..., 23, 24, 25 The formula for placing each character p of the plaintext with a character c of the ciphertext can be expressed as:
WhereE()stands for encryption. The operator returns the integer remainder of the division when is divided by 26, the number of letters in the English alphabet assuming case-insensitive - A more general version of this cipher that allows for any degree of shift would be expressed by 43 views 0 0 RELATED TITLES Cryptography
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base64 encoding
- A simple substitution cipher obviously looks much too simple to be able to provide any security, but that is the case only if you have some idea regarding the nature of plaintext - For example, in the plaintext “Man” , encoded in ASCII the character M, a and n are stored as bytes 77, 97 and 110 which are the 8-bit binary values 01001101, 01100001 and 01101110. These three values are joined together into a 24-bit string, producing 010011010110000101101110. Group of 6-bits (6 bits have a maximum of 26 = 64 different binary values) are converted into individual numbers from left to right (in this case, there are four numbers in a 24-bit string), which are then converted into their corresponding Base64 character values. Text content M a n ASCII 77 (0x4d) 97 (0x61) 110 (0x6e) Bit pattern 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 Index 19 22 5 46 Base64-encoded T W F u
- The table of this encoding will be shown at the Base 64 Encoding Table section. 43 views 0 0 RELATED TITLES Cryptography
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monoalphabetic ciphers
- Basically, Caesar cipher is also a kind of monoalphabetic ciphers. In monoalphabetic ciphers, we have a substitution rule that gives us a replaceme ciphertext letter for each letter of the alphabet used in the plaintext message. - Let‟s now consider a seemingly strong monoalphabetic cipher by making our substitution letters a random permutation of the 26 letters of the alphabet:
- The encryption key is now the sequence of substitution letters. In other words, the key in this case is the actual random permutation of the alphabet used.
- Since there are 26! permutations of the alphabet, we end up with an extremely large key space. The number 26! is much larger than 4 x 10 26. Since each permutation constitutes a key, that means that the monoalphabetic cipher has a key space of size more than 4 x 1026.
- With this extremely large key space, you might think that it is secure. You are WRONG. There is language characteristic problems. 43 views 0 0 RELATED TITLES Cryptography
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Language Statistic and Cryptanalysis on Monoalphabetic ciphers
- A very large key space of a monoalphabetic cipher means that the total number of all possible keys that would need to be guessed in a pure brute-force attack would be much too large for such an attack to feasible. - Obviously, this would rule out a brute-force attack. Even if each key took only a nanosecond to try, it would still take zillions of year to try out even half the keys. - However if you know the nature of plaintext if it is a plain English, it can be broken easily with a statistical attack. In plain English, letters in a text are not equally commonly use. - Using frequency distribution for single characters, for pair of characters, for triple of characters and comparing those with similar statistics for English. 43 views 0 0 RELATED TITLES Cryptography
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- In decreasing order of frequencies : Double letters : th he an in er re es on … Triple letters : the and ent ion tio for nde … - Key concept : monoalphabetic substitution does not change relative letter frequencies. - To attack, we must calculate the letters frequencies for ciphertext and next compare this distribution against the known one. - For example: UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ - Step 1: count relative letters frequencies
P 13.33 H 5.83 F 3.33 B 1.67 C 0.00
Z 11.67 D 5.00 W 3.33 G 1.67 K 0.00
S 8.33 E 5.00 Q 2.50 Y 1.67 L 0.00
U 8.33 V 4.17 T 2.50 I 0.83 N 0.00
O 7.50 X 4.17 A 1.67 J 0.83 R 0.00
M 6.67
- Step 2 : As P has the highest frequency in the ciphertext and it can be map with E if compare with the distribution of the known one. The same thing occurs by mapping T on Z. 43 views 0 0 RELATED TITLES Cryptography
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- Step 4 :Proceeding with trial and error and finally get: it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow 43 views 0 0 RELATED TITLES Cryptography
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Playfair ciphers - With one character at a time substitution obviously leaves too much of the plaintext structure in ciphertext. - So how about destroying some of that structure by mapping multiple characters at a time to ciphertext characters? - In Playfair cipher, you first choose an encryption key. You then enter the letters of the key in the cells of a 5 5 matrix in a left to right fashion starting with the first cell at the top-left corner. You fill the rest of the cells of the matrix with the remaining letters in alphabetic order. In the following example, the key is “playfair example P L A Y F I R E X M B C D G H K N O Q S T U V W Z - Plaintext is encrypted two letters at a time. - If a pair is repeated letter, insert a filter like X, e.g. “Communication” encrypts as “Co mx mu ni ca ti on” - If the letters appear on the same row of your table, replace them with the letters to their immediate right respectively (wrapping around to the left side of the row if a letter in the original pair was on the right side o the row). e.g. XM becomes MI - If the letters appear on the same column of your table, replace them with the letters immediately below respectively (again wrapping around to the top side of the column if a letter in the original pair was on the 43 views 0 0 RELATED TITLES Cryptography
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- Otherwise, each letter is replaced by the letter in the same row but in the column of the other letter of the pair. e.g. TH becomes ZB - To decrypt, use the INVERSE (opposite) of the last 3 rules, and the 1st as is (dropping any extra "X"s that don't make sense in the final message when you finish). - Example : Plaintext : Hide the gold in the tree stump Ciphertext : BM OD ZB XD NA BE KU DM UI XM MO UV IF - Compared to a monoalphabetic cipher with 26 character, a playfair cipher would be more secured with 26 x 26 = 676 characters 43 views 0 0 RELATED TITLES Cryptography
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the hill ciphers - The Hill cipher takes a very different (more mathematical) approach to multi-letter substitution, as we describe in what follows. - You assign an integer to each letter of the alphabet. For the sake of discussion, let‟s say that you have assigned the integers 0 through 25 to the letters „a‟ through „z‟ of the plaintext. - The encryption key, call it k, consists of a 3×3 matrix of integers: - Now we can transform three letters at a time from the plain- text, the letters being represented by the numbers p1, p2, and p3, into three ciphertext letters c1, c2, and c3 in their numerical representations by - Therefore, the mathematical model is k is the key matrix and k -1 is the matrix inverse. - Encryption Example : Plaintext : pay key : 43 views 0 0 RELATED TITLES Cryptography
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- Ciphertext : LNS - Decryption Example : key : inverse key : 43 views 0 0 RELATED TITLES Cryptography
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Polyalphabetic Ciphers : Vigenère cipher - In a poly alphabetic cipher, on the other hand, the substitution rule changes continuously from one character position to the next in the plaintext according to the elements of the encryption key. - In the Vigenere cipher, you first “align” the encryption key with the plaintext message. ( If the plaintext message is longer than the encryption key, you can repeat the encryption key, as I show below where the encryption key is “lemon”.) Now consider each letter of the encryption key denoting a shifted Caesar cipher, the shift corresponding to the letter of the key. - E.g. :
Transposition cipher
rail fence cipher row transposition cipher 43 views 0 0 RELATED TITLES Cryptography
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transposition cipher : rail fence cipher
- Using this cipher, one should write message letters out diagonally over a number of rows. - After that, just read or write off cipher row by row. - It is not that secure. - E.g. plaintext : railfencecipher written : r i f n e i h r a l e c c p e ciphertext : rifneihraleccpe
transposition cipher : row transposition cipher
- It is a more complex scheme compared with rail fence cipher. - First, you should write out letters of message out in rows over a specified number of columns - then reorder the columns according to some key before reading off the columns. - key : 4 3 1 2 5 6 7 - Plaintext : a t t a c k p o s t p o n e d u n t i l t w o a m x y z - ciphertext :ttna aptm tsuo aodw coix knly petz 43 views 0 0 RELATED TITLES Cryptography
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Products Cipher - Ciphers using substitutions or transpositions are not secure because of language characteristic. - Hence, consider using several ciphers in succession to make harder : o Two substitutions make a more complex substitution o Two transposition make a more complex transposition o A substitution followed by a transposition makes a new much harder cipher 43 views 0 0 RELATED TITLES Cryptography
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base 64 encoding table
Value Char Value Char Value Char Value Char 0 A 16 Q 32 g 48 w 1 B 17 R 33 h 49 x 2 C 18 S 34 i 50 y 3 D 19 T 35 j 51 z 4 E 20 U 36 k 52 0 5 F 21 V 37 l 53 1 6 G 22 W 38 m 54 2 7 H 23 X 39 n 55 3 8 I 24 Y 40 o 56 4 9 J 25 Z 41 p 57 5 10 K 26 a 42 q 58 6 11 L 27 b 43 r 59 7 12 M 28 c 44 s 60 8 13 N 29 d 45 t 61 9 14 O 30 e 46 u 62 + 15 P 31 f 47 v 63 /