uni/year2/semester1/logseq-stuff/pages/Introduction to Cryptography.md

• #CT255 - Next Generation Technologies II
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• SQL Injections

  • What is an SQL Injection? #card card-last-interval:: 28.3 card-repeats:: 4 card-ease-factor:: 2.66 card-next-schedule:: 2022-12-09T18:33:16.312Z card-last-reviewed:: 2022-11-11T11:33:16.312Z card-last-score:: 5
    • An SQL Injection is a code injection technique used to attack data-driven applications, in which malicious SQL statements are inserted for execution.
    • It is a way of exploiting user input & SQL statements to compromise the database & retrieve sensitive data.

• Basic Terminology

  • What is Cryptography? #card card-last-interval:: 108 card-repeats:: 5 card-ease-factor:: 3 card-next-schedule:: 2023-03-06T18:36:41.369Z card-last-reviewed:: 2022-11-18T18:36:41.370Z card-last-score:: 5
    • Cryptography is the art of encompassing the principles & methods of transforming an intelligible message into one that is unintelligible, and then retransforming that message back into its original form.
  • What is Plaintext? card-last-score:: 5 card-repeats:: 3 card-next-schedule:: 2022-10-17T21:24:55.999Z card-last-interval:: 11.2 card-ease-factor:: 2.8 card-last-reviewed:: 2022-10-06T17:24:55.999Z
    • Plaintext is the ^^original, intelligible message.^^
  • What is Ciphertext? card-last-interval:: 11.2 card-repeats:: 3 card-ease-factor:: 2.8 card-next-schedule:: 2022-10-18T14:39:00.206Z card-last-reviewed:: 2022-10-07T10:39:00.207Z card-last-score:: 5
    • Ciphertext is the encrypted messsage.
  • What is a Cipher? #card card-last-interval:: 11 card-repeats:: 3 card-ease-factor:: 2.66 card-next-schedule:: 2022-11-25T16:46:20.520Z card-last-reviewed:: 2022-11-14T16:46:20.520Z card-last-score:: 5
    • A Cipher is an algorithm for transforming an intelligible message into one that is unintelligible.
  • What is a Key? #card card-last-interval:: 9.68 card-repeats:: 3 card-ease-factor:: 2.42 card-next-schedule:: 2022-11-24T08:37:27.630Z card-last-reviewed:: 2022-11-14T16:37:27.630Z card-last-score:: 5
    • A Key is some critical information used by the cipher, known only to the sender & receiver, selected from a keyspace (the set of all possible keys).
  • What does Encipher mean? card-last-score:: 5 card-repeats:: 3 card-next-schedule:: 2022-10-17T21:14:43.789Z card-last-interval:: 11.2 card-ease-factor:: 2.8 card-last-reviewed:: 2022-10-06T17:14:43.790Z
    • Enciphering is the process of converting plaintext into ciphertext using a cipher & a key.
  • What does Decipher mean? card-last-interval:: 4 card-repeats:: 2 card-ease-factor:: 2.7 card-next-schedule:: 2022-10-04T12:09:14.829Z card-last-reviewed:: 2022-09-30T12:09:14.829Z card-last-score:: 5
    • Deciphering is the process of converting ciphertext back into plaintext using a cipher & a key.
  • What is Encryption? #card card-last-score:: 5 card-repeats:: 4 card-next-schedule:: 2022-12-08T06:02:35.168Z card-last-interval:: 23.43 card-ease-factor:: 2.42 card-last-reviewed:: 2022-11-14T20:02:35.168Z
    • Encryption is some mathematical function E_K() mapping plaintext P to ciphertext C using the specified key K.
    • E_K(P) = C
  • What is Decryption? #card card-last-interval:: 9.68 card-repeats:: 3 card-ease-factor:: 2.42 card-next-schedule:: 2022-11-24T08:49:17.364Z card-last-reviewed:: 2022-11-14T16:49:17.365Z card-last-score:: 5
    • Decryption is some mathematical function {E_K}^{-1}() mapping the ciphertext C to plaintext P using the specified key K.
    • P={E_K}^{-1}(C)
  • What is Cryptanalysis? #card card-last-interval:: 28.3 card-repeats:: 4 card-ease-factor:: 2.66 card-next-schedule:: 2022-11-16T15:43:11.780Z card-last-reviewed:: 2022-10-19T08:43:11.781Z card-last-score:: 3
    • Cryptanalysis is the study of principles & methods of transforming an unintelligible message into an intelligible message without knowledge of the key.
  • What is Cryptology? card-last-interval:: 9.28 card-repeats:: 3 card-ease-factor:: 2.32 card-next-schedule:: 2022-10-16T16:40:03.776Z card-last-reviewed:: 2022-10-07T10:40:03.777Z card-last-score:: 5
    • Cryptology is the field encompassing both cryptography & cryptanalysis.

• Model of Conventional Cryptosystem

  • {:height 304, :width 610}

• Cryptanalysis via Letter Frequency Distribution

  • Human languages are redundant - letters are not equally commonly used.
  • In the English language:
    • E is by far the most common letter followed by T, R, N, I, O, A, and S.
    • Other letters like Z, J, K, Q, and X are fairly rare.
    • Certain letter combinations like TH are quite common.
    • 

  • C Program for Frequency Analysis of single Characters

    • #include <stdio.h>
      #include <string.h>
      #include <ctype.h>
      
      int main(int argc, char* argv[]) {
        FILE* fp;
        int data[26];
        char c;
      
        memset(data, 0, siezof(data));
      
        if (argc != 2) {
          return(-1);
        }
        if (fp = fopen(argv[1], "r" == NULL)) {
          return(-2);
        }
      
        while(!feof(fp)) {
          c = toupper(fgetc(fp));
      
          if ((c >= 'A') && (c <= 'Z')) {
            data[c-65]++;
          }
        }
      
        for (int i = 0; i < 26; i++) {
          printf("%c:%i\n", i+65, data[i]);
        }
      
        fclose(fp);
        return(0);
      }
      

• Known Plaintext Attacks (KPA)

  • What is a Known Plaintext Attack (KPA)? #card card-last-interval:: 28.3 card-repeats:: 4 card-ease-factor:: 2.66 card-next-schedule:: 2022-12-13T03:02:00.417Z card-last-reviewed:: 2022-11-14T20:02:00.417Z card-last-score:: 5
    • The Known Plaintext Attack (KPA) is an attack model for cryptanalysis where the attacker has access to both:
      • some of, or all of, the plaintext (called a crib)
      • the ciphertext

• Caesar Cipher

  • What is a Caesar Cipher? #card card-last-interval:: 33.64 card-repeats:: 4 card-ease-factor:: 2.9 card-next-schedule:: 2022-12-18T11:04:27.582Z card-last-reviewed:: 2022-11-14T20:04:27.582Z card-last-score:: 5
    • A Caesar Cipher involves using an offset alphabet to encrypt a message.
    • We can use any shift from 1 to 25 to replace each plaintext letter with a letter a fixed distance away.
    • The key letter represents the start of this offset alphabet.
      • For example, a key letter of F means that A -> F, B -> G, and so on.

• Playfair Cipher

  • Not even the large number of keys in a monoalphabetic cipher provides security.
    • What is a monoalphabetic cipher? #card card-last-interval:: 28.3 card-repeats:: 4 card-ease-factor:: 2.66 card-next-schedule:: 2022-12-13T03:02:37.487Z card-last-reviewed:: 2022-11-14T20:02:37.488Z card-last-score:: 5
      • A monoalphabetic cipher is any cipher in which the letters of the plaintext are mapped to ciphertext letters based on a single alphabetic key.
  • One approach to improving security over monoalphabetic ciphers is to to encrypt ^^multiple letters.^^
    • The Playfair Cipher is one example of such an approach.
    • The algorithm was invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair.

  • How does the Playfair Cipher work?

    card-last-score:: 5 card-repeats:: 2 card-next-schedule:: 2022-10-08T00:33:19.557Z card-last-interval:: 3.51 card-ease-factor:: 2.6 card-last-reviewed:: 2022-10-04T12:33:19.558Z
    • 
    • 1. Create a 5x5 grid of letters; insert the keyword as shown, with each letter only considered once; fill the grid with the remaining letters in alphabetic order.
    • 2. The letters are then encrypted in pairs.
    • 3. Repeats have an "X" inserted.
      • BALLOON -> BA LX LO ON
    • 4. Letters that fall in the same row are replaced with the letter on the right.
      • OK -> GM
    • 5. Letters in the same column are replaced with the letter below.
      • FO -> OU
    • 6. Otherwise, each letter gets replaced by the letter in its row but in the other letters column.
      • QM -> TH

  • Security of the Playfair Cipher

    • The security is much improved over simple monoalphabetic ciphers, as the Playfair Cipher has 26^2 = 676 combinations.
      • This requires a 676 entry frequency table to analyse (as compared to a 26 entry frequency table for a monoalphabetic cipher) and correspondingly, more ciphertext.
      • However, the Playfair Cipher can be cracked through frequency analysis of letter pairs, given a few hundred letters.

• Vigenère Cipher

  • Blaise de Vigenère is generally credited as the inventor of the Polyalphabetic Substitution Cipher.
    • What is a Polyalphabetic Substitution Cipher? #card card-last-interval:: 11.2 card-repeats:: 3 card-ease-factor:: 2.8 card-next-schedule:: 2022-11-25T20:35:52.727Z card-last-reviewed:: 2022-11-14T16:35:52.727Z card-last-score:: 5
      • A Polyalphabetic Substitution Cipher uses multiple substitution alphabets, as opposed to a monoalphabetic cipher which uses a single alphabetic key.
  • The Vigenère Cipher improves security by using many monoalphabetic substitution alphabets, so each letter can be replaced by many others.
  • You use a key to select which alphabet is used for each letter of the message.
    • The i^{th} letter of the key specifies the i^{th} alphabet to use.
    • Use each alphabet in turn.
    • Repeat from the start after the end of the key is reached.

  • Vigenère Steps

    • 
    • 1. Write the plaintext out, and write the keyword underneath it, repeated, for the length of the plaintext.
    • 2. Use each key letter in turn as a Caesar cipher key.
    • 3. Encrypt the corresponding plaintext letter.
    • In this example, we use the keyword "CIPHER". Hence, we have the following translation alphabets:
      • 

  • How to crack the Vigenère Cipher

    • 1. Search the ciphertext for repeated strings of letters - the longer the string, the better.
    • 2. For each occurrence of a repeated string, count how many letters are between the first letters in the string, and add one.
    • 3. Factorise that number.
    • 4. Repeat this process with each repeated string you find and make a table of common factors. The most common factor, n is most likely the length of the keyword used to encipher the ciphertext.
    • 5. Do a frequency count on the ciphertext, on every n^{th} letter. You should end up with n different frequency counts.
    • 6. Compare these counts to standard frequency tables to figure out how much each letter was shifted by.
    • 7. Undo the shifts and read the message.

• Enigma (Rotor Ciphers)

  • Rotor Ciphers

    • The mechanisation / automation of encryption.
    • An $\text{N}$-stage polyalphabetic algorithm modulo 26.
    • 26^N steps before a repetition, where N is the number of cylinders.
      • The Enigma machine had 5 cylinders, so:
        • 26^{N=5}=11,881,376 \text{ steps}

  • Breaking Enigma using Cribs

    • The starting point for breaking Enigma was based on the following:
      • Plaintext messages were likely to contain certain phrases.
        • Weather reports contained the term "WETTER VORHERSAGE".
        • Military units often sent messages containing "KEINE BESONDEREN EREIGNISSE" ("nothing to report").
      • A plaintext letter was never mapped onto the same ciphertext letter.
    • While the cryptanalysts in Bletchely Park did not know exactly where these cribs were placed in an intercepted message, they could exclude certain positions.
      • 
      • From here, possible rotor start positions & rotor wiring would be systematically examined using the "bombe" - an electromechanical device designed by Turing that replicated the action of several Enigma machines wired together.

• Transposition Ciphers

  • What are Transposition Ciphers? #card card-last-interval:: 21.53 card-repeats:: 4 card-ease-factor:: 2.32 card-next-schedule:: 2022-12-06T08:01:53.099Z card-last-reviewed:: 2022-11-14T20:01:53.100Z card-last-score:: 5
    • Transposition or Permutation Ciphers hide the message by rearranging the letter order ^^without altering the actual letters used.^^
    • This can be recognised since the ciphertext has the same frequency distribution as the original text.

  • Rail Fence Cipher

    id:: 6344093b-2f4f-4c58-95e4-39a8b30d16c3
    • Write plaintext letters out diagonally over a number of rows, then read off the cipher row by row.
      • 

  • Row Transposition Cipher

    • What are Row Transposition Ciphers? #card card-last-interval:: 86.42 card-repeats:: 5 card-ease-factor:: 2.66 card-next-schedule:: 2023-02-09T06:21:27.811Z card-last-reviewed:: 2022-11-14T20:21:27.811Z card-last-score:: 5
      • Row Transposition Ciphers are a more complex kind of transposition cipher than ((6344093b-2f4f-4c58-95e4-39a8b30d16c3))s.
      • Plaintext letters are written out in rows over a specified number of columns.
      • The columns are then re-ordered according to some key before reading off the columns
    • 

• Product Ciphers

  • Ciphers using just substitutions or transpositions are not secure because of language characteristics.
  • Consider using several ciphers in succession to make it harder to crack:
    • Two substitutions make a more complex substitution.
    • Two transpositions make a more complex transposition.
    • However, a substitution followed by a transposition makes a much harder cipher.

• Steganography

  • What is Steganography? #card card-last-interval:: 33.64 card-repeats:: 4 card-ease-factor:: 2.9 card-next-schedule:: 2022-12-21T10:35:36.194Z card-last-reviewed:: 2022-11-17T19:35:36.195Z card-last-score:: 5
    • Steganography is an alternative to encryption that hides the existence of the message.
    • For example:
      • Using only a subset of letters / words in a message marked in some way.
      • Using invisible ink.
      • Hiding in LSB in graphic image or sound file.
  • The drawback of steganography is that it's not very economical in terms of overheads to hide a message.