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Challenge 3: Single-byte XOR cipher

Problem

The hex encoded string:


1b37373331363f78151b7f2b783431333d78397828372d363c78373e783a393b3736


... has been XOR'd against a single character. Find the key, decrypt the message.
You can do this by hand. But don't: write code to do it for you.
How? Devise some method for "scoring" a piece of English plaintext. Character frequency is a good metric. Evaluate each output and choose the one with the best score.

Solution

Resource

This is the frequency of letters in the English language. It is used to score the plaintexts.

byte('E'):  12.02,
byte('T'):  9.10,
byte('A'):  8.12,
byte('O'):  7.68,
byte('I'):  7.31,
byte('N'):  6.95,
byte('S'):  6.28,
byte('R'):  6.02,
byte('H'):  5.92,
byte('D'):  4.32,
byte('L'):  3.98,
byte('U'):  2.88,
byte('C'):  2.71,
byte('M'):  2.61,
byte('F'):  2.30,
byte('Y'):  2.11,
byte('W'):  2.09,
byte('G'):  2.03,
byte('P'):  1.82,
byte('B'):  1.49,
byte('V'):  1.11,
byte('K'):  0.69,
byte('X'):  0.17,
byte('Q'):  0.11,
byte('J'):  0.10,
byte('Z'):  0.07,


byte(' '): 8,


byte("a")  :08.167,
byte("b")  :01.492,
byte("c")  :02.782,
byte("d")  :04.253,
byte("e")  :12.702,
byte("f")  :02.228,
byte("g")  :02.015,
byte("h")  :06.094,
byte("i")  :06.966,
byte("j")  :00.153,
byte("k")  :00.772,
byte("l")  :04.025,
byte("m")  :02.406,
byte("n")  :06.749,
byte("o")  :07.507,
byte("p")  :01.929,
byte("q")  :00.095,
byte("r")  :05.987,
byte("s")  :06.327,
byte("t")  :09.056,
byte("u")  :02.758,
byte("v")  :00.978,
byte("w")  :02.360,
byte("x")  :00.150,
byte("y")  :01.974,
byte("z")  :00.074,

Decoded

decoded

Code

challenge3.go
package challenge3


import (
  "fmt"


  c1 "cryptopals/Set1/challenge1"
)


/*
XORed against a single string, find the character
1b37373331363f78151b7f2b783431333d78397828372d363c78373e783a393b3736
*/


func charFreq(char byte) float64 {
  wm := map[byte]float64{
    byte('E'): 12.02,
    byte('T'): 9.10,
    byte('A'): 8.12,
    byte('O'): 7.68,
    byte('I'): 7.31,
    byte('N'): 6.95,
    byte('S'): 6.28,
    byte('R'): 6.02,
    byte('H'): 5.92,
    byte('D'): 4.32,
    byte('L'): 3.98,
    byte('U'): 2.88,
    byte('C'): 2.71,
    byte('M'): 2.61,
    byte('F'): 2.30,
    byte('Y'): 2.11,
    byte('W'): 2.09,
    byte('G'): 2.03,
    byte('P'): 1.82,
    byte('B'): 1.49,
    byte('V'): 1.11,
    byte('K'): 0.69,
    byte('X'): 0.17,
    byte('Q'): 0.11,
    byte('J'): 0.10,
    byte('Z'): 0.07,
    byte(' '): 8,
    byte('a'): 8.167,
    byte('b'): 01.492,
    byte('c'): 02.782,
    byte('d'): 04.253,
    byte('e'): 12.702,
    byte('f'): 02.228,
    byte('g'): 02.015,
    byte('h'): 06.094,
    byte('i'): 06.966,
    byte('j'): 00.153,
    byte('k'): 00.772,
    byte('l'): 04.025,
    byte('m'): 02.406,
    byte('n'): 06.749,
    byte('o'): 07.507,
    byte('p'): 01.929,
    byte('q'): 00.095,
    byte('r'): 05.987,
    byte('s'): 06.327,
    byte('t'): 9.056,
    byte('u'): 02.758,
    byte('v'): 00.978,
    byte('w'): 02.360,
    byte('x'): 00.150,
    byte('y'): 01.974,
    byte('z'): 00.074,
  }
  return wm[char]
}


func Challenge3() {
  input1 := []byte("1b37373331363f78151b7f2b783431333d78397828372d363c78373e783a393b3736")


  raw := c1.DecodeHex(input1)
  fmt.Printf("Raw string:%s\n", raw)


  answer, score := SingleXorCipher(raw)
  fmt.Printf("Answer:%s\nScore:%f", answer, score)
}


func SingleXorCipher(raw []byte) ([]byte, float64) {
  var answer []byte
  var score float64
  for i := 0; i < 256; i++ {
    tempAns := make([]byte, len(raw))
    var tempSc float64
    for j := 0; j < len(raw); j++ {
      c := raw[j] ^ byte(i)
      tempSc += charFreq(c)
      tempAns[j] = c
    }
    if tempSc > score {
      answer = tempAns
      score = tempSc
    }
    tempSc = 0
  }
  return answer, score
}