Merge monoalphabetic cracking

README.md

@@ -77,6 +77,29 @@ Notice that `encrypt_monoalphabetic` *does not* convert its input to uppercase
 when a Dict key is supplied.
 It simply makes all specified changes, and leaves the rest of the string unchanged.
 
+Cracking a cipher:
+```julia
+crack_monoalphabetic(str, chatty=0, rounds=10)
+# outputs (key, decrypted_string)
+```
+
+The various optional arguments to `crack_monoalphabetic` are:
+
+* `starting_key=""`, which when specified (for example, as "ABCDEFGHIJKLMNOPQRSTUVWXYZ"),
+  starts the simulation at the given key. The default causes it to start with the most
+  common characters being decrypted to the most common English characters.
+* `min_temp=0.0001`, which is the temperature at which we stop the simulation.
+* `temp_factor=0.97`, which is the factor by which the temperature decreases each step.
+* `chatty=0`, which can be set to 1 to print whenever the key is updated, or 2 to print
+  whenever any new key is considered.
+* `rounds=1`, which sets the number of repetitions we perform. Each round starts with the
+  best key we've found so far.
+* `acceptance_prob=((e, ep, t) -> ep>e ? 1 : exp(-(e-ep)/t))`, which is the probability
+  with which we accept new key of fitness ep, given that the current key has fitness e,
+  at temperature t.
+
+The simulation is set up to start each round off at a successively lower temperature.
+
 ### Vigenère cipher
 
 Encrypt the text "Hello, World!" with a Vigenère cipher of key "ab":

src/ClassicalCiphers.jl

@@ -8,7 +8,7 @@ include("caesar.jl")
 include("vigenere.jl")
 include("solitaire.jl")
 
-export encrypt_monoalphabetic, decrypt_monoalphabetic,
+export encrypt_monoalphabetic, decrypt_monoalphabetic, crack_monoalphabetic,
        encrypt_caesar, decrypt_caesar, crack_caesar,
        encrypt_vigenere, decrypt_vigenere,
        encrypt_solitaire, decrypt_solitaire,

src/common.jl

@@ -64,13 +64,35 @@ Performs a trigram analysis on the input string, to determine how close it
 is to English. That is, splits the input string into groups of three letters,
 and assigns a score based on the frequency of the trigrams in true English.
 """
-function string_fitness(input)
+function string_fitness(input; alreadystripped=false)
-  str = uppercase(letters_only(input))
+  if !alreadystripped
+    str = letters_only(input)
+  else
+    str = input
+  end
+
+  str = uppercase(str)
 
   ans = 0
   for i in 1:(length(str)-2)
     ans += get(trigram_fitnesses, str[i:i+2], 0)
   end
 
+  log(ans/length(str))
+end
+
+"""
+Finds the frequencies of all characters in the input string, returning a Dict
+of 'a' => 4, for instance. Uppercase characters are considered distinct from lowercase.
+"""
+function frequencies(input)
+  ans = Dict{Char, Integer}()
+  for i in input
+    if haskey(ans, i)
+      ans[i] += 1
+    else
+      ans[i] = 0
+    end
+  end
   ans
 end

src/monoalphabetic.jl

@@ -47,3 +47,125 @@ function decrypt_monoalphabetic(ciphertext, key::AbstractString)
   dict = [(a => Char(96 + search(lowercase(key), a))) for a in lowercase(key)]
   encrypt_monoalphabetic(lowercase(ciphertext), dict)
 end
+
+# Cracking
+
+# The method we use for cracking is simulated annealing.
+
+"""
+swap_two(string) swaps two of the characters of the input string, at random.
+The characters are guaranteed to be at different positions, though "aa" would be
+'swapped' to "aa".
+"""
+function swap_two(str)
+  indices = rand(1:length(str), 2)
+  while indices[1] == indices[2]
+    indices = rand(1:length(str), 2)
+  end
+
+  join([i == indices[1] ? str[indices[2]] : (i == indices[2] ? str[indices[1]] : str[i]) for (i, ch) in enumerate(str)], "")
+end
+
+"""
+crack_monoalphabetic cracks the given ciphertext which was encrypted by the monoalphabetic
+substitution cipher.
+Possible arguments include:
+starting_key="", which when specified (for example, as "ABCDEFGHIJKLMNOPQRSTUVWXYZ"),
+  starts the simulation at the given key. The default causes it to start with the most
+  common characters being decrypted to the most common English characters.
+min_temp=0.0001, which is the temperature at which we stop the simulation.
+temp_factor=0.97, which is the factor by which the temperature decreases each step.
+chatty=0, which can be set to 1 to print whenever the key is updated, or 2 to print
+  whenever any new key is considered.
+rounds=1, which sets the number of repetitions we perform. Each round starts with the
+  best key we've found so far.
+acceptance_prob=((e, ep, t) -> ep>e ? 1 : exp(-(e-ep)/t)), which is the probability
+  with which we accept new key of fitness ep, given that the current key has fitness e,
+  at temperature t.
+"""
+function crack_monoalphabetic(ciphertext; starting_key="",
+                              min_temp=0.0001, temp_factor=0.97,
+                              acceptance_prob=((e,ep,t) -> ep > e ? 1. : exp(-(e-ep)/t)),
+                              chatty=0,
+                              rounds=1)
+  
+  if starting_key == ""
+  # most common letters
+    commonest = "ETAOINSHRDLUMCYWFGBPVKZJXQ"
+    freqs = frequencies(uppercase(letters_only(ciphertext)))
+    for c in 'A':'Z'
+      if !haskey(freqs, c)
+        freqs[c] = 0
+      end
+    end
+
+    freqs_input = sort(collect(freqs), by = tuple -> last(tuple), rev=true)
+    start_key = ['a' for c in 1:26]
+    for i in 1:26
+      start_key[Int(commonest[i])-64] = freqs_input[i][1]
+    end
+
+    key = join(start_key, "")
+  else
+    key = starting_key
+  end
+
+  if chatty > 1
+    println("Starting key: $(key)")
+  end
+
+  stripped_ciphertext = letters_only(ciphertext)
+  fitness = string_fitness(decrypt_monoalphabetic(stripped_ciphertext, key))
+  total_best_fitness = fitness
+  total_best_key = key
+  total_best_decrypt = decrypt_monoalphabetic(ciphertext, key)
+
+  for roundcount in 1:rounds
+    temp = 10^((roundcount-1)/rounds)
+    while temp > min_temp
+      for i in 1:round(Int, min(ceil(1/temp), 10))
+        neighbour = swap_two(key)
+        new_fitness = string_fitness(decrypt_monoalphabetic(stripped_ciphertext, neighbour), alreadystripped=true)
+        if new_fitness > total_best_fitness
+          total_best_fitness = new_fitness
+          total_best_key = neighbour
+          total_best_decrypt = decrypt_monoalphabetic(ciphertext, total_best_key)
+        end
+
+        threshold = rand()
+
+        if chatty >= 2
+          println("Current fitness: $(fitness)")
+          println("New fitness: $(new_fitness)")
+          println("Acceptance probability: $(acceptance_prob(fitness, new_fitness, temp))")
+          println("Threshold: $(threshold)")
+        end
+
+        if acceptance_prob(fitness, new_fitness, temp) >= threshold
+          if chatty >= 1
+            println("$(key) -> $(neighbour), threshold $(threshold), temperature $(temp), fitness $(new_fitness), prob $(acceptance_prob(fitness, new_fitness, temp))")
+          end
+          fitness = new_fitness
+          key = neighbour
+        end
+      end
+
+      temp = temp * temp_factor
+
+      if chatty >= 2
+        println("----")
+      end
+    end
+
+    key = total_best_key
+    fitness = total_best_fitness
+    temp = 1
+  end
+
+  if chatty >= 1
+    println("Best was $(total_best_key) at $(total_best_fitness)")
+    println(total_best_decrypt)
+  end
+  (key, decrypt_monoalphabetic(ciphertext, key))
+end
+