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Frequency Tables, Shift Cipher

Solving Ceasar shfit with frequency tables.

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let isalpha = System.Char.IsLetter
       
(* Only do lowers for now *)
let shift n c = 
   if isalpha c then
     char ((( int c - 97 + n ) % 26 ) + 97)
   else if c = ' ' then ' '
   else c

let encode   xs n = String.map (shift n) xs
let countSum xs c = Seq.fold (fun acc x -> if x = c then acc+1.0 else acc) 0.0 xs

let freqTab word =
  let freq = Seq.map (countSum word) ['a'..'z']
  let sum = Seq.sum freq
  Seq.map (fun c -> c * 100.0 / sum) freq
        
(* 
 X^2 = sum i=1 .. n * (o - e)^2 / e
 Where:
  X^2 - is the test statistic that asymptotically approaches a x 2 (Chi) distribution. 
  o  - an observed frequency
  e  - an expected (theoretical) frequency, asserted by the null hypothesis.
  n  - the number of possible outcomes of each event. 
*)

let chisqr (a : float seq) (b : float seq) =
  Seq.zip a b           
  |> Seq.fold (fun acc (o,e) -> acc+((o - e) * (o - e) / e)) 0.0
  

let freqTable = [ 8.2; 1.5; 2.8; 4.3; 12.7; 2.2; 2.0; 6.1; 7.0;
                  0.2; 0.8; 4.0; 2.4; 6.7;  7.5; 1.9; 0.1; 6.0;
                  6.3; 9.1; 2.8; 1.0; 2.4;  0.2; 2.0; 0.1 ]
     
let crack word =
  
  [0..25] 
  |> Seq.map (fun x -> x, chisqr (freqTab (encode word x)) freqTable)
  |> Seq.minBy (fun (x,y) -> y)
  |> fst 
  |> encode word
  
(* Tests *)
//> let test = encode "hello how are you?" 3;;
//val test : string = "khoor krz duh brx?"

//> crack test;;
//val it : string = "hello how are you?"
val isalpha : arg00:char -> bool

Full name: Script.isalpha
namespace System
type Char =
  struct
    member CompareTo : value:obj -> int + 1 overload
    member Equals : obj:obj -> bool + 1 overload
    member GetHashCode : unit -> int
    member GetTypeCode : unit -> TypeCode
    member ToString : unit -> string + 1 overload
    static val MaxValue : char
    static val MinValue : char
    static member ConvertFromUtf32 : utf32:int -> string
    static member ConvertToUtf32 : highSurrogate:char * lowSurrogate:char -> int + 1 overload
    static member GetNumericValue : c:char -> float + 1 overload
    ...
  end

Full name: System.Char
System.Char.IsLetter(c: char) : bool
System.Char.IsLetter(s: string, index: int) : bool
val shift : n:int -> c:char -> char

Full name: Script.shift
val n : int
val c : char
Multiple items
val char : value:'T -> char (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.char

--------------------
type char = System.Char

Full name: Microsoft.FSharp.Core.char
Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>
val encode : xs:string -> n:int -> string

Full name: Script.encode
val xs : string
module String

from Microsoft.FSharp.Core
val map : mapping:(char -> char) -> str:string -> string

Full name: Microsoft.FSharp.Core.String.map
val countSum : xs:seq<'a> -> c:'a -> float (requires equality)

Full name: Script.countSum
val xs : seq<'a> (requires equality)
val c : 'a (requires equality)
module Seq

from Microsoft.FSharp.Collections
val fold : folder:('State -> 'T -> 'State) -> state:'State -> source:seq<'T> -> 'State

Full name: Microsoft.FSharp.Collections.Seq.fold
val acc : float
val x : 'a (requires equality)
val freqTab : word:seq<char> -> seq<float>

Full name: Script.freqTab
val word : seq<char>
val freq : seq<float>
val map : mapping:('T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.map
val sum : float
val sum : source:seq<'T> -> 'T (requires member ( + ) and member get_Zero)

Full name: Microsoft.FSharp.Collections.Seq.sum
val c : float
val chisqr : a:seq<float> -> b:seq<float> -> float

Full name: Script.chisqr
val a : seq<float>
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
Multiple items
val seq : sequence:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Core.Operators.seq

--------------------
type seq<'T> = System.Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>
val b : seq<float>
val zip : source1:seq<'T1> -> source2:seq<'T2> -> seq<'T1 * 'T2>

Full name: Microsoft.FSharp.Collections.Seq.zip
val o : float
val e : float
val freqTable : float list

Full name: Script.freqTable
val crack : word:string -> string

Full name: Script.crack
val word : string
val x : int
val minBy : projection:('T -> 'U) -> source:seq<'T> -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Seq.minBy
val y : float
val fst : tuple:('T1 * 'T2) -> 'T1

Full name: Microsoft.FSharp.Core.Operators.fst

More information

Link:http://fssnip.net/aA
Posted:5 years ago
Author:David Klein
Tags: classic ciphers , frequency table