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# Frequency Tables, Shift Cipher

Solving Ceasar shfit with frequency tables.

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: 64: 65: 66: 67: ``` ``````(* Shift cipher aka caesar *) (* Taken from http://www.paul-abraham.com/CaesarCipher.doc and cleaned up*) let isAlpha c = System.Char.IsLetter c (* Only do lowers for now *) let shift n c = let b = match isAlpha c with | true -> (( int c - 97 + n ) % 26 ) + 97 | false -> match c with | ' ' -> 32 | _ -> int c char b let encode xs n = xs |> Seq.map (shift n) |> Seq.toArray |> fun e -> new string (e) let findall xs e = seq { for i in xs -> if i = e then 1 else 0 } let count xs c = findall xs c |> (float << Seq.fold (+) 0) let freqTab word = [ for x in 'a'..'z' -> (count word x) ] |> fun count' -> count' |> Seq.map (fun c -> c * 100.0 / (count' |> Seq.sum)) (* X^2 = sum i=1 .. n * (Oi - Ei)^2 / Ei Where: X^2 - is the test statistic that asymptotically approaches a x 2 (Chi) distribution. Oi - an observed frequency Ei - 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.map (fun (Oi,Ei) -> (Oi - Ei) * (Oi - Ei) / Ei) |> Seq.sum let freqTable = [ 8.2; 1.5; 2.8; 4.3; 12.7; 2.2; 2.0; 6.1; 0.2; 7.0; 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 = let enc k = encode word k [0..25] |> Seq.map (fun x -> x, chisqr (freqTab (enc x)) freqTable) |> Seq.minBy (fun (x,y) -> y) |> fst |> enc (* 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 : c:char -> bool

Full name: Script.isAlpha
val c : char
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 b : int
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<_>
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
val encode : xs:seq<char> -> n:int -> string

Full name: Script.encode
val xs : seq<char>
module Seq

from Microsoft.FSharp.Collections
val map : mapping:('T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.map
val toArray : source:seq<'T> -> 'T []

Full name: Microsoft.FSharp.Collections.Seq.toArray
val e : char []
Multiple items
val string : value:'T -> string

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

--------------------
type string = System.String

Full name: Microsoft.FSharp.Core.string
val findall : xs:seq<'a> -> e:'a -> seq<int> (requires equality)

Full name: Script.findall
val xs : seq<'a> (requires equality)
val e : 'a (requires equality)
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 i : 'a (requires equality)
val count : xs:seq<'a> -> c:'a -> float (requires equality)

Full name: Script.count
val c : 'a (requires equality)
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<_>
val fold : folder:('State -> 'T -> 'State) -> state:'State -> source:seq<'T> -> 'State

Full name: Microsoft.FSharp.Collections.Seq.fold
val freqTab : word:seq<char> -> seq<float>

Full name: Script.freqTab
val word : seq<char>
val x : char
val count' : float list
val c : float
val sum : source:seq<'T> -> 'T (requires member ( + ) and member get_Zero)

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

Full name: Script.chisqr
val a : seq<float>
val b : seq<float>
val zip : source1:seq<'T1> -> source2:seq<'T2> -> seq<'T1 * 'T2>

Full name: Microsoft.FSharp.Collections.Seq.zip
val Oi : float
val Ei : float
val freqTable : float list

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

Full name: Script.crack
val enc : (int -> string)
val k : int
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