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Description

The ADFGVX cipher was a manually applied field cipher used by the German Army during World War I. It was broken in 1918 by the French cryptanalyst Georges Painvin.

The workings of the cipher are described in the Wikipedia article, linked to above, and so will not be repeated here.

Task

Write routines, functions etc. in your language to:

1. Encrypt suitable plaintext and decrypt the resulting cipher text using the ADFGVX cipher algorithm given a Polybius square (see 2. below) and a suitable key. For this purpose suitable means text consisting solely of ASCII upper case letters or digits.

2. Create a 6 x 6 Polybius square using a random combination of the letters A to Z and the digits 0 to 9 and then display it.

3. Given the number of letters (between 7 and 12 say) to use, create a key by selecting a suitable word at random from unixdict.txt and then display it. The word selected should be such that none of its characters are repeated.

Use these routines to create a Polybius square and a 9 letter key.

These should then be used to encrypt the plaintext: ATTACKAT1200AM and decrypt the resulting cipher text. Display here the results of both operations.

Note

As it's unclear from the Wikipedia article how to handle a final row with fewer elements than the number of characters in the key, either of the methods mentioned in Columnar transposition may be used. In the case of the second method, it is also acceptable to fill any gaps after shuffling by moving elements to the left which makes decipherment harder.

11l

Translation of: Nim

<lang 11l>V adfgvx = ‘ADFGVX’

F encrypt(plainText, polybius, key)

  V s = ‘’
  L(ch) plainText
     L(r) 6
        L(c) 6
           I polybius[r][c] == ch
              s ‘’= :adfgvx[r]‘’:adfgvx[c]

  DefaultDict[Char, String] cols
  L(ch) s
     cols[key[L.index % key.len]] ‘’= ch

  V result = ‘’
  L(k) sorted(cols.keys())
     I !result.empty
        result ‘’= ‘ ’
     result ‘’= cols[k]
  R result

F decrypt(cipherText, polybius, key)

  V skey = sorted(key)
  V cols = [‘’] * key.len
  V idx = 0
  L(col) cipherText.split(‘ ’)
     cols[key.findi(skey[idx])] = col
     idx++

  V s = ‘’
  L(i) 0 .< key.len
     L(col) cols
        I i < col.len
           s ‘’= col[i]

  V result = ‘’
  L(i) (0 .< s.len - 1).step(2)
     V r = :adfgvx.findi(s[i])
     V c = :adfgvx.findi(s[i + 1])
     result ‘’= polybius[r][c]
  R result

V polybius = [[Char("\0")] * 6] * 6 V alphabet = ‘ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789’ random:shuffle(&alphabet) L(r) 6

  L(c) 6
     polybius[r][c] = alphabet[6 * r + c]

print("6 x 6 Polybius square:\n") print(‘ | A D F G V X’) print(‘---------------’) L(row) polybius

  print(adfgvx[L.index]‘ | ’row.join(‘ ’))

V words = File(‘unixdict.txt’).read().split("\n").filter(w -> w.len == 9 & w.len == Set(Array(w)).len) V key = random:choice(words).uppercase() print("\nThe key is "key)

V PlainText = ‘ATTACKAT1200AM’ print("\nPlaintext : "PlainText)

V cipherText = encrypt(PlainText, polybius, key) print("\nEncrypted : "cipherText)

V plainText = decrypt(cipherText, polybius, key) print("\nDecrypted : "plainText)</lang>

Output:

6 x 6 Polybius square:

  | A D F G V X
---------------
A | X O F P D 6
D | V H C 4 0 Z
F | J M K R U 5
G | I A 9 Y B W
V | 3 L 2 1 N G
X | Q T E 7 8 S

The key is EXCURSION

Plaintext : ATTACKAT1200AM

Encrypted : XFD GFVD GDG DGF DVD XDD DXV DGV DFF

Decrypted : ATTACKAT1200AM

F#

<lang fsharp> // ADFGVX cipher. Nigel Galloway: August 23rd., 2021 let polybus=let n=[|yield! {'A'..'Z'}; yield! {'0'..'9'}|] in MathNet.Numerics.Combinatorics.GeneratePermutation 36|>Array.map(fun g->n.[g]),[|'A';'D';'F';'G';'V';'X'|] let printPolybus(a,g)=printf " "; g|>Array.iter(printf "%c "); printfn ""; printfn " ----------------"

                     g|>Array.iteri(fun n g->printf " %c|" g; [0..5]|>List.iter(fun g->printf " %c " (Array.item(n*6+g) a)); printfn "")

let c2p n g=let g=(fst>>(Array.findIndex((=) g))) n in let (n:char[])=(snd n) in [|n.[g/n.Length];n.[g%n.Length]|] let p2c n (g:char[])=Array.item(let n=snd n in (Array.findIndex((=)g.[0]) n)*n.Length+(Array.findIndex((=)g.[1]) n))(fst n) let fN(g:string)=let e,d=let n=g|>Seq.sort|>List.ofSeq in (g|>Seq.mapi(fun i l->(List.findIndex((=)l)n)-i)|>Array.ofSeq,n|>Seq.mapi(fun i l->(Seq.findIndex((=)l)g)-i)|>Array.ofSeq)

                (fun i->i+(e.[i%g.Length])),(fun i->i+(d.[i%g.Length]))

let ADFGVX n (g:string)=let pE,pD=fN g

                       (fun(s:string)->let a,b=s|>Seq.collect(c2p n)|>Array.ofSeq|>Array.splitAt(2*s.Length-(2*s.Length)%g.Length)
                                       Array.append(Array.permute(pE) a)(Array.permute(fst(fN(g.[..b.Length-1]))) b)|>System.String),
                       (fun(s:string)->let a,b=s.ToCharArray()|>Array.splitAt(s.Length-(s.Length)%g.Length)
                                       Array.append(Array.permute(pD) a)(Array.permute(snd(fN(g.[..b.Length-1]))) b)|>Array.chunkBySize 2|>Array.map(p2c n)|>System.String)

printPolybus polybus let encrypt,decrypt=ADFGVX polybus "nigel" //Using "nigel" as the key no hacker will guess that! let n=encrypt "ATTACKAT1200AM" in printfn $"\nATTACKAT1200AM encrypted is %s{n} which decrypted is %s{decrypt n}" </lang>

Output:

    A  D  F  G  V  X
    ----------------
 A| 6  U  9  B  2  H
 D| C  G  O  N  Y  R
 F| T  8  D  E  V  K
 G| 1  Q  X  P  L  W
 V| Z  0  I  A  J  S
 X| 7  4  3  M  F  5

ATTACKAT1200AM encrypted is AFGFVDGVAAGVXFFAAGVADVDVVGXG which decrypted is ATTACKAT1200AM

Go

Translation of: Wren

<lang go>package main

import (

   "bytes"
   "fmt"
   "io/ioutil"
   "log"
   "math/rand"
   "sort"
   "strings"
   "time"

)

var adfgvx = "ADFGVX" var alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"

func distinct(bs []byte) []byte {

   var u []byte
   for _, b := range bs {
       if !bytes.Contains(u, []byte{b}) {
           u = append(u, b)
       }
   }
   return u

}

func allAsciiAlphaNum(word []byte) bool {

   for _, b := range word {
       if !((b >= 48 && b <= 57) || (b >= 65 && b <= 90) || (b >= 97 && b <= 122)) {
           return false
       }
   }
   return true

}

func orderKey(key string) []int {

   temp := make([][2]byte, len(key))
   for i := 0; i < len(key); i++ {
       temp[i] = [2]byte{key[i], byte(i)}
   }
   sort.Slice(temp, func(i, j int) bool { return temp[i][0] < temp[j][0] })
   res := make([]int, len(key))
   for i := 0; i < len(key); i++ {
       res[i] = int(temp[i][1])
   }
   return res

}

func createPolybius() []string {

   temp := []byte(alphabet)
   rand.Shuffle(36, func(i, j int) {
       temp[i], temp[j] = temp[j], temp[i]
   })
   alphabet = string(temp)
   fmt.Println("6 x 6 Polybius square:\n")
   fmt.Println("  | A D F G V X")
   fmt.Println("---------------")
   p := make([]string, 6)
   for i := 0; i < 6; i++ {
       fmt.Printf("%c | ", adfgvx[i])
       p[i] = alphabet[6*i : 6*(i+1)]
       for _, c := range p[i] {
           fmt.Printf("%c ", c)
       }
       fmt.Println()
   }
   return p

}

func createKey(n int) string {

   if n < 7 || n > 12 {
       log.Fatal("Key should be within 7 and 12 letters long.")
   }
   bs, err := ioutil.ReadFile("unixdict.txt")
   if err != nil {
       log.Fatal("Error reading file")
   }
   words := bytes.Split(bs, []byte{'\n'})
   var candidates [][]byte
   for _, word := range words {
       if len(word) == n && len(distinct(word)) == n && allAsciiAlphaNum(word) {
           candidates = append(candidates, word)
       }
   }
   k := string(bytes.ToUpper(candidates[rand.Intn(len(candidates))]))
   fmt.Println("\nThe key is", k)
   return k

}

func encrypt(polybius []string, key, plainText string) string {

   temp := ""

outer:

   for _, ch := range []byte(plainText) {
       for r := 0; r <= 5; r++ {
           for c := 0; c <= 5; c++ {
               if polybius[r][c] == ch {
                   temp += fmt.Sprintf("%c%c", adfgvx[r], adfgvx[c])
                   continue outer
               }
           }
       }
   }
   colLen := len(temp) / len(key)
   // all columns need to be the same length
   if len(temp)%len(key) > 0 {
       colLen++
   }
   table := make([][]string, colLen)
   for i := 0; i < colLen; i++ {
       table[i] = make([]string, len(key))
   }
   for i := 0; i < len(temp); i++ {
       table[i/len(key)][i%len(key)] = string(temp[i])
   }
   order := orderKey(key)
   cols := make([][]string, len(key))
   for i := 0; i < len(key); i++ {
       cols[i] = make([]string, colLen)
       for j := 0; j < colLen; j++ {
           cols[i][j] = table[j][order[i]]
       }
   }
   res := make([]string, len(cols))
   for i := 0; i < len(cols); i++ {
       res[i] = strings.Join(cols[i], "")
   }
   return strings.Join(res, " ")

}

func decrypt(polybius []string, key, cipherText string) string {

   colStrs := strings.Split(cipherText, " ")
   // ensure all columns are same length
   maxColLen := 0
   for _, s := range colStrs {
       if len(s) > maxColLen {
           maxColLen = len(s)
       }
   }
   cols := make([][]string, len(colStrs))
   for i, s := range colStrs {
       var ls []string
       for _, c := range s {
           ls = append(ls, string(c))
       }
       if len(s) < maxColLen {
           cols[i] = make([]string, maxColLen)
           copy(cols[i], ls)
       } else {
           cols[i] = ls
       }
   }
   table := make([][]string, maxColLen)
   order := orderKey(key)
   for i := 0; i < maxColLen; i++ {
       table[i] = make([]string, len(key))
       for j := 0; j < len(key); j++ {
           table[i][order[j]] = cols[j][i]
       }
   }
   temp := ""
   for i := 0; i < len(table); i++ {
       temp += strings.Join(table[i], "")
   }
   plainText := ""
   for i := 0; i < len(temp); i += 2 {
       r := strings.IndexByte(adfgvx, temp[i])
       c := strings.IndexByte(adfgvx, temp[i+1])
       plainText = plainText + string(polybius[r][c])
   }
   return plainText

}

func main() {

   rand.Seed(time.Now().UnixNano())
   plainText := "ATTACKAT1200AM"
   polybius := createPolybius()
   key := createKey(9)
   fmt.Println("\nPlaintext :", plainText)
   cipherText := encrypt(polybius, key, plainText)
   fmt.Println("\nEncrypted :", cipherText)
   plainText2 := decrypt(polybius, key, cipherText)
   fmt.Println("\nDecrypted :", plainText2)

}</lang>

Output:

Sample run:

6 x 6 Polybius square:

  | A D F G V X
---------------
A | R W H N I 7 
D | 1 J O 2 P 5 
F | 3 A T 4 M 9 
G | D U L K V 0 
V | Z B E F 6 Q 
X | G Y S 8 C X 

The key is EUCHARIST

Plaintext : ATTACKAT1200AM

Encrypted : FDG FGG FVDV FFX FFF FFX DDD XAF DGG

Decrypted : ATTACKAT1200AM

J

Implementation:<lang J>polybius=: {{6 6$8 u:({~?~&#)(48+i.10),65+i.26}} lenword=: {{ ;({~ ?@#)(#~ (-:~.)@>)(#~ y=#@>)cutLF fread'unixdict.txt'}} ADFGVX=: Template:Deb,' ',.n/:~ XVGFDA=: {{ (,m){~($m)#.'ADFGVX'i._2]\deb,|:(>cut y)/:/:n }}</lang>

Example:<lang J> echo W=: lenword 9 roughcast

  echo P=: polybius

PV5M6Q KR0391 4ZS7LA FUT28E GXOBYW ICJDNH

  echo E=: P ADFGVX W 'ATTACKAT1200AM'

FFF FGF FFF GXD XDG FDGG XDX XXA GAD

  echo D=: P XVGFDA W E

ATTACKAT1200AM</lang>

That said, note that we could also eliminate spaces from the encrypted text, as they are recoverable if we have the code word.

<lang J>spaces=: Template:Deb y

  echo S=: E-.' '

FFFFGFFFFGXDXDGFDGGXDXXXAGAD

  P spaces W S

FFF FGF FFF GXD XDG FDGG XDX XXA GAD</lang>

(Technically, we do not need the Polybius square to recover the spaces, but it's passed as an argument here for symmetry.)

Julia

<lang julia>"""

   The ADFGVX cipher.
   See also eg. https://www.nku.edu/~christensen/092hnr304%20ADFGVX.pdf

"""

using Random

""" The WWI German ADFGVX cipher. """ struct ADFGVX

   polybius::Vector{Char}
   pdim::Int
   key::Vector{Char}
   keylen::Int
   alphabet::Vector{Char}
   encode::Dict{Char, Vector{Char}}
   decode::Dict{Vector{Char}, Char}

end

""" ADFGVX constructor, takes 2 strings, option for third string if polybius len != 36 """ function ADFGVX(s, k, alph = "ADFGVX")

   poly = collect(uppercase(s))
   pdim = isqrt(length(poly))
   al = collect(uppercase(alph))
   enco::Dict = Dict([(poly[(i - 1) * pdim + j] => [al[i], al[j]])
       for i in 1:pdim, j in 1:pdim])
   deco = Dict(last(p) => first(p) for p in enco)
   @assert pdim^2 == length(poly) && pdim == length(al)
   return ADFGVX(poly, pdim, collect(uppercase(k)), length(k), al, enco, deco)

end

""" Encrypt with the ADFGVX cipher. """ function encrypt(s::String, k::ADFGVX)

   chars = reduce(vcat, [k.encode[c] for c in
       filter(c -> c in k.polybius, collect(uppercase(s)))])
   colvecs = [lett => chars[i:k.keylen:length(chars)] for (i, lett) in enumerate(k.key)]
   sort!(colvecs, lt = (x, y) -> first(x) < first(y))
   return String(mapreduce(p -> last(p), vcat, colvecs))

end

""" Decrypt with the ADFGVX cipher. Does not depend on spacing of encoded text """ function decrypt(s::String, k::ADFGVX)

   chars = filter(c -> c in k.alphabet, collect(uppercase(s)))
   sortedkey = sort(collect(k.key))
   order = [findfirst(c -> c == ch, k.key) for ch in sortedkey]
   originalorder = [findfirst(c -> c == ch, sortedkey) for ch in k.key]
   a, b = divrem(length(chars), k.keylen)
   strides = [a + (b >= i ? 1 : 0) for i in order]           # shuffled column lengths
   starts = accumulate(+, strides[begin:end-1], init=1)      # shuffled starts of columns
   pushfirst!(starts, 1)                                     # starting index
   ends = [starts[i] + strides[i] - 1 for i in 1:k.keylen]   # shuffled ends of columns
   cols = [chars[starts[i]:ends[i]] for i in originalorder]  # get reordered columns
   pairs, nrows = Char[], (length(chars) - 1) ÷ k.keylen + 1 # recover the rows
   for i in 1:nrows, j in 1:k.keylen
       (i - 1) * k.keylen + j > length(chars) && break
       push!(pairs, cols[j][i])
   end
   return String([k.decode[[pairs[i], pairs[i + 1]]] for i in 1:2:length(pairs)-1])

end

const POLYBIUS = String(shuffle(collect("ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"))) const KEY = read("unixdict.txt", String) |>

   v -> split(v, r"\s+") |>
   v -> filter(w -> (n = length(w); n == 9 && n == length(unique(collect(w)))), v) |>
   shuffle |> first |> uppercase

const SECRETS, message = ADFGVX(POLYBIUS, KEY), "ATTACKAT1200AM" println("Polybius: $POLYBIUS, Key: $KEY") println("Message: $message") encoded = encrypt(message, SECRETS) decoded = decrypt(encoded, SECRETS) println("Encoded: $encoded") println("Decoded: $decoded")

</lang>

Output:

Polybius: L4VZJIB8OXGFM1H3CTNKU9PE75WQ2DAYRS06, Key: SUNFLOWER
Message: ATTACKAT1200AM
Encoded: AFAXXVFAXFDXXFVFDFXVVAAGVXXX
Decoded: ATTACKAT1200AM

Nim

Translation of: Wren

It started as a translation, but actually we use a different method, better suited to Nim, to encrypt and decrypt. And there are many other differences. Output is similar though.

<lang Nim>import algorithm, random, sequtils, strutils, sugar, tables

const Adfgvx = "ADFGVX"

type PolybiusSquare = array[6, array[6, char]]

iterator items(p: PolybiusSquare): (int, int, char) =

 ## Yield Polybius square characters preceded by row and column numbers.
 for r in 0..5:
   for c in 0..5:
     yield (r, c, p[r][c])

proc initPolybiusSquare(): PolybiusSquare =

 ## Initialize a 6x6 Polybius square.
 var alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
 alphabet.shuffle()
 for r in 0..5:
   for c in 0..5:
     result[r][c] = alphabet[6 * r + c]

proc createKey(n: Positive): string =

 ## Create a key using a word from "unixdict.txt".
 doAssert n in 7..12, "Key should be within 7 and 12 letters long."
 let candidates = collect(newSeq):
                  for word in "unixdict.txt".lines:
                    if word.len == n and
                       word.deduplicate().len == n and
                       word.allCharsInSet(Letters + Digits): word
 result = candidates[rand(candidates.high)].toUpperAscii

func encrypt(plainText: string; polybius: PolybiusSquare; key: string): string =

 ## Encrypt "plaintext" using the given Polybius square and the given key.

 # Replace characters by row+column letters.
 var str: string
 for ch in plainText:
   for (r, c, val) in polybius:
     if val == ch:
       str.add Adfgvx[r] & Adfgvx[c]

 # Build ordered table of columns and sort it by key value.
 var cols: OrderedTable[char, string]
 for i, ch in str:
   let tkey = key[i mod key.len]
   cols.mgetOrPut(tkey, "").add ch
 cols.sort(cmp)

 # Build cipher text from sorted column table values.
 for s in cols.values:
   result.addSep(" ")
   result.add s

func decrypt(cipherText: string; polybius: PolybiusSquare; key: string): string =

 ## Decrypt "cipherText" using the given Polybius square and the given key.

 # Build list of columns.
 let skey = sorted(key)
 var cols = newSeq[string](key.len)
 var idx = 0
 for col in cipherText.split(' '):
   cols[key.find(skey[idx])] = col
   inc idx

 # Build string of row+column values.
 var str: string
 for i in 0..key.high:
   for col in cols:
     if i < col.len: str.add col[i]

 # Build plain text from row+column values.
 for i in countup(0, str.len - 2, 2):
   let r = Adfgvx.find(str[i])
   let c = Adfgvx.find(str[i+1])
   result.add polybius[r][c]

randomize()

var polybius = initPolybiusSquare() echo "6 x 6 Polybius square:\n" echo " | A D F G V X" echo "---------------" for i, row in polybius:

 echo Adfgvx[i], " | ", row.join(" ")

let key = createKey(9) echo "\nThe key is ", key

const PlainText = "ATTACKAT1200AM" echo "\nPlaintext : ", PlainText

let cipherText = PlainText.encrypt(polybius, key) echo "\nEncrypted : ", cipherText

let plainText = cipherText.decrypt(polybius, key) echo "\nDecrypted : ", plainText</lang>

Output:

6 x 6 Polybius square:

  | A D F G V X
---------------
A | U 1 C N H F
D | E M 4 R S G
F | P I 8 9 6 5
G | X 2 Z B 7 K
V | A 3 Y V O D
X | 0 W Q T J L

The key is PHAGOCYTE

Plaintext : ATTACKAT1200AM

Encrypted : XXX GXA ADD GVA AGD XAX VFGD AAA VGV

Decrypted : ATTACKAT1200AM

Perl

<lang perl>#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/ADFGVX_cipher use warnings; use List::Util qw( shuffle );

my $plaintext = 'ATTACKAT1200AM'; my $keysize = 9;

my $polybius = <<END;

 | A D F G V X

--+------------ A | x x x x x x D | x x x x x x F | x x x x x x G | x x x x x x V | x x x x x x X | x x x x x x END $polybius =~ s/x/$_/ for my @letters = shuffle "A" .. 'Z' , 0 .. 9; print "Polybius square =\n\n$polybius\n"; my %char2pair; @char2pair{ @letters } = glob '{A,D,F,G,V,X}' x 2; # map chars to pairs my %pair2char = reverse %char2pair; # map pairs to chars my ($keyword) = shuffle grep !/(.).*\1/,

 do { local (@ARGV, $/) = 'unixdict.txt'; <> =~ /^.{$keysize}$/gm };

my ($n, @deorder) = 0; my @reorder = map /.(.+)/, sort map $_ . $n++, split //, $keyword; @deorder[@reorder] = 0 .. $#reorder; print " keyword = $keyword\n\nplaintext = $plaintext\n\n";

my $encoded = encode( $plaintext, \%char2pair, \@reorder ); print " encoded = $encoded\n\n";

my $decoded = decode( $encoded, \%pair2char, \@deorder ); print " decoded = $decoded\n";

sub encode

 {
 my ($plain, $c2p, $order) = @_;
 my $len = @$order;
 join ' ', (transpose( $plain =~ s/./$c2p->{$&}/gr =~ /.{1,$len}/g ))[@$order];
 }

sub decode

 {
 my ($encoded, $p2c, $order) = @_;
 (join , transpose((split ' ', $encoded)[@$order])) =~ s/../$p2c->{$&}/gr;
 }

sub transpose { map join(, map {s/.// ? $& : } @_), 1 .. length $_[0] }</lang>

Output:

Polybius square =

  | A D F G V X
--+------------
A | 6 V Y E P N
D | 1 C M 9 L H
F | 8 T O U D F
G | A R G 7 S 5
V | J 2 W Q I Z
X | K B 3 0 X 4

  keyword = benchmark

plaintext = ATTACKAT1200AM

  encoded = GDG GDVF DGG AXD FAX DAD DFG FAX ADA

  decoded = ATTACKAT1200AM

Phix

Translation of: Wren

We can make some nice use of the standard builtin routines here, with only a modest amount of whitespace cleanup.

with javascript_semantics
constant ADFGVX = "ADFGVX",
         ALEPH = tagset('Z','A')&tagset('9','0')

function create_polybius()
    string aleph = shuffle(ALEPH)
--  string aleph = "U1CNHFEM4RSGPI8965X2ZB7KA3YVOD0WQTJL"   -- Nim
--  string aleph = "T71VB5HYG2JKIQM8REOPDUNCZ063FXAW9S4L"   -- Wren
--  string aleph = "NA1C3H8TB2OME5WRPD4F6G7I9J0KLQSUVXYZ"   -- wp
    sequence tmp = split(join_by(aleph,1,6," "),'\n')
    printf(1,"6 x 6 Polybius square:\n")
    printf(1,"  | A D F G V X\n")
    printf(1,"---------------\n")
    for i=1 to length(tmp) do
        printf(1,"%s | %s\n",{ADFGVX[i],tmp[i]})
    end for
    return aleph
end function

function lnua(string word, integer n)
    return length(word)==n 
       and length(unique(word))==n
       and length(filter(word,"in",ALEPH))==n
end function

function create_key(integer n)
    assert(n>=7 and n<=12)
    sequence candidates = filter(upper(unix_dict()),lnua,n)
    string res = candidates[rand(length(candidates))]
--  string res = "PHAGOCYTE" -- Nim
--  string res = "SUNFLOWER" -- Wren
--  string res = "PRIVACY" -- wp
    printf(1,"\nThe key is %s\n",{res})
    return res
end function

function encrypt(string polybius, key, plaintext)
    integer l = length(key)
    sequence tags = custom_sort(key,tagset(l)),
             res = ""
    for i=1 to length(plaintext) do
        integer k = find(plaintext[i],polybius)
        if k then   -- (simply ignore any non-alphanum)
            res &= ADFGVX[floor((k-1)/6)+1]&
                   ADFGVX[remainder((k-1),6)+1]
        end if
    end for
    res = substitute(join(columnize(split_by(res,l),tags,' ')),"  "," ")
    return res
end function

function decrypt(string polybius, key, encrypted)
    integer l = length(key)
    sequence tags = custom_sort(key,tagset(l)),
             tmp = columnize(split(encrypted,' '),{},' ')
    tmp = trim(join(apply(true,extract,{tmp,{tags},true}),""))
    string plaintext = ""
    for i=1 to length(tmp) by 2 do
        integer r = find(tmp[i],ADFGVX)-1,
                c = find(tmp[i+1],ADFGVX)
        plaintext &= polybius[r*6+c]
    end for
    return plaintext   
end function

string polybius = create_polybius(),
            key = create_key(9),
       plaintext = "ATTACKAT1200AM",
       encrypted = encrypt(polybius,key,plaintext),
       decrypted = decrypt(polybius,key,encrypted)
printf(1,"\nPlainText : %s\n\nEncrypted : %s\n\nDecrypted : %s\n",
           {plaintext,        encrypted,        decrypted})

Output matches Wren/Nim/wp when the appropriate lines are uncommented.

Python

This version and the Julia version do not reveal the key length by preserving spaces between columns, which completely removes column information, not just hiding which columns are first in the encoding. According to historical sources the original encrypted text was spaced in 5 character blocks regardless of message and key length, which means that decryption should not rely on spacing. <lang python>"""

   The ADFGVX cipher implemented as a Python class 
   See also eg. https://www.nku.edu/~christensen/092hnr304%20ADFGVX.pdf

"""

from random import shuffle, choice from itertools import product, accumulate from numpy import floor, sqrt

class ADFGVX:

   """ The WWI German ADFGVX cipher. """
   def __init__(self, spoly, k, alph='ADFGVX'):
       self.polybius = list(spoly.upper())
       self.pdim = int(floor(sqrt(len(self.polybius))))
       self.key = list(k.upper())
       self.keylen = len(self.key)
       self.alphabet = list(alph)
       pairs = [p[0] + p[1] for p in product(self.alphabet, self.alphabet)]
       self.encode = dict(zip(self.polybius, pairs))
       self.decode = dict((v, k) for (k, v) in self.encode.items())

   def encrypt(self, msg):
       """ Encrypt with the ADFGVX cipher. """
       chars = list(.join([self.encode[c] for c in msg.upper() if c in self.polybius]))
       colvecs = [(lett, chars[i:len(chars):self.keylen]) \
           for (i, lett) in enumerate(self.key)]
       colvecs.sort(key=lambda x: x[0])
       return .join([.join(a[1]) for a in colvecs])

   def decrypt(self, cod):
       """ Decrypt with the ADFGVX cipher. Does not depend on spacing of encoded text """
       chars = [c for c in cod if c in self.alphabet]
       sortedkey = sorted(self.key)
       order = [self.key.index(ch) for ch in sortedkey]
       originalorder = [sortedkey.index(ch) for ch in self.key]
       base, extra = divmod(len(chars), self.keylen)
       strides = [base + (1 if extra > i else 0) for i in order]    # shuffled column lengths
       starts = list(accumulate(strides[:-1], lambda x, y: x + y))  # shuffled starts of columns
       starts = [0] + starts                                        # starting index
       ends = [starts[i] + strides[i] for i in range(self.keylen)]  # shuffled ends of columns
       cols = [chars[starts[i]:ends[i]] for i in originalorder]     # get reordered columns
       pairs = []                                                   # recover the rows
       for i in range((len(chars) - 1) // self.keylen + 1):
           for j in range(self.keylen):
               if i * self.keylen + j < len(chars):
                   pairs.append(cols[j][i])

       return .join([self.decode[pairs[i] + pairs[i + 1]] for i in range(0, len(pairs), 2)])

if __name__ == '__main__':

   PCHARS = list('ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789')
   shuffle(PCHARS)
   POLYBIUS = .join(PCHARS)
   with open('unixdict.txt') as fh:
       WORDS = [w for w in (fh.read()).split() \
           if len(w) == 9 and len(w) == len(set(list(w)))]
       KEY = choice(WORDS)

   SECRET, MESSAGE = ADFGVX(POLYBIUS, KEY), 'ATTACKAT1200AM'
   print(f'Polybius: {POLYBIUS}, key: {KEY})
   print('Message: ', MESSAGE)
   ENCODED = SECRET.encrypt(MESSAGE)
   DECODED = SECRET.decrypt(ENCODED)
   print('Encoded: ', ENCODED)
   print('Decoded: ', DECODED)

</lang>

Output:

Polybius: A9GKMF1DQRSBVX8Z0WTEJLOPY5U4CN2H76I3, key: volcanism
Message:  ATTACKAT1200AM
Encoded:  GAFAAVAAAGGFVAAAGVAAAADAAVXV
Decoded:  ATTACKAT1200AM

Raku

Slightly different results from every other entry so far. See discussion page for reasons. It is impossible to tell from casual observation which column comes first in the Raku example. In every other (so far), the sub group with 4 characters is the first column. <lang perl6>srand 123456; # For repeatability

my @header = < A D F G V X >; my $polybius = (flat 'A'..'Z', 0..9).pick(*).join;

my $key-length = 9; my $key = uc 'unixdict.txt'.IO.words.grep( { (.chars == $key-length) && (+.comb.Set == +.comb) } ).roll;

my %cypher = (@header X~ @header) Z=> $polybius.comb;

my $message = 'Attack at 1200AM';

use Terminal::Boxer; say "Key: $key\n"; say "Polybius square:\n", ss-box :7col, :3cw, :indent("\t"), , |@header, |(@header Z $polybius.comb.batch: 6); say "Message to encode: $message"; say "\nEncoded: " ~ my $encoded = encode $message; say "\nDecoded: " ~ decode $encoded;

sub encode ($text is copy) {

   $text = $text.uc.comb(/<[A..Z 0..9]>/).join;
   my @order = $key.comb.pairs.sort( *.value )».key;
   my @encode = %cypher.invert.hash{ $text.comb }.join.comb.batch($key-length).map: { [$_] };
   ((^$key-length).map: { @encode».[@order]».grep( *.defined )».[$_].grep( *.defined ).join }).Str;

}

sub decode ($text is copy) {

   my @text = $text.split(' ')».comb;
   my $chars = @text[0].chars;
   $_ = flat |$_, ' ' if .chars < $chars for @text;
   my @order = $key.comb.pairs.sort( *.value )».key.pairs.sort( *.value )».key;
   %cypher{ ( grep { /\w/ }, flat [Z] @order.map( { |@text.batch($key-length)».[$_] } ) ).batch(2)».join }.join;

}</lang>

Output:

Key: GHOSTLIKE

Polybius square:
	┌───┬───┬───┬───┬───┬───┬───┐
	│   │ A │ D │ F │ G │ V │ X │
	├───┼───┼───┼───┼───┼───┼───┤
	│ A │ H │ O │ S │ 5 │ 7 │ Q │
	├───┼───┼───┼───┼───┼───┼───┤
	│ D │ 0 │ I │ 6 │ J │ C │ V │
	├───┼───┼───┼───┼───┼───┼───┤
	│ F │ 4 │ 8 │ R │ X │ G │ A │
	├───┼───┼───┼───┼───┼───┼───┤
	│ G │ Y │ F │ P │ B │ Z │ 3 │
	├───┼───┼───┼───┼───┼───┼───┤
	│ V │ M │ W │ 9 │ D │ 1 │ N │
	├───┼───┼───┼───┼───┼───┼───┤
	│ X │ 2 │ E │ U │ T │ L │ K │
	└───┴───┴───┴───┴───┴───┴───┘

Message to encode: Attack at 1200AM

Encoded: DVVA FVX XXA FGF XVX GXA XXD GFA XXD

Decoded: ATTACKAT1200AM

Wren

Library: Wren-ioutil

Library: Wren-seq

Library: Wren-str

<lang ecmascript>import "random" for Random import "/ioutil" for FileUtil import "/seq" for Lst import "/str" for Char, Str

var rand = Random.new() var adfgvx = "ADFGVX" var alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789".toList

var createPolybius = Fn.new {

   rand.shuffle(alphabet)
   var p = Lst.chunks(alphabet, 6)
   System.print("6 x 6 Polybius square:\n")
   System.print("  | A D F G V X")
   System.print("---------------")
   for (i in 0...p.count) {
       System.write("%(adfgvx[i]) | ")
       System.print(p[i].join(" "))
   }
   return p

}

var createKey = Fn.new { |n|

   if (n < 7 || n > 12) Fiber.abort("Key should be within 7 and 12 letters long.")
   var candidates = FileUtil.readLines("unixdict.txt").where { |word| 
       return word.count == n && Lst.distinct(word.toList).count == n &&
              word.all { |ch| Char.isAsciiAlphaNum(ch) }
   }.toList
   var k = Str.upper(candidates[rand.int(candidates.count)])
   System.print("\nThe key is %(k)")
   return k

}

// helper function to sort the key into alphabetical order // and return a list of the original indices of its letters. var orderKey = Fn.new { |key|

   var temp = (0...key.count).map { |i| [key[i], i] }.toList
   temp.sort { |x, y| x[0].bytes[0] < y[0].bytes[0] }
   return temp.map { |e| e[1] }.toList

}

var encrypt = Fn.new { |polybius, key, plainText|

   var temp = ""
   for (ch in plainText) {
       var outer = false
       for (r in 0..5) {
           for (c in 0..5) {
               if (polybius[r][c] == ch) {
                   temp = temp + adfgvx[r] + adfgvx[c]
                   outer = true
                   break
               }
           }
           if (outer) break
       }
   }
   var colLen = (temp.count / key.count).floor
   // all columns need to be the same length
   if (temp.count % key.count > 0) colLen = colLen + 1
   var table = Lst.chunks(temp.toList, key.count)
   var lastLen = table[-1].count
   if (lastLen < key.count) table[-1] = table[-1] + ([""] * (key.count - lastLen))
   var order = orderKey.call(key)
   var cols = List.filled(key.count, null)
   for (i in 0...cols.count) {
       cols[i] = List.filled(colLen, null)
       for (j in 0...table.count) cols[i][j] = table[j][order[i]]
   }
   return cols.map { |col| col.join() }.join(" ")

}

var decrypt = Fn.new { |polybius, key, cipherText|

   var colStrs = cipherText.split(" ")
   // ensure all columns are same length
   var maxColLen = colStrs.reduce(0) { |max, col| max = (col.count > max) ? col.count : max }
   var cols = colStrs.map { |s| 
       return (s.count < maxColLen) ? s.toList + ([""] * (maxColLen - s.count)) : s.toList
   }.toList
   var table = List.filled(maxColLen, null)
   var order = orderKey.call(key)
   for (i in 0...maxColLen) {
       table[i] = List.filled(key.count, "")
       for (j in 0...key.count) table[i][order[j]] = cols[j][i]
   }
   var temp = table.map { |row| row.join("") }.join("")
   var plainText = ""
   var i = 0
   while (i < temp.count) {
       var r = adfgvx.indexOf(temp[i])
       var c = adfgvx.indexOf(temp[i+1])
       plainText = plainText + polybius[r][c]
       i = i + 2
   }
   return plainText

}

var plainText = "ATTACKAT1200AM" var polybius = createPolybius.call() var key = createKey.call(9) System.print("\nPlaintext : %(plainText)") var cipherText = encrypt.call(polybius, key, plainText) System.print("\nEncrypted : %(cipherText)") var plainText2 = decrypt.call(polybius, key, cipherText) System.print("\nDecrypted : %(plainText2)")</lang>

Output:

Sample run:

6 x 6 Polybius square:

  | A D F G V X
---------------
A | T 7 1 V B 5
D | H Y G 2 J K
F | I Q M 8 R E
G | O P D U N C
V | Z 0 6 3 F X
X | A W 9 S 4 L

The key is SUNFLOWER

Plaintext : ATTACKAT1200AM

Encrypted : AAA AXD AAV AXV AAD GFF XXDF ADG XAX

Decrypted : ATTACKAT1200AM

REXX

<lang rexx> /* REXX */ cls eol=x2c(0D0A) ; msg="ATTACKAT1200AM" keyword= upper('lifeguard') ; cyph= 'ADFGVX'

  s_sort= keyword ; new_key=   
  do while length(s_sort) > 0 
     nmax= 0
     do i=1 to length(s_sort)
        ch= substr(s_sort,i,1)
        num= c2d(ch)
        if num > nmax then do
           nmax= num
           max_i = i
           end
     end
     s_sort= delstr(s_sort,max_i,1)
     new_key= d2c(nmax)||new_key
  end        /* Alphabetical sorting */
  
  j=0 ; num_str=  ; rnd_s=  
  do while j < 36
     num= random(0,35)
     if wordpos(num,num_str) = 0 then do
        j= j + 1
	     num_str= num_str||num||' '

if num >= 10 then do num= num - 10 + x2d(41)

           num= d2c(num)

end rnd_s= rnd_s||num

     end
  end	  /* say 'Generated string: '||rnd_s||eol */

say 'Polybius square:'||eol call tab cyph, rnd_s ,1 say "Only characters from the '"|| msg||"'"||eol t= translate(rnd_s,' ',msg) _t= translate(rnd_s,' ',t) call tab cyph, _t ,1

  len_c= length(cyph) ; cyph_T=
  do i=1 to len_c
     ch_i= substr(cyph,i,1)
     do j=1 to len_c
        ch_j= substr(cyph,j,1)
        cyph_T= cyph_T||ch_i||ch_j||' '
     end
  end

  enc_msg= 
  do i=1 to length(msg)
     ch= substr(msg,i,1)
      j= pos(ch,rnd_s,1)
     enc_msg= enc_msg||word(cyph_T,j) 
  end

say "Conversion by table: "||eol||eol||msg||" ==> "||enc_msg||eol call tab keyword, enc_msg

  len= length(keyword)
  n_row= 0 ; column.=  
   do while enc_msg <> 
      parse var enc_msg 1 s1 +(len) enc_msg
      n_row= n_row+1
      do m= 1 to len
         ch_m= substr(s1,m,1)
         column.m= column.m||ch_m 
         end 
   end

  s_lst=  
  do m= 1 to len
     ch= substr(new_key,m,1)
      i= pos(ch,keyword,1)
     w_i= column.i                 
     s_lst= s_lst||w_i||' '
  end
  
  row.=  ; t_row=               
  do i=1 to len                              
     w_i= word(s_lst,i)                        
     do j=1 to n_row             
        row.j= row.j||substr(w_i,j,1)   
     end 
  end
  do j=1 to n_row; t_row= t_row||row.j; end

say "Sorted by columns:"||eol call tab new_key, t_row

say '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' say 'Encrypted message: '||s_lst say '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'

exit tab: parse arg h, s, p /* header, string, param */

  lh= length(h) ;
  s= h||copies('-',lh)||s ; ls= length(s)
  h=' -'||h

  t=   ; j= 1                   
  do i= 1 to ls by lh 
     row= substr(s,i,lh)
     r_ch=  
     do l=1 to lh
        ch= substr(row,l,1)
        r_ch= r_ch||ch||' '
     end
     row= r_ch
     if p <>  then row= row||'|'||substr(h,j,1)
     t= t||row||eol
     j= j + 1   
  end 
  say t

return </lang>

Output:

Polybius square:

A D F G V X | 
- - - - - - |-
D H 8 P U 4 |A
E T S C 5 9 |D
A 3 Z F R I |F
Y O 1 Q 7 W |G
J 2 G V N X |V
L 6 0 K M B |X

Only characters from the 'ATTACKAT1200AM'

A D F G V X | 
- - - - - - |-
            |A
  T   C     |D
A           |F
    1       |G
  2         |V
    0 K M   |X

Conversion by table: 

ATTACKAT1200AM ==> FADDDDFADGXGFADDGFVDXFXFFAXV

L I F E G U A R D 
- - - - - - - - - 
F A D D D D F A D 
G X G F A D D G F 
V D X F X F F A X 
V                 

Sorted by columns:

A D E F G I L R U 
- - - - - - - - - 
F D D D D A F A D 
D F F G A X G G D 
F X F X X D V A F 
            V     

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Encrypted message: FDF  DFX  DFF  DGX  DAX  AXD  FGVV AGA  DDF  
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~