ADFGVX cipher
- 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.
Nim
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
Phix
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.
Wren
<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