Cipher Identifier

A to Z counts letters in either case and ignores everything else. Custom counts your own symbols, folding case unless the alphabet holds both cases of a letter; the English tests (chi-squared, letter order, the shift and affine keys, Playfair's shape) need A to Z. Word breaks reads the spaces as the original spacing; Ignore reads a stream of letters.

Letter counts

Each letter's count O beside E, the count English would give: E = N x the letter's share of the English table. Chi-squared adds (O - E)^2 / E over the 26 letters; the thin mark on each bar is the English share.

Each of the 312 affine keys (a x + b mod 26, which include the 26 shifts and Atbash) undone on these counts: the closest to English is affine a = 25, b = 22 (A becomes W), chi-squared 457.3, outside the limit of 220.5.

Letter order: 10 of 320 adjacent pairs (3.1%) are one of TH HE IN ER AN RE ON AT EN ND. English order gives at least 12.0% on this test; English letters in random order give about 6.3%, the sum of each pair's two letter shares multiplied.

Index of coincidence

The chance that two letters picked from different places in the text are the same letter. One alphabet swapped for another keeps it; a repeating key pulls it toward random.

Index by key length

For each key length L, the letters are split into L columns (every Lth letter) and the columns' indexes averaged. Under a repeating key of length L, each column is one alphabet and reads near English. Tried up to 16: longer keys would leave a column under 20 letters. A possible key length is the smallest whose columns read in the English range and come within 0.005 of the best average, while the whole text reads below it.

The thin mark is the start of the English range, 0.0560.

Repeats and Kasiski spacings

For every three-letter sequence, the distance from each occurrence to the next. Under a repeating key, a repeat that lines up with the key gives a distance the key length divides; by chance, a length L divides about 1 in L.

Repeated trigrams (31 in all, the commonest 10 shown): SCE 12 times, DJB 4 times, ETS 3 times, SEP 3 times, JBS 3 times, BSC 3 times, CEP 3 times, CER 2 times, SSC 2 times, AKU 2 times

Words, reading the spaces as word breaks

Words

74, 4.3 letters on average

One-letter words

L (4 times); English has two, A and I

Repeated words

SCE 10 times, LJT 2 times, CLT 2 times, WLQ 2 times

Character set

Tests on every non-space character, whatever the alphabet setting.

• • passMostly letters A to Z. 321 of 327 non-space characters are letters A to Z (98.2%); at least half is the test.
• • failMorse code characters. Not only dots, dashes and slashes, or not both dots and dashes.
• • failOnly 0 and 1. Characters other than 0 and 1 appear.
• • failOnly digits and separators. Letters or other characters appear beside the digits, or there are no digits.
• • failEvery number from 1 to 26. Not digit text, or a number falls outside 1 to 26.
• • failDigits of a Polybius square. Not digit text, fewer than 3 different digits, or digits outside one square's 1 to 6 or 0 to 5.
• • failEvery number from 22 to 110. Not digit text, or a number falls outside 22 to 110.
• • failOnly two different letters. The text uses 23 different letters, or characters besides letters.
• • failOnly the letters A D F G V X. Letters outside A D F G V X appear, or fewer than 4 of them are used.
• • failOnly hexadecimal digits. Characters outside 0 to 9 and A to F appear, or it lacks either digits or letters.
• • failThe Base64 alphabet. Characters outside the Base64 alphabet appear, = is not only at the end, or one case is missing.

Every family, and why

A family fits when every test it has passes, and fits less when its first test passes and at least half pass. Families from the letter statistics need 100 letters; families from the character set need 100 non-space characters. A fit is a possibility, not an identification.

1. 1. Monoalphabetic substitutionfits best

   shift (Caesar), Atbash, affine, keyword or mixed alphabet

   • passIndex of coincidence 0.0654 is in the English range, 0.0560 to 0.0952
   • passLetters are replaced: not in English proportions (chi-squared 1,646.1 against a limit of 220.5)
   • passOne-letter words use 1 different symbol (L); English has two, A and I

   Unsure: Counts cannot tell a keyword alphabet from a random mixed alphabet, and a short or unusual text can move chi-squared either way.

   Classical Cipher Workbench (new tab)

2. 2. Transpositionfits less

   rail fence, columnar, route, scytale

   • passIndex of coincidence 0.0654 is in the English range, 0.0560 to 0.0952
   • failLetters are not in English proportions: chi-squared 1,646.1 against a limit of 220.5
   • pass3.1% of adjacent pairs are common English pairs such as TH and HE (English order: at least 12.0%; shuffled English letters: about 6.3%)

   Unsure: Counts cannot say which transposition or which key; they show only that the letters are English and their order is not.

   Scytale Cipher (new tab)

3. 3. Not enciphered, or a light transpositiondoes not fit

   English letters still in English order

   • passIndex of coincidence 0.0654 is in the English range, 0.0560 to 0.0952
   • failLetters are not in English proportions: chi-squared 1,646.1 against a limit of 220.5
   • fail3.1% of adjacent pairs are common English pairs such as TH and HE (English order: at least 12.0%; shuffled English letters: about 6.3%)

   Unsure: Letter counts cannot tell English that was never enciphered from a transposition that moved only a few letters.

4. 4. Playfair or another digraphic cipherdoes not fit

   letters enciphered two at a time

   • failIndex 0.0654 is not between random (up to 0.0452) and English (from 0.0560)
   • fail321 letters: an odd count
   • fail3 pairs of the same letter among the 160 letter pairs
   • pass23 different letters; never used: F, X, Z

   Unsure: Other digraphic ciphers, and some Vigenère texts, can pass the same tests; the missing letter is often J but can be any letter.

   Playfair Cipher (new tab)

5. 5. Polyalphabetic with a short repeating keydoes not fit

   Vigenère, Beaufort, Gronsfeld

   • failIndex 0.0654 is not below the English range, 0.0560 to 0.0952
   • not testedKey lengths not tried: the index is already in the English range

   Unsure: A multiple of the key length also reads near English, and Vigenère, Beaufort and Gronsfeld give the same counts.

   Vigenère Cipher (new tab)

6. 6. Long key or random lettersdoes not fit

   autokey, running key, a long repeating key, a one-time pad, or random letters

   • failIndex 0.0654 is above the near-random line of 0.0452
   • not testedKey lengths not tried: the index is not below the English range

   Unsure: An autokey, a running key, a long key, a one-time pad and random letters all look like this, and a true one-time pad cannot be read from the text alone.

Three checks of the arithmetic

Each row is worked by the same code as the stage. Load puts it in the box.

• AAAA4 letters, all the same
  index of coincidence 1, from 12 / (4 x 3); insufficient evidence: 4 letters, fewer than 100, so no family is ranked
  LoadCopy
• ABCD4 letters, all different
  index of coincidence 0, from 0 / (4 x 3); insufficient evidence: 4 letters, fewer than 100, so no family is ranked
  LoadCopy
• Empty, or fewer than 100 lettersfor example XQZ
  index of coincidence 0, from 0 / (3 x 2); insufficient evidence: 3 letters, fewer than 100, so no family is ranked
  LoadCopy