DecipherTechnical reference

Ciphers

Gronsfeld cipher

Vigenère with a repeating string of digits for the Key.

Also found as Gronsfeld · numeric Vigenère

How it works

Gronsfeld is Vigenère with digits for the Key. Repeat the digit string and add each digit as a Caesar shift. Each Key position is limited to 0–9. In Decipher, only ASCII letters advance the Key.ACA GronsfeldMilitary Cryptanalysis, Part II

C[i] = (P[i] + D[i mod m]) mod 26D[j] ∈ {0, 1, …, 9}

Worked example

Digit Key 314
Plaintext
CODE
Keystream
3143
Ciphertext
FPHH

What to look for

Period tests work much as they do for Vigenère. Once the text is split by phase, each position has only ten possible shifts. That narrows the search, although other periodic ciphers can produce similar clues.

Sources

  1. American Cryptogram Association, Gronsfeld instructions
  2. William F. Friedman, Military Cryptanalysis, Part II