The ADFGVX cipher

The German army introduced ADFGX in 1918 and added V soon after. The letters were chosen because they sound very different in Morse code. Each character is found in a keyed square and replaced by its row and column labels, so A might become DG. Then all those letters are shuffled with a columnar transposition under a second keyword.

You need both keys: the square, as a keyword or all 25 or 36 characters, and the transposition keyword. A ciphertext made only of the letters A, D, F, G, V and X is the giveaway.

Example

DGDDDAGDDGAFADDFDADVDVFAADVX with the square NA1C3H8TB2OME5WRPD4F6G7I9J0KLQSUVXYZ and the keyword PRIVACY decodes to ATTACKAT1200AM.