How to calculate a multiple-character checksum for authentication using a tabula recta?

Question

I am not sure if this is possible to do using a tabula recta, but I would like to know how to calculate a multiple-character checksum of a text. For a single-character checksum, it's easy. You just begin on the table at the first letter of text, go down to the second, left/right to the third, up/down to the fourth, left/right to the fifth, etc., then make a 90-degree turn and keep going until you hit the last letter of text.

How would one calculate a double-character checksum? In other words, the sum of the text with a modulus of 676 in base 26 [A-Z].

Answer 1

I just realized that you could use a 676x676 table with 2-character entries. But hopefully there is an easier way.

Answer 2

It is possible to use only one tabula recta.

Let $f$ be the steps to find the checksum, i.e. up x, down y, etc.

After the first character, continue to the second where it left with $f$; this time when faced with the boundary from below or right take mod 26 and continue from top or left...

Answer 3

Since I posted this question I learned the answer is to calculate the checksum as already described in the single-character checksum method, but take both letters which comprise the coordinates of the last letter you land on. Actually you should trace over the entire plaintext twice, otherwise if the length of the text were fraudently modified by exactly 1 character, they could get away with it with odds only 26 to 1, instead of the hoped-for 676 to 1. This is because removing or adding a single character only alters a single checksum character.