# Number of possible keys in a Play fair cipher [duplicate]

This question already has an answer here:

So for the play fair case, the number of possible keys is : 26x26 = 676 possible keys

But if we consider the repeated letters, how many unique keys will the play fair have? I mean how will considering the redundant letters affect the number of possible keys?

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## marked as duplicate by figlesquidge, e-sushi♦, DrLecter, rath, AFSMar 9 '14 at 1:44

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

## 1 Answer

The Playfair cipher has a key consisting of a square of $5 \times 5$ letters (usually the J is not used, or I/J are considered one letter).

Filling the square can be done in $25!$ ways (pick a letter for left upper corner, a new one for the place next to it, and so on), but then every square has equivalent forms, formed by rotating the columns and/or rotating the rows. So we have get $\frac{25!}{5 \cdot 5}$ different keys.

See also here, where the same question is asked.

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thanks for this! I was actually wondering if a similar question was asked. – Scarl Mar 8 '14 at 6:11