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one of the "systems" of remez (hints) is a"t b"sh where the first letter of the aleph bet can be switched to the last letter. The pattern continues moving inward toward the center with bet pairing with shin etc. Using this system you can derive 'new' or 'hidden' meanings to words.

I'd like to know where this system came from. Who says it is legitimate?

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Define legitimate. – Double AA Jul 4 '13 at 4:32

In Yermiyahu 25:26, there is a mention of King of Shishah (מלך ששך), AFAIR the commentators say that the talk is about the King of Bavel (מלך בבל) because shishah = bavel in atbash.

Also mentioned here.

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