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Yes, it is possible to implement the primitive asked, with a 32-bit block cipher that is secure (indistinguishable from a random permutation) no matter how many input-output pairs are known, keyed with a fixed secret randomly-chosen key. That's a standard building block in Format Preserving Encryption. One such block cipher is: Louis Granboulan and Thomas ...


Typically, the output of format-preserving encryption is easily distinguishable from a random bitstream, precisely because the ciphertexts conform to some non-random format. Thus, you cannot use standard statistical tests on them, at least not directly. If the format of your FPE scheme is flexible enough, you may be able to test some aspects of it by ...

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