DES Decryption followed by Encryption, will it produce the original text?

Question

This is regarding DES.

My question is, if a plain text is first decrypted (with the decryption algorithm) using Key K1 and then encrypted using same K1, would the result still be the original plain text?

Answer 1

Yes, like all block ciphers, DES is a PRP. That is a Pseudo Random Permutation. A permutation is a reordering of all possible input values.

In the case of DES there are 2^64 possible input values as the block size of DES is 64 bits. If you have a key and DES in encrypt or decrypt modus then the key will indicate a reordering of all 2^64 possible values. In other words, each value will be translated into another value at the same position in the re-ordered array.

Now of course decryption does the reverse translation to encryption. But if decryption is the exact reverse of encryption, then encryption is the reverse of decryption.

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Lets take a look at a possible permutation of two bits for a specific, unspecified key (as writing down a 2^64 permutation is impossible):

00 ENC 11
01 --> 01
10 DEC 00
11 <-- 10

You can simply rewrite this as

00 DEC 10
01 --> 01
10 ENC 11
11 <-- 00

So in the first column there are all possible plaintext and in the last column all the possible ciphertext.

Obviously it doesn't matter if you switch encryption and decryption.

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As some ciphers implementations are actually somewhat more efficient in the decryption direction it may make some sense to switch encryption and decryption around. I haven't seen many protocols that do though; the advantages are minimal while the confusion would be high.

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In the case of triple-DES this property is actually used. Triple-DES uses an EDE (encrypt, decrypt, encrypt) scheme for encryption and a DED scheme for decryption. As you can see, the middle part of the encryption and decryption is in reverse.

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Side note: The actual number of possible permutations - the number of ways you can reorder all possible plaintext blocks - is very high. To be precise, it's 2^N! where N is the block size. So there are 2^64! (that's about 10^(10^88) - a truly scary number) possible permutations for DES; only one of those is selected by the key.