# Is there any way to have a coded string such that it can be decoded in multiple ways?

This is more out of curiosity than anything, having no knowledge of cryptography.

But say I have strings "test1" and "test2", is there any way/algorithm to encode the two strings to an encoded string "string" such that when "string" is decoded with "key1", it returns "test1", and likewise for "key2" and "test2"?

Thanks!

• With the right one-time pad, you can "decrypt" a message to mean anything of the same length. Jun 1 '17 at 2:28
• @Kevin yep this is why I don't like the accepted answer, its not "secure communications cryptography", its just "uses ideas from cryptography". You can't receive double the information you send. Jun 1 '17 at 7:13
• @daniel I accepted OTP not because it is the best instance of secure communications cryptography, but rather it is what I ended up implementing, hopefully that clarifies things. Jun 1 '17 at 14:00

## 6 Answers

The One-Time Pad can be made to do this. With plaintext1 ("test1") and plaintext2 ("test2") given, we can chose (perhaps, randomly) any one of ciphertext (encoded string), pad1 ("key1"), pad2 ("key2"); the rest follows from the standard OTP equations

plaintext1pad1 = ciphertext = plaintext2pad2

where ⊕ is bitwise eXclusive-OR; but watch that

1. The two plaintexts must have the same length, also the length of the common ciphertext and pads;
2. The pads are not really keys, which implies re-usability with security, that the OTP does not allow;
3. The OTP methods needs significant adaptation if it was desired that the pads appears random to an observer holding both.

Example: we generate random ciphertext, then use

pad1 = plaintext1ciphertext   and   pad2 = plaintext2ciphertext

ciphertext           = DF 23 87 E8 A2
plaintext1 = "test1" = 74 65 73 74 31
plaintext2 = "test2" = 74 65 73 74 32
pad1                 = AB 46 F4 9C 93
pad2                 = AB 46 F4 9C 90


This has the property asked that when ciphertext is decoded with pad1, it returns "test1", and likewise for pad2 and "test2".

The value of ciphertext was not really obtained by encoding "test1" and "test2" using pad1 and pad2. However if that is performed, both yield ciphertext, which is close to what's asked.

• Is this a two time pad, or are you making the cypher text as long as plain text 1 + plain text 2? May 31 '17 at 16:33
• @daniel: I removed any idea of two-time pad (what I had in mind did not work), and stick to the regular one-time pad except in point 3. Hope this is all clarified now.
– fgrieu
May 31 '17 at 18:05
• So essentially, two key/value pairs can equate to the same string post encryption on this method? Could you kindly provide an example? The Wikipedia one doesn't cover this particular case. Jun 1 '17 at 0:33
• What is this? If the ciphertext is for secure communications I would say plaintext2 could be changed to anything while you are picking pad2. Jun 1 '17 at 7:16

Maybe this example is only remotely related to the question, but anyway:

VeraCrypt application for encrypting computer's disks has an ability to offer part of the disk capacity to reach the plausible deniability with the help of 2 different passwords:

• the first one unlocks so called outer volume with a non-important content,
• the second one unlocks inner, hidden volume with the important content.

So both passwords are used in the same manner (in a command or a dialog box) and only by choosing between them decides which content will be accessible.

• Yes that seems to be what I was looking for (though on a larger scale); is there a name for this type of encryption? Jun 1 '17 at 0:29
• It is not a type of encryption, and the terms Steganography (concealing a file, message, image, video, etc. within another file, message, image, video, etc) and Plausible deniability are more appropriate. Jun 1 '17 at 0:54
• It's worth mentioning that (a) the "free space" of one is utilized as the actual content of the other; (b) you can't store more on one volume than is "free space" on the other; (c) if you don't want to risk destroying data in the "other" volume, you must use BOTH passwords regardless of which volume you are modifying. (For plausible deniability you just give the one password, but then if changes are made by the investigator, the other, hidden volume will end up corrupt/unrecoverable.) Jun 1 '17 at 0:55
• And you also can't deny that having a big random chunk of data isn't at least a bit suspicious. Jun 1 '17 at 8:44

I'll try to lay out a scenario that I think you are describing. You have a publisher that is sending out one message that goes out to two people, and you want these two people to be able to get different information from that message. This is only possible if the whole message is the same size or larger than the sum of the two separate pieces of information the people get out of the message. You can put whatever encryption on top of this but it will either make a message the same size or larger.

You could do something else, have the information already encrypted at person 1 and different information encrypted at person 2 with the same key, and then broadcast the same key to both people at a later date.

Another relevant term is "deniable encryption". See the answer to the question one ciphertext multiple keys multiple messages, from which I quote:

Deniable encryption makes it impossible to prove the existence of the plaintext message without the proper encryption key. This may be done by allowing an encrypted message to be decrypted to different sensible plaintexts, depending on the key used. This allows the sender to have plausible deniability if compelled to give up his or her encryption key. The notion of "deniable encryption" was used by Julian Assange and Ralf Weinmann in the Rubberhose filesystem and explored in detail in a paper by Ran Canetti, Cynthia Dwork, Moni Naor, and Rafail Ostrovsky in 1996.

You can always devise clever solutions like this. However, it may dramatically increase the length of the string.

As a trivial example, you could make an encryption scheme which takes your messages ("test1", "test2"), encrypts them with each key and concatenate the results, along with the hash of each message and enough message-length information to break the message back into pieces later

Enc(M1, M2, K1, K2) = Concat(Hash(M1), Hash(M2),
Length(Enc(M1, K1)), Enc(M1, K1),
Enc (M2, K2))


For decryption, say with key1, you split the cypher message up, and decrypt both halves with the same key. One of them will produce "test1" and the other will produce gobldygook (beacuse the other half was encrypted with key2). Checking the hashes, you'll confirm that "test1" was decrypted properly.

Interestingly enough, this also permits deniable encryption. If you only have one key, and simply use random data for the "encrypted second message" and a random hash, nobody can prove that there is or is not a key which decrypts the second message.

Myself, I find this sort of pattern more interesting in polyglot language problems. They're not encryption, but they're fun. For example:

(*a/*/ % #)(PostScript)/Helvetica 40 selectfont 9 400 moveto show%v"f"a0
true showpage quit%#) 2>/dev/null;echo bash;exit #*/);int main()/*>"eb"v
%a*0)unless print"perl\n"__END__*/{printf("C\n");/*>>#;"egnu">:#,_@;,,,<
*)begin writeln(*\output={\setbox0=\box255}\eject\shipout\hbox{\TeX}\end
*)('pascal');end.{*/return 0;}


That's a program which can be executed in multiple languages. In each language, it prints out the name of the language:

• C
• Pascal
• Post Script
• TeX
• Bash
• Perl
• Befunge98

There's also a fascinating example of a program on PCG which outputs a different number for each of the 65 languages that it can run in! How's that for different keys!

A simple solution is to encrypt the message with a truly random password, then encrypt the random password in as many ways as you wish and store them with the encrypted message.

Suppose you want both Bob and Alice to be able to decode your message. Your ultimate encrypted file would look like:

  (real password encrypted for Bob)
(real password encrypted for Alice)
(message encrypted with the real password)