Identifying An Encryption Algorithm

Question

Hello everybody, and thanks for your help. First off, I would like to ask if any of you know of an encryption algorithm that uses a key to encrypt the data, but no key to decrypt the data. This seems highly unlikely, if not impossible to me, so sorry if it's a stupid question. My final question is, say you have access to the plain text data before it is encrypted, the key used to encrypt the plain text data, and the resulting encrypted data, would figuring out which algorithm used to encrypt the data be feasible?

Answer 1

I don't believe that there is such an algorithm that would use a key to encrypt, but not to decrypt. (Silly answers like a 26 character Caesar cipher aside...)

To your second question, yes; it just depends on how much time you're willing to spend on it. In theoretical cryptography it is assumed that the algorithm can always be determined. Whether that be through theft of the algorithm or a physical machine, or as in your case having a plain text and cipher text pair.

Answer 2

First off, I would like to ask if any of you know of an encryption algorithm that uses a key to encrypt the data, but no key to decrypt the data.

No. There are algorithms that use a different key to decrypt than to encrypt, but a keyless method would rely on secrecy of the algorithm, generally regarded as a poor idea.

My final question is, say you have access to the plain text data before it is encrypted, the key used to encrypt the plain text data, and the resulting encrypted data, would figuring out which algorithm used to encrypt the data be feasible?

Most likely yes, especially given the key. A good crypto algorithm relies on the secrecy of the key, and the key alone. See kerckhoff's principle.

Also if a common algorithm is used it would be a simple matter of trial and error, and besides cryptotext often is accompanied by metadata which tells you algorithm details.

edit: as per comments, you may be thinking of digital signature (which requires a secret only on the sender side), a hash algorithm (which requires no key but isn't encryption), or a zero-knowledge proof (which can prove knowledge of a secret without revealing it).

Answer 3

First off, I would like to ask if any of you know of an encryption algorithm that uses a key to encrypt the data, but no key to decrypt the data.

What are you getting at? It's trivial to come up with a pair of functions that fits the letter of the specification, but without knowing the intent it's hard to give a more helpful answer.

say you have access to the plain text data before it is encrypted, the key used to encrypt the plain text data, and the resulting encrypted data, would figuring out which algorithm used to encrypt the data be feasible?

If the algorithm is any good the output will be indistinguishable from random noise, so there is no analytic solution to this. As a practical matter, there are only so many trusted algorithms in wide use. Trying each one in turn would be quick, but would be complicated by the fact that an implementation has some freedom with regard to things like byte order (little-endian vs big-endian), key derivation (if you had a pass-phrase instead of the actual cryptographic key itself), encryption modes and padding.

As frankodwyer points out, this situation is not part of usual threat models. This would work in your favor, as it makes it more likely that the algorithm is a well-known one.

Answer 4

Abstractly, we can think of the encryption system this way:

               -------------------
plaintext ---> | algorithm & key | ---> ciphertext
               -------------------

The system must guarantee the following:

decrypt(encrypt(plaintext, algorithm, key), algorithm, key) = plaintext

First off, I would like to ask if any of you know of an encryption algorithm that uses a key to encrypt the data, but no key to decrypt the data.

Yes, in such a system the key is redundant; all the "secrecy" lies in the algorithm.

My final question is, say you have access to the plain text data before it is encrypted, the key used to encrypt the plain text data, and the resulting encrypted data, would figuring out which algorithm used to encrypt the data be feasible?

In practice, you'll probably have a small space of algorithms, so a simple brute-force search is feasible. However, there may be more than one algorithm that fits the given information. Consider the following example:

We define the following encryption and decryption operations, where plaintext, ciphertext, algorithm, and key are real numbers (assume algorithm is nonzero):

encrypt(plaintext, algorithm, key) = algorithm x (plaintext + key) = ciphertext

decrypt(ciphertext, algorithm, key) = ciphertext/algorithm - key = plaintext

Now, suppose that plaintext + key = 0. We have ciphertext = 0 for any choice of algorithm. Hence, we cannot deduce the algorithm used.