Cryptography Stack Exchange is a question and answer site for software developers, mathematicians and others interested in cryptography. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've see in several places (here or there) the notation $c = (U, V)$ or $c =\langle U, V \rangle$, where $c$ is a ciphertext (to be transmitted).

But as both $U$ and $V$ are "key-like". I can't find if the key to be used on the other is $U$ or $V$.

From the context, I guessed it means "Encrypt $V$ with $U$ (ie the key) to produce $c$".

Can anyone confirm me this ? They are quite commons notations, but I can't find their meaning.

share|improve this question
up vote 6 down vote accepted

$c = (U,V)$ means that the ciphertext is actually a tuple, made of two parts, $U$ and $V$. It is very common to have ciphertexts that are actually tuples of elements. In this particular case, this scheme is reminiscent to Hashed ElGamal, where ciphertexts are composed of two parts: $U$, which essentially encodes the randomness used, and $V$, which contains the message XORed with a hashed value.

Apart from that, note that, in general, a ciphertext never includes the key...otherwise, they would be trivially decrypted. The key or keys needed for decryption are separate values, and must be kept secret by the intended recipient of the ciphertext.

share|improve this answer
It would be nice to include the meaning of the tuple and the parts into the answer. – Maarten Bodewes Feb 15 at 9:10
@MaartenBodewes "the meaning of the tuple and the parts" is system-dependent; as I understand the question was only about notation, with specific systems provided only as examples. – fkraiem Feb 15 at 9:45
Here, in the case, the tuple consists only of 2 elements. Are they simply concatenated ? I can't find anything on the web speaking of the elaboration of the tuples. – EisenHeim Feb 15 at 10:00
@EisenHeim It depends on the level of abstraction in which you are working. You have to distinguish between the "mathematical" description of the scheme, which is usually very abstract, and the implementation level. In the mathematical description, tuples are an abstraction that contains a sequence of elements, and you don't care about how is it done. In the implementation level, however, you do have to think how are you going to represent the tuple; in this case, concatenation is an option. – cygnusv Feb 15 at 10:12
Well, just saying, the mathematicians care about how an ordered pair is done and it is usually defined as $(a, b) = \{\{a\},\{a, b\}\}$ XD (but sure, I think it is already off-topic and your answer is good enough @cygnusv) – Vitor Feb 15 at 10:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.