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.


$c = (U,V)$ 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.

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    $\begingroup$ It would be nice to include the meaning of the tuple and the parts into the answer. $\endgroup$ – Maarten Bodewes Feb 15 '16 at 9:10
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    $\begingroup$ @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. $\endgroup$ – fkraiem Feb 15 '16 at 9:45
  • $\begingroup$ 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. $\endgroup$ – 3isenHeim Feb 15 '16 at 10:00
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    $\begingroup$ @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. $\endgroup$ – cygnusv Feb 15 '16 at 10:12
  • $\begingroup$ 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) $\endgroup$ – Hilder Vitor Lima Pereira Feb 15 '16 at 10:53

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