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I am studying elliptic curves problems, which also includes study of related protocols such as ECIES. A there is a problem I don't understand operation $||$. What this operation mean?

Some stuff is mentioned on Wikipedia's Integration Encryption Scheme article, but this algoritm is better explain in book Guide to Elliptic Curves. This operation is mentioned in Alice's 3rd step:

$$ k_E || k_M = \operatorname{KDF}(S || S_1) $$

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up vote 4 down vote accepted

In terms of algorithms, it usually means concatenate - as in, join two binary (or otherwise defined) strings together (in this order). For wikipedia's cryptography articles that's nearly always the case.

When it is on the left side of an assignment, this means split the string from the right side into these component strings. This makes only sense if the length of most components is already fixed, of course – like here for the encryption and MAC keys.

In terms of programming languages such as C, however, it means logical or. Whilst it is unlikely the authors have confused them, it is something to be aware of.

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Thanks, I know what it means in programming but in this context I have not seen it before , so If I understand it correctly, it works as simple join of Ke and Km? –  eXPi May 16 '12 at 10:26
    
@eXPi yep. It also means, in this case, that the output of the KDF is split into two parts - one part for each key. –  Ninefingers May 16 '12 at 10:30
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