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I am doing a project in cryptography and while reading a tag generation algorithm for files, I got stuck with the meaning of $\Pi$. The screenshot of the algorithm is inserted below.

Fig

Here KeyGen algorithm generates 1 public key and 2 secret keys and the TagGen algorithm takes a file $M$ (which is divided into $n$ blocks which is again divided into $s$ sectors) and the secret keys generated by KeyGen algorithm. TagGen has to compute tags for blocks of file $M$. I am stuck with how data tag is computed here.

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@JMCF125: I don't think that's reasonable. It is perfectly plausible that it might have a specific meaning in cryptography. To use your example, if I see the word "literally" in a newspaper it probably means "figuratively", which is of course the opposite of what it means to a linguist. Moreover, $\Pi$ is often used to denote a protocol, so its not unreasonable to check. –  figlesquidge Jan 26 at 20:19
    
@figlesquidge, as CodeInChaos points out, a quick search would solve it right away. And indeed journalists are misinformed. :) Also, I don't (didn't) see what you mean (meant) by protocol; but $\Pi$ would make no sense as a protocol in this context. –  JMCF125 Jan 26 at 20:24
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up vote 9 down vote accepted

This is standard mathematical notation and not specific to cryptography. The $\Pi$ symbol means Product in much the same sense $\Sigma$ means Sum. For instance,

$\Pi_{i=0}^2{u_i^{m_i}} = u_0^{m_0}u_1^{m_1}u_2^{m_2}$

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