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.


Here the 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 the KeyGen algorithm. TagGen has to compute tags for blocks of the file $M$. I am stuck with how the data tags are computed here.

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    $\begingroup$ Wikipedia: Multiplication - Capital Pi notation $\endgroup$ Jan 26, 2014 at 16:27
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    $\begingroup$ @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. $\endgroup$ Jan 26, 2014 at 20:19
  • $\begingroup$ @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. $\endgroup$
    – JMCF125
    Jan 26, 2014 at 20:24

2 Answers 2


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


It's the notation for the Encryption scheme in use, consisting key generation, decryption and encryption algorithms. Open form: Π = (Gen,Enc,Dec)

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    $\begingroup$ It can be "notation for the Encryption scheme in use", but isn't here. $\;$ $\endgroup$
    – user991
    Nov 18, 2014 at 22:52

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