2
$\begingroup$

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 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.

$\endgroup$
3
  • 6
    $\begingroup$ Wikipedia: Multiplication - Capital Pi notation $\endgroup$ Jan 26, 2014 at 16:27
  • 1
    $\begingroup$ @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

14
$\begingroup$

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

$\endgroup$
1
$\begingroup$

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

$\endgroup$
1
  • 2
    $\begingroup$ It can be "notation for the Encryption scheme in use", but isn't here. $\;$ $\endgroup$
    – user991
    Nov 18, 2014 at 22:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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