1
$\begingroup$

When the sigma functions are defined in equations (4.4) and (4.5) in FIPS PUB 180-4, the defined functions show the traditional sigma summation symbol, with limits 0 to {256} and 1 to {256}. The definitions, however, are in terms of circular right shift and XOR operations. Why is a summation symbol used here?

$\endgroup$
  • $\begingroup$ I'm reading the {256} as meaning for SHA-256 (and derivatives). $\endgroup$ – fgrieu Sep 22 at 8:41
0
$\begingroup$

It is the naming of functions and the functions are already defined - rotations (ROTR) and x-ors ($\oplus$). There are two $\Sigma$ and $\sigma$ functions for SHA-256 and SHA-512 series. And, in Greek, the $\Sigma$ is capital of $\sigma$.

The upper index represents the SHA family as 256 and 512. The sub-index, selects the function. $\Sigma_{0}^{\{256\}}$ means the first $\Sigma$ function of SHA-256 series. Note the curly braces.

Note: the functions are started to appear with SHA-2 series. It is not listed with SHA-1, the document can be seen from archive.org

$\endgroup$
  • 1
    $\begingroup$ So these indices are nothing to do with the traditional use of the sigma symbol for summation, then. $\endgroup$ – user258279 Sep 22 at 9:55
  • $\begingroup$ That is correct. $\endgroup$ – kelalaka Sep 22 at 9:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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