1
$\begingroup$

I have been working on signcryption scheme and its security proof. I want to compute the efficiency in terms of number of scalar multiplication operation, number of exponential operations, and number of bilinear pairing operation. I am comparing it with other schemes as well. I think I am missing out some information regarding point scalar multiplication and couldn't figure how should I count the number of multiplication operation. For example if Usigncryption step in the figure below, I see only 2 multiplication operations U1=r1P2 and U2=r1QA. Is it correct? For the reference, I am looking into Heterogeneous hybrid signcryption for multimessage and multi-receiver.

$\endgroup$

1 Answer 1

1
$\begingroup$

Presumably you are working from Heterogeneous hybrid signcryption for multi-message and multi-receiver by Niu et al (it would've been useful for you to include this information). In this case the value $sk_A$ is an element of $G_1$ and so all $n$ of the operations $S_i=(r_1+h_i)sk_A$ are also scalar multiplications.

This gives a total of $n+2$ scalar multiplications in $G_1$; $2n$ pairing computations at step 2, and $2n$ exponentiations in $G_2$ (also at step 2).

$\endgroup$
3
  • $\begingroup$ Thank you for highlighting. Yes I am working from Heterogeneous hybrid signcryption for multimessage and multi-receiver by Niu et. al and have included this information now. I understand the pairing and exponentiation operations however, regarding multiplication operation, do we consider all those elements which are in G1? $\endgroup$
    – Alia
    Aug 6, 2022 at 13:59
  • $\begingroup$ Yes we consider all expressions that are elements of $G_1$ preceded by an element of $Z_q^*$ as requiring a scalar multiplication. $\endgroup$
    – Daniel S
    Aug 6, 2022 at 16:09
  • $\begingroup$ Thank you very much. $\endgroup$
    – Alia
    Aug 6, 2022 at 17:18

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.