# How do I calculate number of multiplication, exponential, and pairing operations in a cryptographic algorithm (signcryption/unsigncryption)?

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 U 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.

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).
• Yes we consider all expressions that are elements of $G_1$ preceded by an element of $Z_q^*$ as requiring a scalar multiplication. Commented Aug 6, 2022 at 16:09