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In the paper Efficient and Secure Pairing-Free Certificateless Aggregate Signature Scheme for Healthcare Wireless Medical Sensor Networks, on the signature generation part (Page 5), there is an equation $Y_{2i} = [(y_2x_i + h_{2i}d_i)modq]P_{Pub} = (u_i, v_i)$. How is a group element assigned to two integers? $u_i$ is used as an integer in the following steps while $v_i$ is never used again.

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  • $\begingroup$ A recent open access sibling says of this question's paper: "([29]) devised an anonymous CLAS scheme without bilinear pairings to further reduce the computational overhead. However, ([30]) substantiated that ([29]) cannot withstand malicious MS attacks and public key replacement attacks. In addition, ([30]) proposed an improved scheme to resist the above attacks. Recently, ([31]) found that ([30]) is insecure for the reason that it cannot withstand malicious MS attacks." I wish I understood the true purpose of all this. $\endgroup$
    – fgrieu
    Apr 26, 2023 at 12:44

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Without looking behind the paywall, I assume that $Y_{2i}$ and $P_{pub}$ are elements in an elliptic curve group whose elements are represented by a pair of coordinates satisfying the elliptic curve equation. It is common practice to take the first ("$x$"-) coordinate and treat this as an integer when the curve is defined over a prime field.

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