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No, it's not a problem. What you've found is known as the square computational diffie-hellman problem(SCDH) and it can be shown that this is equivalent to the computational diffie-hellman problem(CDH). For completeness: SCDH: Given $g$ (your $G$) and $g^x$ (your $Q$), find $g^{x^2}$ (your $d_A^2G$). It is shown here that this problem is as hard as the ...


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Yes, you can use a (semi) static key pair for (Elliptic Curve) Diffie-Hellman. If you want to check for sure that you use ECDH correctly take a look at the NIST SP 56A which shows the various way that key agreement can be used. In this case you'd probably look for 6.2.2.2. Note that you should check the public keys for validity. Furthermore, this ...



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