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If we use a self-signed certificate, is ephemeral Diffie–Hellman key exchange protocol vulnerable to a man in the middle attack?

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Unless the users connecting to your site have imported your self-certificate from a trusted source, then yes, you will be vulnerable to MITM attacks. The reason for this is that an attacker could use his own self-signed certificate, and there would be no way for end users to tell that it is not the correct one.

Don't use a self-signed certificate. Teaching users to ignore the browser warnings and click through teaches them bad habits. If you don't want to spend money on a certificate, you can use a free service like Let's Encrypt. This is a CA which provides free domain validation-based certificates.

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