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ECC stands for Elliptic Curve Cryptography. Elliptic curves are a mathematical structure which allow to define cryptographic operations on them.

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Generating ECDSA certificate and private key in one step

This seemed to be the command you want: openssl req -new -x509 -nodes -newkey ec:<(openssl ecparam -name secp384r1) -keyout cert.key -out cert.crt -days 3650
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