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I was wondering if is it possible to generate EC private key:

openssl ecparam -name sect571r1 -out ecparam.pem

openssl ecparam -in ecparam.pem -genkey -noout -out eckey.pem

then generate CSR, which would tell CA to sign it normally as RSA:

openssl req -new -sha512 -key eckey.pem -nodes -out csr.csr

and give it to CA, which will sign it and make RSA certificate. Is there any way to do this? If not, is there at least some EC curve that can produce a key of 2048 bits or more? The longest I know is sect571r1.

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    I am trying to understand your requirement for 2,048 bit ECC key? There are no 2,048 bit ECC keys just like there are no 384,000 bit RSA keys. Key size =/= key strength.
    – Gerald Davis
    Jul 1, 2015 at 17:01
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    Yes, beacuse my certification authority requires >= 2048 keys.
    – Vilican
    Jul 1, 2015 at 17:04
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    Your CA requires 2048 bit RSA keys. No CA requires 2048 bit ECC keys. A blanket statement like that probably means your CA does not support ECC.
    – Gerald Davis
    Jul 1, 2015 at 17:05
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    You are right RSA key. But have you read the title: EC private key, RSA certificate.
    – Vilican
    Jul 1, 2015 at 17:09
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    There is no such thing as an RSA cert with ECC keys. That would be like saying I need a wood bench made out of metal. You can have a wood bench or a metal bench and either one is a usable bench but you can't have a wood bench made out of metal. Right?
    – Gerald Davis
    Jul 1, 2015 at 17:54

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The simple answer is no you can't have an RSA cert which has a ECC public key. By definition an RSA cert is a cert which has an RSA public key. The CA could sign your ECC cert with their RSA key but that wouldn't make it a RSA cert it would make it a ECC cert signed with an RSA key. Likewise a CA could sign a RSA cert with their ECC key but that wouldn't make it an ECC cert it would make it a RSA cert signed by a ECC key.

Do you need an RSA cert or do you just need some digital cert signed by your CA? If you must have a RSA cert why are you generating ECC keypairs? Generate an RSA keypair, a CSR and have the CA create a cert from that.

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    And is there some EC curve that can produce a key of 2048 bits or more?
    – Vilican
    Jul 1, 2015 at 17:51
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    No there are no ECC curves which produce 2,048 bit keys. No CA requires 2,048 bit ECC keys. A 512 bit ECC key is stronger than a 15,360 bit RSA key. The main advantage of ECC is the ability to use smaller keys without reducing security. 2,048 bit RSA key is roughly as secure as a 224 bit ECC key.
    – Gerald Davis
    Jul 1, 2015 at 17:55
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    The CA must verify your digital signature of the CSR. They only verify RSA signatures. You can't get them to verify an ecdsa signature by using "2048 bit ecc key". The signature verification algo is different.
    – Z.T.
    Jul 1, 2015 at 18:06
  • @Z.T. Some CA support ECDSA cert keys (and thus ECDSA signed CSRs) but there are no 2,048 bit ecc keys because that would be pointless.
    – Gerald Davis
    Jul 2, 2015 at 22:35

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