C# - ECDSA - a common curve between OpenSSL, C# and C++ Microsoft CNG

So in the previous post we saw how to generate a ECDSA key in C#, then export its public representation to be used in another C# program. Ultimately, I'd want a Linux server probably using OpenSSL to sign licence certificates, for C# programs we use the .Net managed classes to verify hashes and for C++ programs we'd using the Microsoft CNG C++ API. I know I want to use 384-bit ECDSA and use SHA256 hash twice because this is what BitCoin uses and it would be nice to say my encryption is as strong a BitCoin (buzzword advertising!).

Here is an example of the C# export for a key, I have added line breaks

<ECDSAKeyValue xmlns="http://www.w3.org/2001/04/xmldsig-more#">
  <DomainParameters>
    <NamedCurve URN="urn:oid:1.3.132.0.34" />
  </DomainParameters>
  <PublicKey>
    <X Value="1902202729747667972037907690858726927598735515
9453131739849441348197140389889215510822928340340114265083966753527920" 
xsi:type="PrimeFieldElemType" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" />
    <Y Value="2166460856334825178504234528741952408073634514
9497343748736063144545323191375900071111148263795957487183518893659845" 
xsi:type="PrimeFieldElemType" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" />
  </PublicKey>
</ECDSAKeyValue>

So one can see the very long co-ordinate pair, X & Y but also what matters is the curve name/id. In the above export from (C#) it says Named Curve "urn:oid:1.3.132.0.34" and this tallies to secp384r1 because IBM say so here. Here is a fuller list

• NIST recommended curves
• secp192r1 – {1.2.840.10045.3.1.1}
• secp224r1 – {1.3.132.0.33}
• secp256r1 – {1.2.840.10045.3.1.7}
• secp384r1 – {1.3.132.0.34}
• secp521r1 – {1.3.132.0.35}

This matters because OpenSSL lists its curves using the text name and not the oid. Like so ...

C:\OpenSSL-Win64\bin>openssl ecparam -list_curves
  secp112r1 : SECG/WTLS curve over a 112 bit prime field
  secp112r2 : SECG curve over a 112 bit prime field
  secp128r1 : SECG curve over a 128 bit prime field
  secp128r2 : SECG curve over a 128 bit prime field
  secp160k1 : SECG curve over a 160 bit prime field
  secp160r1 : SECG curve over a 160 bit prime field
  secp160r2 : SECG/WTLS curve over a 160 bit prime field
  secp192k1 : SECG curve over a 192 bit prime field
  secp224k1 : SECG curve over a 224 bit prime field
  secp224r1 : NIST/SECG curve over a 224 bit prime field
  secp256k1 : SECG curve over a 256 bit prime field
  secp384r1 : NIST/SECG curve over a 384 bit prime field