Many thanks, Douglas!

You helped me to sort this problem out after I had spent a week or so.

Some words to finish this topic:

My goal was to encrypt/decrypt some data with the PIV card (i.e., only the
card keeper may use the data). It can be done in the easier way:

1. PIV cards can have their Key Management Key destined to provide key
establishment during transactions.
2. If this KMK uses ECDH, I can emulate C(1;1) scheme (NIST
SP800-73-3,part2). That is:
2.1. I create and store in code my own EC public key (openssl affords to
create EC private keys and certificates with public keys included).
2.2. The card is authorized.
2.3. I call its 'General authentication' operation with KMK and this public
key.
2.4. As a result, I have the secret code. This code is suitable for AES
encryption.

Therefore, I use openssl in order to create this public key and to operate
with AES encryption.

Best regards,
Max Ushakov
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