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While I am checking the fields of X.509 I've noticed there is field called public key parameter and its value is 05, what is the use of this field? I have searched and did not find a clear answer for that.

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Nowadays the most important use of field "key parameters" is within ECDSA certificate; the field holds an elliptic curve per RFC 5480 section 2.1.1.

Still, as of 2017, most people use RSA certificates; for these RFC 4055 section 1.2 says "the parameters field MUST contain NULL" (except the fringe RSASSA-PSS or RSAES-OAEP). Bytes 05 00 simply mean NULL in DER (and CER and BER).

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