Private key

ECC is based on domain parameters defined by various standards. You can see the list of all available standards defined and recommended curves available in OpenSSL using the following command. (Once again, only partial output is shown here, and it is truncated in the middle.):

$ 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
secp521r1 : NIST/SECG curve over a 521 bit prime field
prime192v1: NIST/X9.62/SECG curve over a 192 bit prime field
 .
 .
 .
 .
brainpoolP384r1: RFC 5639 curve over a 384 bit prime field 
brainpoolP384t1: RFC 5639 curve over a 384 bit prime field 
brainpoolP512r1: RFC 5639 curve over a 512 bit prime field 
brainpoolP512t1: RFC 5639 curve over a 512 bit prime field  

In the following example, secp256k1 is employed to demonstrate ECC usage.