First, the private key is generated using the following commands:

$ openssl ecparam -genkey -name secp256k1 -noout -out eccprivatekey.pem
$ cat eccprivatekey.pem
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIMVmyrnEDOs7SYxS/AbXoIwqZqJ+gND9Z2/nQyzcpaPBoAcGBSuBBAAK oUQDQgAEEKKS4E4+TATIeBX8o2J6PxKkjcoWrXPwNRo/k4Y/CZA4pXvlyTgH5LYm QbU0qUtPM7dAEzOsaoXmetqB+6cM+Q==
-----END EC PRIVATE KEY-----  

Next, the public key is generated from the private key:

$ openssl ec -in eccprivatekey.pem -pubout -out eccpublickey.pem 
read EC key
writing EC key
$ cat eccpublickey.pem
-----BEGIN PUBLIC KEY----- 
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAEEKKS4E4+TATIeBX8o2J6PxKkjcoWrXPw
NRo/k4Y/CZA4pXvlyTgH5LYmQbU0qUtPM7dAEzOsaoXmetqB+6cM+Q==
-----END PUBLIC KEY-----  

Now, suppose a file named testsign.txt needs to be signed and verified. This can be achieved as follows:

1. Create a test file:

      $ echo testing > testsign.txt
      $ cat testsign.txt 
      testing 

2. Run the following command to generate a signature using a private key for the testsign.txt file:

      $ openssl dgst -ecdsa-with-SHA1 -sign eccprivatekey.pem  
        testsign.txt > ecsign.bin  

3. Finally, the command for verification can be run as shown here:

      $ openssl dgst -ecdsa-with-SHA1 -verify eccpublickey.pem 
        -signature ecsign.bin testsign.txt 
      Verified OK

A certificate can also be produced by using the private key generated earlier by using the following command:

$ openssl req -new -key eccprivatekey.pem -x509 -nodes -days 365 
  -out ecccertificate.pem     

This command will produce the output similar to the one shown here. Enter the appropriate parameters to generate the certificate:

You are about to be asked to enter information that will be incorporated into your certificate request.
What you are about to enter is what is called a Distinguished Name or a DN. There are quite a few fields but you can leave some blank
For some fields there will be a default value, 
If you enter '.', the field will be left blank.
-----
Country Name (2 letter code) [AU]:GB
State or Province Name (full name) [Some-State]:Cambridge 
Locality Name (eg, city) []:Cambridge
Organization Name (eg, company) [Internet Widgits Pty Ltd]:Dr.Equinox! Organizational Unit Name (eg, section) []:NA
Common Name (e.g. server FQDN or YOUR name) []:drequinox 
Email Address []:[email protected]  

The certificate can be explored using the following command:

$ openssl x509 -in ecccertificate.pem -text -noout  

The following output shows the certificate:

There following topics in cryptography are presented because of their relevance to blockchain, or their potential use in future blockchain ecosystems.