This article explains how to encrypt large files with OpenSSL and Public/Private keys.
Create your key-pair:
openssl req -x509 -nodes -newkey rsa:2048 -keyout private.pem -out public_nopass.pem
Encrypt your larger file:
openssl smime -encrypt -aes256 -in bigfile.tar -binary -outform DEM -out bigfile.tar.ssl public.pem
Decrypt your file:
openssl smime -decrypt -in bigfile.tar.ssl -binary -inform DEM -inkey privatekey.pem -out bigfile.tar
At this stage you’ve been able to create your key-pair, encrypt and decrypt files.