In this guide I will update CentOS 7 native OpenSSL to version 1.1.1m.

Let’s begin.
1. Install the prerequisites.
yum -y install gcc perl-core pcre-devel zlib-devel pkcs11-helper-devel
2. Download the latest version of OpenSSL 1.x.
cd /opt
wget https://www.openssl.org/source/openssl-1.1.1m.tar.gz
3. Extract the downloaded tarball and delete the tarball after extracted (Optional).
tar -xvzf openssl-1.1.1m.tar.gz
rm -f openssl-1.1.1m.tar.gz
4. Configure the installation.
cd openssl-1.1.1m
./config –prefix=/usr –openssldir=/usr/local/ssl –libdir=lib64 shared -Wl,-rpath=/usr/lib64 -Wl,–enable-new-dtags enable-ec_nistp_64_gcc_128
5. Compile the configured installation.
make
6. Test the compiled installation.
make test
Make sure the result is PASS.

7. Install the latest version of OpenSSL 1.x.
make install
8. Verify the latest version of OpenSSL 1.x is installed.

9. Delete the configuration folder. (Optional)
cd ..
rm -rf openssl-1.1.1m