Here is my simple script to setup shared SSH keys on Cluster. You can put this script called ssh-shared-keys.sh into /etc/skel/.bash_profile so that the new users have their keys shared between all the compute nodes.

#!/bin/bash

# Exit script on Error
set -e

# Check for SSH Directory
if [ ! -d ~/.ssh ]; then
   mkdir -p ~/.ssh/
fi


# Check for existence of passphrase
if [ ! -f ~/.ssh/id_rsa.pub ]; then
        ssh-keygen -t rsa -N "" -f ~/.ssh/id_rsa
        echo "Execute ssh-keygen --[done]"
fi

# Check for existence of authorized_keys and append the shared ssh keys
if [ ! -f ~/.ssh/authorized_keys ]; then
        touch ~/.ssh/authorized_keys
        echo "Create ~/.ssh/authorized_keys --[done]"
        chmod 700 ~/.ssh/authorized_keys
        cat ~/.ssh/id_rsa.pub >> ~/.ssh/authorized_keys
        echo "Append the public keys id_rsa into authorized keys --[done]"
        chmod 400 ~/.ssh/authorized_keys
        chmod 700 ~/.ssh/
fi

# Create user's ssh config it not exist
if [ ! -f ~/.ssh/config ]; then
        touch ~/.ssh/config
        echo "StrictHostKeyChecking no" > ~/.ssh/config
        echo "StrictHostKeyChecking no --[done]"
        chmod 644 ~/.ssh/config
fi
# Unset error on exit or it will affect after bash command :)
set +e

References:

1. Helping users to SSH without password into the Compute Nodes manually