How did you installed php7 ? What OS are you running? Are you using php-mod or php-fpm?
If you are running ubuntu and you installed using PPA, then try this
Check if mcrypt module is there:
php -m | grep mcrypt
If not then install mcrypt:
sudo apt-get install php7.0-mcrypt
Then enable the module:
Then restart php.
MCrypt is not used for password and URL key hashing but for encrypting and decrypting sensitive data such as API passwords, e.g. stored in / retrieved from the system configuration.
All MCrypt functionality is encapsulated in Varien_Crypt_Mcrypt. This class again is accessed via Mage_Core_Model_Encryption. The encryption model that should be used throughout ...
It looks like you are missing the mcrypt php extension.
I've read in various places that it's not that straight forward to install mcrypt on php 7.2.
But you can follow this tutorial on how to do it: https://www.techrepublic.com/article/how-to-install-mcrypt-for-php-7-2/
Warning : This feature was DEPRECATED in PHP 7.1.0, and REMOVED in PHP 7.2.0.
Alternatives to this feature include:
Sodium (available as of PHP 7.2.0)
You could patch the Magento code (for example via the app/local codepool) and replace the mcrypt functionality by those from PHPSecLib which offer an implementation of the functionality in pure PHP http://phpseclib.sourceforge.net/
According to Inchoo (they guys that created the Magento patch for PHP 7), the PHP 7.2 patch was created before the 184.108.40.206 version but not included.
However, Magento 220.127.116.11 will include a revised core with the PHP 7.2 patch built in.
Source: Link to github