Validation algorithm in checkout field

First of all, you need to learn WordPress Plugin development, especially how to use WordPress Hooks: https://developer.wordpress.org/plugins/hooks/

Then, you need to learn how to implement Woocommerce specific hooks: https://docs.woocommerce.com/document/introduction-to-hooks-actions-and-filters/

Finally, use appropriate Woocommerce hook to filter & validate Personal Identification Number provided by the user according to your algorithm.

Since it’s not clear at what stage you are receiving those Personal Identification numbers, you need to check Woocommerce hook reference to find and implement appropriate hook for your use case.

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