Password-less login for online access

An authentication computer configured to execute on a processor of a hardware platform to perform the following steps to allow a customer to log in to an account of the customer with a vendor that provides goods or a service:

• in response to a request to authenticate the customer based on a first phone number that is registered with the account, generate a code that encodes a uniform resource locator (URL), and then transmit the generated code to a computer of the vendor that is managing access to the account;
• examine network packets transmitted by a computer of the customer to the URL and determine a second phone number using the network packets;
• compare the first phone number to the second phone number;
• and
• based on a determination that the first phone number matches the second phone number, determine that the customer is authenticated, and then transmit a message to the computer of the vendor that the customer is permitted to log in to the account.