Each group shares a set of access credentials. The application scenario that directly motivated this work is the following: “ In a company, employees can belong to multiple groups, such as projet teams or departments. In the workplace and at home, there may be need to manage dynamic groups of users and to share passwords and other access codes within those groups. If used as one-factor authentication, the short codes cannot be personalized because of the birthday paradox would make them easy to guess. Also, short access codes are common in doors or photocopiers. For example, third-party services may not allow creation of multiple user accounts, or the cost may lower with one shared user account. While the majority of our passwords should remain secret, sharing passwords is useful in some scenarios. Moreover, password managers enable users to select stronger and more random passwords, since they only need to memorize the master password that opens the vault. Password managers offer a solution to these issues because they store passwords in an encrypted password vault, in which the encryption key is typically derived from a master password. The main security issues in password authentication are that users tend to choose weak passwords and re-use them in multiple services. Despite the growing awareness of the security limitations of passwords, they remain the most widespread mean of user authentication.
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