An inner product space-based hierarchical key assignment/access control scheme is presented in this work. The proposed scheme can be utilized in any cloud delivery model where the data controller implements a hierarchical access control policy. In other words, the scheme adjusts any hierarchical access control policy to a digital medium. The scheme is based on inner product spaces and the method of orthogonal projection. While distributing a basis for each class by the data controller, the

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... to-right and bottom-up policy can ensure much more flexibility and efficiency, especially during any change in the structure. For each class, the secret keys can be derived only when a predetermined subspace is available. The parent class can obtain the keys of the child class, which means a one-way function, and the opposite direction is not allowed. Our scheme is collusion attack and privilege creep problem resistant, as well as key recovery and indistinguishability secure. The performance analysis shows that the data storage overhead is much more tolerable than other schemes in the literature. In addition, the other advantage of our scheme over many others in the literature is that it needs only one operation for the derivation of the key of child classes.