Circular Security Reconsidered

The notion of circular security of pseudorandom functions (PRF) was introduced in Distance Bounding Protocols. So far, only a construction based on a random oracle model was proposed. Circular security stands between two new notions which we call Key Dependent Feedback (KDF) security and Leak security. So far, only a construction based on a random oracle was proposed. We give an algebraic construction based on a q-DDH assumpsion. We first prove that a small-domain Verifiable Random Functions (VRF) from Dodis-Yampolskiy is a circular secure PRF. We then use the extension to large-domain VRF by augmented cascading by Boneh et. al. This gives the first construction in the standard model.