 Hello, and welcome to this talk titled Cryptographic Primitives with Hinting Property. This is based on joint work with Navi. In real life, a hint is typically something that reveals partial information about a secret such as a password without revealing the entire secret itself. Depending on their usage hints may or may not be helpful. In this talk, we focus on the constructive usage of hinting properties in the context of a fundamental and widely used cryptographic primitive called a pseudorandom generator or PRG in short. Traditionally, a PRG is an expanding function that on input a uniformly random seed outputs a pseudorandom expanded sequence of bits. However, it provides no such pseudorandomness guarantees in its traditional form if the distinguishing has some information about the seed. But what if the distinguisher did have some information about the seed? For example, what if we take the output of the PRG which in this case is a sequence of n strings y1 through yn and a sequence of uniformly random strings z1 through zn and then for each position from 1 through n, we swap yi and zi if the bit si is equal to 1. Here is a toy example for s equals 110001. Clearly, this 2 cross n matrix of n bit strings leaks some information about each bit of the seed which is encoded into the arrangement of the elements in each row. A hinting PRG introduced by Coppola and Waters in 2019 has the property that this matrix is pseudorandom even if the distinguishing has some hints about the seed. Hinting PRG's have been used as a cryptographic booster to transform CPS secure public encryption and other advanced forms of encryption into their CCS secure counterparts. In recent years, hinting PRG's have found a myriad of applications in other advanced cryptographic primitives which makes them very interesting to study. Hinting PRG's have some apparent similarities with another symmetric key primitive namely circular secure symmetric key encryption. In fact, one could view the hinting property as a deterministic form of circular security with respect to the bits of the PRG seed. However, unlike circular secure symmetric key encryption, hinting PRG's have complicated cryptographic constructions which are heavily rooted in structured mathematical assumptions. In addition, their complexity is also less understood. Here is what the current landscape of hinting PRG's looks like in terms of known ways of constructing them and of their implications. In this paper, we ask the following questions. Can we realize simpler constructions and proofs for hinting PRG's from a wider variety of assumptions including plausibly post-quantum safe isogenic based assumptions? Can we naturally extend the hinting property beyond PRG's to other cryptographic primitives? Finally, can we have a more concrete understanding of the cryptographic complexity of hinting PRG's and if they necessarily require mathematically structured public key assumptions? Our contributions are as follows. In this paper, we present new extensions of the hinting property to PRF's and weak PRF's where the pseudo-randomness properties hold in the presence of hints about the secret key across multiple evaluations of the PRF. A hinting PRF implies a hinting big PRF which in turn implies a hinting PRG. We then show stronger implications of the hinting property. In particular, a hinting weak PRF implies a full-fledged circular secure-symmetric key encryption scheme as opposed to a hinting PRG which only implies a one-time circular secure-symmetric key encryption scheme. We then show a simpler construction strategy for hinting PRG's and hinting weak PRF's from the standard DDH assumption. Our constructions are more direct and allow simpler proofs while also yielding new instantiations from plausibly quantum-safe assumptions over isogenic-based group actions. Finally, we show that publicly techniques are not inherently required to realize cryptographic limitives with the hinting property. Concretely, we show a construction of hinting PRF given just a random order. This also yields a new black box separation result between cryptographic limitives with the hinting property and public key encryption. We also introduce in the paper a new strengthening of the hinting property to a functional hinting property where the adversary can also learn hints about some function of the secret seed or the secret key. We show certain interesting implications of the functional hinting property. For example, we show that a functional hinting weak PRF with respect to some function family implies in a black box manner a KDM secure-symmetric key encryption scheme with respect to the same function family. This yields a new approach for achieving black box constructions of KDM secure encryption with respect to Boolean function families. Finally, we also show an instantiation of functional hinting weak PRFs from the DTH assumption where the construction is with respect to the function family consisting of projective quadratic functions and functions of higher degree over the bits of the secret key. For more details about our results and techniques, do tune into our talk in the first session of AsiaCream 2022. Thank you for your attention and see you at the conference.