 Hi everyone, I am Mokshaya and this is joint work with Joseph Jekyll. In our work, we can see serious security encryption schemes with proofs in a multi-user, multi-channel setting that are tied with respect to time, advantage, and memory. We start by recalling why memory is important in the concrete security analysis of schemes. Traditionally, the most commonly considered resource in concrete security analysis is computational time. Our bucket all introduced the notion of memory type reductions in crypto 17, but they advocated that on top of the reduction being tied in advantage and computational time, it should also be tied in memory. This is important in particular for memory sensitive problems, that is, problems that are easier to solve with more memory. A concrete example is the discrete logarithm problem in prime fields. Here's a memory time plot for the discrete log problem in prime fields. Each point in the plot represents the success probability of the adversary for the corresponding resources. As we can see, the problem becomes easier to solve with sufficient memory. Let us say we want a scheme to be secured against all adversaries constrained by the resources at point A. If our reduction uses significantly greater memory than A, we end up with an algorithm whose resources suffice to break the discrete log problem in finite fields. This does not yield any meaningful conclusions about the security of the scheme. If instead we have a memory type reduction for the same scale, it allows us to be secured even for a massively larger computational time. Our work was motivated by this observation and we could construct schemes for which reductions are tied in time, advantage and memory. We call such reductions TAM-Tite. Specifically, we give TAM-Tite results for PKE schemes in the CAM-DEM paradigm. The CAM-DEM construction of PKEs can be visualized as three components, the CAM, the DEM, and finally the composition. We analyze the public key components of the CAM-DEM construction in the multi-challenge, multi-user setting. And we advocate the analysis of schemes in the multi-user, multi-challenge setting as schemes get deployed across multiple users, each of whom uses the scheme multiple times. We would want that the security of the scheme does not decrypt with users or queries. The memory tightness of key encapsulation mechanisms or CAMs has been widely analyzed in literature. Hashtag Amal family of CAMs has been of specific interest. In 2017, our bucket all conjectured the memory type proofs for Hashtag Amal CAMs for impossible. In EuroCrypt 2020, Kaushal and Desero gave impossibility results and a memory lower bound for Hashtag Amal CAMs. At the same time, but Acharya gave memory tight proofs for Hashtag Amal CAMs in Asia-Crypt 2020. In our work, we unravel the facts and fallacies of these seemingly contradicting results and give proofs for Hashtag Amal CAMs that are tight, that are time tight in the multi-user, multi-challenge setting. Our contributions are the following. First, we give time tight proofs for augmented versions of various Hashtag Amal CAMs in the multi-user, multi-challenge setting. We also introduce a new Diffie-Helmin assumption for one of our proofs which we believe to may be of independent interest. Additionally, we give time tight proofs for augmented versions of the Fujisaki Okamoto transformations. Finally, we lift our results for the CAMs to time tightly prove the security of PKE schemes in the Camden paradigm. Please attend the full version of our talk and refer to the full version of our paper to see the details of our proof techniques and much more. Thank you.