In the last thirty years cryptographic research laid the foundations for facing security problems whose solutions impact our daily life. A prominent example of the high influence of this research is the possibility of achieving secure connections in the Internet using SSL or IPSEC.

The IT field, however, rapidly evolves and poses new security challenges in which traditional cryptographic tools (such as public key encryption and digital signatures) do not properly fit. Notably, we witness the rise of cloud computing, a paradigm in which clients or businesses lease computing and storage services from powerful entities usually referred to as “cloud providers”. While cloud computing is predicted to be “the future”, many security questions are still left unanswered: how to ensure that the cloud computes what it should? How to guarantee the confidentiality of the outsourced data?

Motivated by these questions, I will discuss recent advances in the design of cryptographic primitives that will help securing cloud computing. More specifically, I will focus on the problem of delegating computations on outsourced data. At a high level, this problem involves a client who outsources its data to the cloud, and later wants to delegate computations on such data while being able to verify the correctness of the result. I will show how standard primitives such as digital signatures and message authentication codes fall short of the requirements of this setting. Nevertheless, I will describe how homomorphic versions of these cryptographic tools can elegantly solve the problem. I will then present the notions of homomorphic digital signature and message authentication, and will finally discuss their efficient realizations as well as future challenges in this area.

During the presentation I will also highlight how the interplay of foundational research and practical applications has a significant role in this research activity.