In modern network settings, secure protocols are run concurrently with other arbitrary protocols. The interaction of different protocols with each other can be exploited by malicious parties to carry out successful attacks, even if each protocol is secure when considered in isolation. The problem of constructing secure protocols in this setting (known also as "protocol composition") is currently receiving a lot of interest from the cryptography community, and much progress has been made in the last few years.

In this talk, we will discuss recent work on this topic. In particular, we will present definitions for the notion of "security under composition" in a number of variants, and will survey a series of positive and negative results that draw a rather comprehensive picture of what may and may not be securely computed under composition, and under what assumptions. We will also discuss some open questions for future research on this topic.