Abstract: We live in technologically exciting times. The big data revolution promises technology bordering on science fiction -- personalized medicine via genome sequencing, the "internet of things" offering the potential of smart cities, smart appliances for healthcare, smart metering and many such applications. But as our technology has increased, so has our vulnerability. In the age of Wikileaks and Snowden, we worry increasingly about the security of our data and about our privacy at large. Can we enable technology while still having reasonable guarantees on security? This is a complex question and we study how cryptography can offer solutions to the demands placed by the above applications.
Broadly speaking, the challenges placed on cryptography are twofold.
Modelling: The usage scenarios in which cryptographic schemes are deployed are becoming more and more complex, hence modeling security mathematically and designing systems to achieve it is becoming increasingly harder. Even basic cryptographic objects like public key encryption and signatures face new modeling and achievability challenges.
Constructions: The functionality being asked from cryptographic objects is becoming elaborate and sophisticated, with many nontrivial generalizations of standard primitives, like encryption and signatures, being desired.
In this talk, I will discuss some recent results pertaining to both these aspects.
First, I will describe a new model of cryptographic computation, that unifies and extends existing cryptographic primitives such as Obfuscation, Functional Encryption, Fully Homomorphic Encryption, Witness encryption, Property Preserving Encryption and the like, all of which can be cleanly modeled in our framework. We provide a new definition of security that finds the sweet spot between achievability and impossibility -- implying most achievable security definitions while sidestepping the impossibilities that plague "too-strong" definitions. We also provide powerful reduction and composition theorems that yield a modular means to build and analyze complicated cryptographic objects from simpler ones.
Second, I will describe some recent work in the construction of novel encryption schemes that generalize and extend public key encryption. An attractive feature of one of our constructions is an "online-offline" property, that enables the encryptor to do a large amount of work before it receives the data, i.e. "offline", so that encryption is very efficient after data becomes available. This makes the construction suitable for streaming data applications.