Lattice-based approaches are emerging as a common theme in modern cryptography and coding theory. In communications, they are useful mathematical tools to construct powerful error-correction codes achieving the capacity of wireless channels. In cryptography, they are used to building lattice-based schemes with provable security, better asymptotic efficiency, resilience against quantum attacks and new functionalities such as fully homomorphic encryption.
This meeting — on Wednesday 8 May 2019 — is aimed at connecting the two communities with a common interest in lattices. It will consist of several talks on related topics, with a format aimed at encouraging interaction.
Existing polarization theories (including channel polarization and source polarization) have mostly been concerned with Shannon’s information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. Although Shannon’s information measures are sufficient in many communication theories, they may not be so in some other scenarios (such as cryptography). In these areas, Rényi’s information measures, as a class of more general information measures, have been widely adopted. In this talk, I will introduce the polarization phenomenon when conditional Rényi entropies are used. Based on the results, I will discuss the code design problem when Rényi divergence is used to measure the difference between the induced distribution and the target distribution, and possible applications in cryptography.
Frequently quantum cryptography is associated with information theoretic security (ITS) and specifically with ITS key expansion. However, this is a very limited view. In reality quantum protocols can offer other advantages such as better efficiency. In that setting, where the benefit from using quantum protocols comes in form of efficiency, it is meaningful to consider protocols that offer security guarantees based on computational assumptions. In this talk, after giving a brief introduction to quantum computing, I will give examples of computationally secure quantum protocols and focus on our recent work on how to enable a fully classical party to participate in quantum protocols (including delegated blind quantum computation) and why this is important. The primitive of delegated pseudo-secret random qubit generator will be introduced, and a protocol achieving this based on trapdoor one-way functions with extra properties will be given.
In this talk I delve further in the primitive PSRQG defined in the previous talk. I first give a concrete construction of the function required for the simplest construction (secure only against honest-but-curious adversaries), based on the Learning-With-Errors problem and the trapdoor function of Micciancio and Peikert. Then I will give the second protocol that is secure against malicious adversaries, giving also the intuition of the proof and the new, modified functions used.
In recent years number field lattices have collected great interest both in crypto and communication theory communities. The main reason for this is their additional algebraic structure. This algebraic structure do not only provide the lattices special properties, but also methods to analyse them and prove existence results by applying the vast theory of algebraic numbers.
The emergence of multiple antenna communication systems and related communication theory has also raised interest on lattices that are built from noncommutative fields. Just like in the case of commutative fields such lattices have rich structure and tight connections to the underlying fields.
In this talk I will discuss lattices that are constructed from noncommutative division algebras and show how some of the key properties of such lattices are defined by algebraic invariants of the corresponding division algebras. Throughout the presentation I’ll contrast these results to the corresponding ones in the commutative case.
In recent years, several hard problems from lattice theory have become popular for constructing post-quantum PKC. Besides post-quantum cryptography, lattice-problems have been used to construct homomorphic encryption schemes. Homomorphic encryption has applications in privacy-preserving cloud computing: users can upload their encrypted data in the cloud and can still perform computation on the encrypted data. While in theory, lattice-based cryptography offers wide applicability and strong security, its real deployment in a wide range of computing devices faces several challenges.
I will talk about the challenges in computing polynomial arithmetic in a ring and the computational and architectural solutions to overcome these challenges. I will describe how our post-quantum PKC scheme SABER, which is a candidate in the ongoing NIST’s post-quantum standardization event, was constructed to achieve both strong security guarantee and efficiency. I will conclude my talk by presenting a methodology for designing high-performance parallel architectures for homomorphic computing on encrypted data in the cloud.
Room: BEDSQ-1-03
11 Bedford Square
Bloomsbury
London WC1B 3RF
Everyone is welcome. Two caveats: