It is known that the development of quantum computers will break the cryptographic schemes that are in use today. Since Shor’s algorithm is able to solve the factoring and discrete logarithm problems, all cryptographic systems based on these two problems will get broken in the presence of large-scale quantum computers. Lattice-based schemes, however, are considered secure against attacks with t...

The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present cryptographic schemes (symmetric and asymmetric), differences between quantum and classical computing, challenges in quantum computing, quantum algorithms (Shor’s ...

Although lattice-based cryptography has proven to be a particularly efficient approach to post-quantum cryptography, its security against side-channel attacks is still a very open topic. There already exist some first works that use masking to achieve DPA security. However, for public-key primitives SPA attacks that use just a single trace are also highly relevant. For lattice-based cryptograph...

Although rather recent, lattice-based cryptography has stood out on numer-ous points, be it by the variety of constructions that it allows, by its expectedresistance to quantum computers, of by its efficiency when instantiated on someclasses of lattices.One of the most powerful tools of lattice-based cryptography is Gaussiansampling. At a high level, it allows to prove the k...

W e provide a brief history and overview of lattice based cryptography and cryptanalysis: shortest vector problems, closest vector problems, subset sum problem and knapsack systems, GGH, Ajtai-Dwork and NTRU. A detailed discussion of the algorithms NTRUEncrypt and NTRUSign follows. These algorithms have attractive operating speed and keysize and are based on hard problems that are seemingly int...

Lattice-based cryptography has been received significant attention in the past decade. It has attractive properties such as being a major post-quantum cryptography candidate, enjoying worst-case to average-case security reductions, and being supported by efficient implementations. In recent years, lattice-based schemes have achieved enough maturity to become interesting also for the industry. A...

New research allows construction of SNARK’s from lattice-based primitives, instead of pairings-based cryptography [BISW17]. We implement a proposed construction in libsnark, a popular existing zkSNARK library, using a quadratic arithmetic program representation and a ’crypto compiler’ based on an extension of standard Regev encryption [Reg05] into a linear-only vector encryption scheme [PVW08]....

The emerging technologies for large scale data analysis raise new challenges to the security and privacy of sensitive user data. In this work we investigate the problem of private statistical analysis of time-series data in the distributed and semi-honest setting. In particular, we study some properties of Private Stream Aggregation (PSA), first introduced by Shi et al. 2011. This is a computat...