Tensor-based trapdoors for CVP and their application to public key cryptography

We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme

A New Lattice-Based Cryptosystem Mixed with a Knapsack

In this paper, we present a new lattice-based public-key cryptosystem mixed with a knapsack, which has reasonable key size and quick encryption and decryption. The module strategy in our cryptosystem can also be used to construct a framework for some GGH-type cryptosystems to improve their security

Accelerating lattice reduction with FPGAs

International audienceWe describe an FPGA accelerator for the Kannan­–Fincke­–Pohst enumeration algorithm (KFP) solving the Shortest Lattice Vector Problem (SVP). This is the first FPGA implementation of KFP specifically targeting cryptographically relevant dimensions. In order to optimize this implementation, we theoretically and experimentally study several facets of KFP, including its efficient parallelization and its underlying arithmetic. Our FPGA accelerator can be used for both solving stand-alone instances of SVP (within a hybrid CPU­–FPGA compound) or myriads of smaller dimensional SVP instances arising in a BKZ-type algorithm. For devices of comparable costs, our FPGA implementation is faster than a multi-core CPU implementation by a factor around 2.12

The Impact of Quantum Computing on Present Cryptography

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 and Grover's), public key encryption schemes affected, symmetric schemes affected, the impact on hash functions, and post quantum cryptography. Specifically, the section of Post-Quantum Cryptography deals with different quantum key distribution methods and mathematicalbased solutions, such as the BB84 protocol, lattice-based cryptography, multivariate-based cryptography, hash-based signatures and code-based cryptography.Comment: 10 pages, 1 figure, 3 tables, journal article - IJACS

Will quantum computers be the end of public key encryption?

The emergence of practical quantum computers poses a significant threat to the most popular public key cryptographic schemes in current use. While we know that the well-understood algorithms for factoring large composites and solving the discrete logarithm problem run at best in superpolynomial time on conventional computers, new, less well understood algorithms run in polynomial time on certain quantum computer architectures. Many appear to be heralding this next step in computing as ‘the end of public key encryption’. We argue that this is not the case and that there are many fields of mathematics that can be used for creating ‘quantum resistant’ cryptographic schemes. We present a high-level review of the threat posed by quantum computers, using RSA and Shor’s algorithm as an example but we explain why we feel that the range of quantum algorithms that pose a threat to public key encryption schemes is likely to be limited in future. We discuss some of the other schemes that we believe could form the basis for public key encryption schemes, some of which could enter widespread use in the very near future, and indicate why some are more likely to be adopted