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

Survey on Lightweight Primitives and Protocols for RFID in Wireless Sensor Networks

The use of radio frequency identification (RFID) technologies is becoming widespread in all kind of wireless network-based applications. As expected, applications based on sensor networks, ad-hoc or mobile ad hoc networks (MANETs) can be highly benefited from the adoption of RFID solutions. There is a strong need to employ lightweight cryptographic primitives for many security applications because of the tight cost and constrained resource requirement of sensor based networks. This paper mainly focuses on the security analysis of lightweight protocols and algorithms proposed for the security of RFID systems. A large number of research solutions have been proposed to implement lightweight cryptographic primitives and protocols in sensor and RFID integration based resource constraint networks. In this work, an overview of the currently discussed lightweight primitives and their attributes has been done. These primitives and protocols have been compared based on gate equivalents (GEs), power, technology, strengths, weaknesses and attacks. Further, an integration of primitives and protocols is compared with the possibilities of their applications in practical scenarios

Decoding by Embedding: Correct Decoding Radius and DMT Optimality

The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's \emph{embedding technique} is a powerful technique for solving the approximate CVP, yet its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a \emph{bounded distance decoding} (BDD) viewpoint. We present two complementary analyses of the embedding technique: We establish a reduction from BDD to Hermite SVP (via unique SVP), which can be used along with any Hermite SVP solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL) algorithm), and show that, in the special case of LLL, it performs at least as well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis helps to explain the folklore practical observation that unique SVP is easier than standard approximate SVP. It is proven that when the LLL algorithm is employed, the embedding technique can solve the CVP provided that the noise norm is smaller than a decoding radius $\lambda_1/(2\gamma)$, where $\lambda_1$ is the minimum distance of the lattice, and $\gamma \approx O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $\gamma \approx {O}(2^{n})$. Focusing on the applications of BDD to decoding of multiple-input multiple-output (MIMO) systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT), and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.Comment: To appear in IEEE Transactions on Information Theor