Cumulative-Separable Codes

q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved boundaries of the minimum distance and dimension are obtained.Comment: 14 pages, 1 figur

Decoding Cyclic Codes up to a New Bound on the Minimum Distance

A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special cases of our bound. For some classes of codes the bound on the minimum distance is refined. Furthermore, a quadratic-time decoding algorithm up to this new bound is developed. The determination of the error locations is based on the Euclidean Algorithm and a modified Chien search. The error evaluation is done by solving a generalization of Forney's formula

Describing A Cyclic Code by Another Cyclic Code

A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a second cyclic code to the original one and bound its minimum distance in terms of parameters of the associated code

Challenges of Multi-Factor Authentication for Securing Advanced IoT (A-IoT) Applications

The unprecedented proliferation of smart devices together with novel communication, computing, and control technologies have paved the way for the Advanced Internet of Things~(A-IoT). This development involves new categories of capable devices, such as high-end wearables, smart vehicles, and consumer drones aiming to enable efficient and collaborative utilization within the Smart City paradigm. While massive deployments of these objects may enrich people's lives, unauthorized access to the said equipment is potentially dangerous. Hence, highly-secure human authentication mechanisms have to be designed. At the same time, human beings desire comfortable interaction with their owned devices on a daily basis, thus demanding the authentication procedures to be seamless and user-friendly, mindful of the contemporary urban dynamics. In response to these unique challenges, this work advocates for the adoption of multi-factor authentication for A-IoT, such that multiple heterogeneous methods - both well-established and emerging - are combined intelligently to grant or deny access reliably. We thus discuss the pros and cons of various solutions as well as introduce tools to combine the authentication factors, with an emphasis on challenging Smart City environments. We finally outline the open questions to shape future research efforts in this emerging field.Comment: 7 pages, 4 figures, 2 tables. The work has been accepted for publication in IEEE Network, 2019. Copyright may be transferred without notice, after which this version may no longer be accessibl

Multi-Factor Authentication: A Survey

Today, digitalization decisively penetrates all the sides of the modern society. One of the key enablers to maintain this process secure is authentication. It covers many different areas of a hyper-connected world, including online payments, communications, access right management, etc. This work sheds light on the evolution of authentication systems towards Multi-Factor Authentication (MFA) starting from Single-Factor Authentication (SFA) and through Two-Factor Authentication (2FA). Particularly, MFA is expected to be utilized for human-to-everything interactions by enabling fast, user-friendly, and reliable authentication when accessing a service. This paper surveys the already available and emerging sensors (factor providers) that allow for authenticating a user with the system directly or by involving the cloud. The corresponding challenges from the user as well as the service provider perspective are also reviewed. The MFA system based on reversed Lagrange polynomial within Shamir’s Secret Sharing (SSS) scheme is further proposed to enable more flexible authentication. This solution covers the cases of authenticating the user even if some of the factors are mismatched or absent. Our framework allows for qualifying the missing factors by authenticating the user without disclosing sensitive biometric data to the verification entity. Finally, a vision of the future trends in MFA is discussed.Peer reviewe

Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes

Two generalizations of the Hartmann-Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved. Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them

Joint safety and security analysis for complex systems

The problem of joint safety and security analysis is considered. For complex systems method of fault tree analysis for safety and security is proposed. The effectiveness of new approach of joint safety and security analysis is shown on example of the European Railway Traffic Management System (ERTMS)

Efficient decoding of some classes of binary cyclic codes beyond the Hartmann-Tzeng bound

International audienceA new bound on the distance of binary cyclic codes is proposed. The approach is based on the representation of a subset of the roots of the generator polynomial by a rational function. A new bound on the minimum distance is proven and several classes of binary cyclic codes are identified. For some classes of codes, this bound is better than the known bounds (e.g. BCH or Hartmann-Tzeng bound). Furthermore, a quadratic-time decoding algorithm up to this new bound is developed

McEliece in the world of Escher

We present a new family of linear binary codes of length n and dimension k accompanied with a fast list decoding algorithm that can correct up to n/2 errors in a bounded channel with an error density $\rho$. The decisional problem of decoding random codes using these generalized error sets is NP-complete. Next we use the properties of these codes to design both an encryption scheme and a signature scheme. Although in the open literature there have been several proposals how to produce digital signatures from the McEliece public key scheme, as far as we know, this is the first public key scheme based on codes where signatures are produced in a straightforward manner from the decryption procedure of the scheme. The security analysis of our scheme have four parts: 1. An extensive list of attacks using the Information Set Decoding techniques adopted for our codes; 2. An analysis of the cost of a distinguishing attack based on rank attacks on the generator matrix of the code or on its dual code; 3. An analysis of the cost of cheap distinguishing attacks on the generator matrix of the code or on its dual code that have expensive list-decoding properties; 4. We interpret our scheme as multivariate quadratic system and discuss difficulties of solving that system using algebraic approaches such as Gröbner bases. Based on this security analysis we suggest some concrete parameters for the security levels in the range of $2^{80} - 2^{128}$. An additional feature of the decryption process is that it admits massive and trivial parallelization that could potentially make our scheme in hardware as fast as the symmetric crypto primitives