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.

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. A. Ometov, V. Petrov, S. Andreev, and Y. Koucheryavy are with Tampere University of Technology, Finland. A. Ometov and Y. Koucheryavy are also

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The authors would like to acknowledge Enecuum community support in the testing of the developed system.

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.

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann-Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes.We define syndromes and formulate a Key Equation that allows an efficient decoding up to our bound with the Extended Euclidean Algorithm. It turns out that lowest-code-rate cyclic codes with small minimum distances are useful for our approach. Therefore, we give a sufficient condition for binary cyclic codes of arbitrary length to have minimum distance two or three and lowest code-rate.

Abstract-A new lower bound on the minimum distance of qary cyclic codes is proposed. This bound improves upon the BoseChaudhuri-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.

Abstract-It is shown that subclasses of separable binary Goppa codes , Γ(L, G) -codes, with L = {α ∈ GF (2 2l ) : G(α) = 0} and special Goppa polynomials G(x) can be presented as a chain of embedded codes. The true minimal distance has been obtained for all codes of the chain.