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 blockchain technology is currently penetrating different areas of the modern Information and Communications Technology community. Most of the devices involved in blockchain-related processes are specially designed targeting only the mining aspect, i.e., solving the computational puzzle task. At the same time, the use of wearable and mobile devices may also become a part of eCommerce blockchain operation, especially during the on-charge time. The paper considers the possibility of using a large number of constrained devices to support the operation of the blockchain with a low impact on battery consumption. The utilization of such devices is expected to improve the system efficiency as well as to attract a more substantial number of users. This paper contributes to the body of knowledge with a survey of the main applications of blockchain for smartphones along with existing mobile blockchain projects. It also proposes a novel consensus protocol based on a combination of Proof-of-Work (PoW), Proof-of-Activity (PoA), and Proof-of-Stake (PoS) algorithms for efficient and on-the-fly utilization on resource-constrained devices. The system was deployed in a worldwide testnet with more than two thousand smartphones and compared with other projects from the user-experienced metrics perspective. The results prove that the utilization of PoA systems on a smartphone does not significantly affect the lifetime of the smartphone battery while existing methods based on PoW have a tremendous negative impact. Finally, the main open challenges and future investigation directions are outlined.

A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem bound and, for some codes, upon the Hartmann-Tzeng 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.

The subclass of cyclic Goppa codes is proposed. It is proved that this subclass contains all cyclic codes of length n|q^m±1 with generator polynomial g(x), g(αⁱ)=g(α^-j)=0, i=0,1,..., s₁, j=1,..., s₂, αⁿ=1, α ∈ GF(q^2m).