Related papers: An Algebraic Characterization of Security of Crypt…

In this paper, we propose two cryptosystems based on group rings and existing cryptosystem. First one is Elliptic ElGamal type group ring public key cryptosystem whose security is greater than security of cryptosystems based on elliptic…

We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

Our work focuses on modeling the security of systems from their component-level designs. Towards this goal, we develop a categorical formalism to model attacker actions. Equipping the categorical formalism with algebras produces two…

Private queries allow a user Alice to learn an element of a database held by a provider Bob without revealing which element she was interested in, while limiting her information about the other elements. We propose to implement private…

A theorem is proved which states that no classical key generating protocol could ever be provably secure. Consequently, candidates for provably secure protocols must rely on some quantum effect. Theorem relies on the fact that BB84 Quantum…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

This paper quantitatively explores the social and socio-semantic patterns of constitution of academic collaboration teams. To this end, we broadly underline two critical features of social networks of knowledge-based collaboration: first,…

We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…

Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…

Increasing incidents of security compromises and privacy leakage have raised serious privacy concerns related to cyberspace. Such privacy concerns have been instrumental in the creation of several regulations and acts to restrict the…

Anonymity in networked communication is vital for many privacy-preserving tasks. Secure key distribution alone is insufficient for high-security communications, often knowing who transmits a message to whom and when must also be kept hidden…

Presentations of racks is studied and a cryptographic protocol defined on racks is proposed.

Our goal is to provide different semiring-based formal tools for the specification of security requirements: we quantitatively enhance the open-system approach, according to which a system is partially specified. Therefore, we suppose the…

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

Third-party analysis on private records is becoming increasingly important due to the widespread data collection for various analysis purposes. However, the data in its original form often contains sensitive information about individuals,…

A notion of one-dimensional formal ring is presented. It consists of a triple $(A,\Phi,\Psi)$ where $A$ is a unital ring and $\Phi$ and $\Psi$ are two formal power series in $2$ variables ${\Phi(x,y),\Psi(x,y)\in A\llbracket…

We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…

In this work we provide a suite of protocols for group key management based on general semigroup actions. Construction of the key is made in a distributed and collaborative way. Examples are provided that may in some cases enhance the…

Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…