Related papers: Pell hyperbolas in DLP-based cryptosystems
Lattice based encryption schemes and linear code based encryption schemes have received extensive attention in recent years since they have been considered as post-quantum candidate encryption schemes. Though LLL reduction algorithm has…
In this paper, we define a new product over $\mathbb{R}^{\infty}$, which allows us to obtain a group isomorphic to $\mathbb R^*$ with the usual product. This operation unexpectedly offers an interpretation of the R\'edei rational functions,…
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group…
We study a recursively defined two-parameter family of graphs which generalize Fibonacci cubes and Pell graphs and determine their basic structural and enumerative properties. In particular, we show that all of them are induced subgraphs of…
We describe a system, PEP3, for storage and retrieval of IP flow information in which the IP addresses are replaced by pseudonyms. Every eligible party gets its own set of pseudonyms. A single entity, the transcryptor, that is composed of…
Difficulty of calculation of discrete logarithm for any arbitrary Field is the basis for security of several popular cryptographic solutions. Pohlig-Hellman method is a popular choice to calculate discrete logarithm in finite field $F_p^*$.…
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…
Oblivious data processing has been an on and off topic for the last decade or so. It provides great opportunities for secure data management and processing, especially in the cloud. At the same time, modern computing resources seem to be…
Pregel is a popular distributed computing model for dealing with large-scale graphs. However, it can be tricky to implement graph algorithms correctly and efficiently in Pregel's vertex-centric model, especially when the algorithm has…
This paper describes how to determine the parameter values of the chaotic Lorenz system used in a two-channel cryptosystem. The geometrical properties of the Lorenz system are used firstly to reduce the parameter search space, then the…
Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly…
This article proposes a comprehensive approach to implementing encryption schemes based on the automorphism group of the Hermitian function field. We utilize a three-parameter group with logarithmic representations outside the group's…
Encrypted control employs homomorphic encryption (HE) to protect both the computation and communication stages, making it a promising approach for secure networked control systems. Most existing results pre-design a controller in the…
Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify…
In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and…
We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
Privacy is a major issue in learning from distributed data. Recently the cryptographic literature has provided several tools for this task. However, these tools either reduce the quality/accuracy of the learning algorithm---e.g., by adding…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…