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We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q-matrices, and prove that it preserves the original error correction properties of the encryption.…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
One of the most important consideration techniques when one want to solve the protecting of digital signal is the golden matrix. The golden matrices can be used for creation of a new kind of cryptography called the golden cryptography. Many…
Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes…
Coding/decoding algorithms are of great importance to help in improving information security since information security is a more significiant problem in recent years. In this paper we introduce two new coding/decoding algorithms using…
In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further,…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
A system is offered for imitation resistant transmitting of encrypted information in wireless communication networks on the basis of redundant residue polynomial codes. The particular feature of this solution is complexing of methods for…
An innovative strategy to enhance the security of symmetric substitution ciphers is presented, through the implementation of a randomized key matrix suitable for various file formats, including but not limited to binary and text files.…
A novel cryptography method based on the Lorenz's attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
Post-quantum cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP).…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued…
We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…
Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in…
We present a novel approach to post-quantum cryptography that employs directed-graph decryption of noise-enhanced high-memory convolutional codes. The proposed construction generates random-like generator matrices that effectively conceal…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…