Related papers: A public key cryptography using multinacci block m…
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine…
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and…
In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…
In this paper, we define and discuss {\phi}-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key encryption schemes, one is McEliece and Niederriter's…
Due to the weakness of public key cryptosystems encounter of quantum computers, the need to provide a solution was emerged. The McEliece cryptosystem and its security equivalent, the Niederreiter cryptosystem, which are based on Goppa…
We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new…
Two different kinds of synchronization have been applied to cryptography: Synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the…
Like all of quantum information theory, quantum cryptography is traditionally based on two level quantum systems. In this letter, a new protocol for quantum key distribution based on higher dimensional systems is presented. An experimental…
Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential…
In this paper, we have studied on adapting to asymmetric cryptography power Fibonacci sequence module m . To do this, We have restructed Discreate Logarithm Problem which is one of mathematical difficult problems by using power Fibonacci…
In this study, a collocation method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. Some illustrative examples are given to verify the efficiency and…
With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers…
In this paper we introduce a rank $2$ lattice over a polynomial ring arising from the public key of the BIKE cryptosystem. The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of…
Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The…
This paper presents a novel post-quantum cryptosystem based on high-memory masked convolutional codes. Unlike conventional code-based schemes that rely on block codes with fixed dimensions and limited error-correction capability, our…
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of…
A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then we use polyadic techniques…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…