Related papers: A Generalization of Cyclic Code and Applications t…
We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes…
NTRU cryptosystem has allowed designing a range of cryptographic schemes due to its flexibility and efficiency. Although NTRU cryptosystem was introduced nearly two decades ago, it has not yet received any attention like designing a secret…
Group ring NTRU (GR-NTRU) provides a general structure to design different variants of NTRU-like schemes by employing different groups. Although, most of the schemes in literature are built over cyclic groups, nonabelian groups can also be…
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number…
Xinyu et al. proposed a public key exchange protocol, which is based on the NTRU-lattice based cryptography. In this paper, we show how Xinyu et al.'s NTRU-KE: A lattice based key exchange protocol can be broken, under the assumption that a…
In this paper, we have proposed a public key cryptography using recursive block matrices involving generalized Fibonacci numbers over a finite field Fp. For this, we define multinacci block matrices, a type of upper triangular matrix…
Number theoretic transform (NTT) is the most efficient method for multiplying two polynomials of high degree with integer coefficients, due to its series of advantages in terms of algorithm and implementation, and is consequently…
We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product.…
The paper presents a comprehensive study of group codes from non-abelian split metacyclic group algebras. We derive an explicit Wedderburn-like decomposition of finite split metacyclic group algebras over fields with characteristic coprime…
Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel…
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use…
This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as…
This article introduces a novel cryptographic paradigm based on nonderived polyadic algebraic structures. Traditional cryptosystems rely on binary operations within groups, rings, or fields, whose well-understood properties can be exploited…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
The cyclic code is a subclass of linear codes and has applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In 2013, Ding, et al. presented nine open…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
The punctured binary Reed-Muller code is cyclic and was generalized into the punctured generalized Reed-Muller code over $\gf(q)$ in the literature. The major objective of this paper is to present another generalization of the punctured…
We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements,…