Public Key Cryptosystem Based on Polynomial Composition (original) (raw)

A Novel Public Key Cryptosystem and Digital Signatures

European Journal of Engineering Science and Technology, 1970

In this article, we develop a new algebraic public key cryptosystem, which is based on generally non-commutative ring. Firstly, we define the polynomials over the non-commutative rings and then take it as underlying work structure. The hard problem of the scheme is the mixture of matrix discrete log problem under modular classes and polynomial symmetric decomposition problem. Using matrices of higher order and large modular classes resist the brute force and other well-known attacks exists in the literature. We also discuss the computational complexity of proposed scheme. On the other hand, we propose a signature scheme over a non-commutative division semiring. The key idea behind the signature scheme is that, for a given non-commutative division semiring, we build a polynomial and then implement digital signatures on multiplicative structure of semiring.

New Practical Algebraic Public-Key Cryptosystem and Some Related Algebraic and Computational Aspects

Applied Mathematics, 2013

The most popular present-day public-key cryptosystems are RSA and ElGamal cryptosystems. Some practical algebraic generalization of the ElGamal cryptosystem is considered-basic modular matrix cryptosystem (BMMC) over the modular matrix ring. An example of computation for an artificially small number n is presented. Some possible attacks on the cryptosystem and mathematical problems, the solution of which are necessary for implementing these attacks, are studied. For a small number n, computational time for compromising some present-day public-key cryptosystems such as RSA, ElGamal, and Rabin, is compared with the corresponding time for the ВММС. Finally, some open mathematical and computational problems are formulated.

A Note on Public Key Cryptosystems

International Journal of Advanced Networking and Applications

Public key or asymmetric cryptosystems use public-private key pair for the secure transmission of data. RSA and ECC (Elliptic Curve Cryptography/Cryptosystems) are widely used cryptosystems in this category. Public key cryptosystems rely on mathematical problems known as hard problems. The security of these cryptosystems is based on these hard problems. Public key cryptosystems solve the key transportation problem of symmetric key cryptosystems and able to provides digital signatures also.

Public Key Cryptosystem based on Matrices

International Journal of Computer Applications

In this article, a novel public key cryptosystem is introduced by using an abelian subgroup of GL(k, Z n) where n and k are positive integers. Instead of exponentiation, the conjugation automorphisms are mainly used to define the public and private keys. This allows the calculations to be fast and effective. The security analysis of the cryptosystem is discussed and it is shown that the cryptosystem is highly secure. Moreover, proposed scheme also generalizes the main scheme given in [1].

A Public Key Cryptosystem Using a Group of Permutation Polynomials

Tatra Mountains Mathematical Publications, 2020

In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field F q m. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2 k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m 3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m 2+3m – 4 left cyclic shifts, 5m 2 +3m + 4 xor operations and 7 permutations on bits for decryption.

A new cryptosystem based on elliptic curves and polynomial matrices

The system we propose is a mathematical problem with the necessary properties to define public key cryptosystems. It is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP) and polynomial matrices. In this way, we achieve to increase the possible number of keys and, therefore, we augment the resolution complexity of the system. Also, we make a cryptanalisys of the system detecting its weaknesses and verifying that, even so, it is harder to solve than the ECDLP.

Public key cryptography using Permutation P-Polynomials over Finite Fields

In this paper we propose an ecient multivariate public key cryptosystem based on per- mutation p-polynomials over finite fields. We first characterize a class of permutation p- polynomials over finite fields Fqm and then construct a trapdoor function using this class of permutation p-polynomials. The complexity of encryption in our public key cryptosystem is O(m3) multiplication which is equivalent to other multivariate public key cryptosystems. However the decryption is much faster than other multivariate public key cryptosystems. In decryption we need O(m2) left cyclic shifts and O(m2) xor operations.

Public Key Cryptosystem Based on Singular Matrix

Trends in Sciences

The algorithms such as RSA, ElGamal and ECC work on integers. Commutative operations on integer multiplication leave these algorithms vulnerable to attack by eavesdroppers. For this reason, experts develop the concept of non-commutative algebra in the public key cryptosystem by adding non-commutative properties to groups, semirings, semiring division, matrices and matrix decomposition. However, the key generating process in some public key cryptosystems is quite complicated to carry out. Therefore, in previous research, Liu used nonsingular matrices to form a simpler public key cryptosystem. However, eavesdroppers use the inverse of nonsingular matrices to construct the private key. As a result, this public key cryptosystem is still vulnerable to attacks. Therefore, we use a singular matrix to modify and build the proposed public key cryptosystem in this study. This study indicates that the singular matrix can be used to modify the public key cryptosystem. The results also show that...

Algebraic Structures in Cryptography

The combination of the set and operations that are applied on the elements of the set is called an algebraic structure. Three common algebraic structures are groups, rings and fields. In this paper we will present our research on algebraic structures in cryptography. Some results are the basis conversion between polynomial and normal basis, an identification of some weak class of elliptic curves not suitable for cryptography and an implementation of composite field in Elliptic Curve Cryptography. We will also briefly explain the use of higher algebraic structures in cryptography and coding theory.

A Public Key Cryptosystem Based on Sparse Polynomials

Springer eBooks, 2000

This paper introduces a new type of cryptosystem which is based on sparse polynomials over finite fields. We evaluate its theoretic characteristics and give some security analysis. Some prelilninary timings are presented as well, which compare quite favourably with published optimized RSA timings. We believe that similar ideas can be used in some other settings as well.