China
Africa
Explore chapters and articles related to this topic
A Comparative Analysis of Classical Cryptography versus Quantum Cryptography for Web of Medical Things (WoMT)
Published in Aboul Ella Hassanien, Nilanjan Dey, Surekha Borra, Medical Big Data and Internet of Medical Things, 2018
K. Anitha Kumari, G. Sudha Sadasivam
Some of the concepts connected with the field are as follows: The number of elements in a finite field is called the order of ‘F’ and such order exists only if the order is a prime power pr where ‘p’ is a prime number and ‘r’ is a positive integer;The characteristic of any field can be either ‘0’ or a prime number. ‘p’ is called the characteristic of a field when adding an element ‘r’ times results in zero. A field is called a finite characteristic field or field of positive characteristic if it has a non-zero characteristic; andA multiplicative group is said to be a finite field consisting of non-zero elements. When all non-zero elements are expressed as powers of a single element, called a primitive element of the field, it is said to be cyclic. In field theory, a primitive element of a finite field Fp is a generator of the multiplicative group of the field. In other words, a ∈ Fp is called a primitive element, when all the non-zero elements of Fp can be written as ai for some positive integer.
An Introduction to Error-Correcting Codes
Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018
GF(8) can be obtained as a power of the element α. In this case, α is called a primitive element and the irreducible polynomial f(x) that defines the field is called a primitive polynomial. It can be proven that it is always the case that the multiplicative group of a finite field is cyclic, so there is always a primitive element. A convenient description of GF(8) is given in Table 1.1.
DTN Coding
Published in Aloizio Pereira da Silva, Scott Burleigh, Katia Obraczka, Delay and Disruption Tolerant Networks, 2019
Marius Feldmann, Felix Walter, Tomaso de Cola, Gianluigi Liva
Finite fields are mathematical structures containing a finite number of elements. Both addition and multiplication are defined on these structures. The results of these operations are again elements of the selected finite field. In the context of network coding, the use of finite fields guarantees that encoded messages have the same size as the original messages. This section provides an overview of finite fields. If more details about this domain are required, we recommend e.g. [177].
A Component-Position Model, Analysis and Design for Order-of-Addition Experiments
Published in Technometrics, 2021
Jian-Feng Yang, Fasheng Sun, Hongquan Xu
We need the concept of Galois fields in order to describe our next construction method for component orthogonal arrays. A Galois field (or finite field) is a field that contains a finite number of elements, on which the operations of multiplication, addition, subtraction and division are defined and satisfy the rules of arithmetic. The number of elements, called the order of a Galois field, must be a prime power. For any prime p and positive integer u, there is a unique Galois field of order pu up to isomorphism. Let be a Galois field. For a prime number p, is simply the ring of integers modulo p. For u > 1, . In other words, the elements of are polynomials with degree less than u and coefficients from GF(p). The addition of is ordinary polynomial addition with coefficients modulo p, and the multiplication is ordinary polynomial multiplication and then modulo a given irreducible polynomial of degree u. An irreducible polynomial (or primitive polynomial) is a polynomial that cannot be factored into the product of two non-constant polynomials. For a selected primitive polynomial over GF(p), see Table A.19 of Hedayat et al. (1999).
Certificateless pairing-free authentication scheme for wireless body area network in healthcare management system
Published in Journal of Medical Engineering & Technology, 2020
Philemon Kasyoka, Michael Kimwele, Shem Mbandu Angolo
In studies by Kobiltz [26] and Miller [27], they independently proposed using group of points on an elliptic curve defined over a finite field in discrete log cryptosystems. A finite field is a field with a finite number of elements also known as Galois field [28]. The security of ECC is based on the mathematical difficulty of discrete logarithm in elliptic curve fields [29] rather than the discrete logarithm in prime fields.