Page 297 - AWSAR 2.0

is a presumed difficult problem, which may take hundreds of years to factor. It is on this premise, the RSA cryptosystem is based.
My current research problem is to develop new ciphers and analyze existing ciphers while finding some weaknesses in their structures and eventually, find a way to completely break them , that is, to recover the secret key. In our lab, we study different stream ciphers and block ciphers, which differ in their modes of encryption as bit by bit and block by block, respectively. In a constrained environment, we need a cryptosystem that occupies less memory, is efficient and has a low time factor (known as lightweight cryptosystem). In order to make a block cipher more immune to attacks, a Maximum Diffusion Separable (MDS) matrix should be used. MDS matrix is one of the best examples of labyrinths of mathematics, as it drastically changes its output even on a slight change
in the input values making the
guesswork of adversary almost
impossible. Usually, these
matrix entries are from a finite
field elements. A field is a set
on which addition, subtraction,
multiplication and division are
defined, for example, the field
of real numbers and the field of
complex numbers. These are
the examples of infinite fields
but there are some finite fields
also, for example, a field with
two elements 0 and 1, known
as binary field. Note that the set
of integers is not a field, because the inverse of 2 (on the multiplication operation) is 1⁄2 and 1⁄2 doesn’t belong to the integer set but it forms a ring (not a ceremony ring, of course). The ring is different from the field in the sense that the necessary condition for the existence of inverse (w.r.t multiplication operation) of each element is relaxed.
Mr. Abhishek Kesarwani || 273
Usually, the MDS matrices over finite field majorly face two issues: high implementation cost and unavailability of involutory matrix (a matrix that is its own inverse) in some cases. MDS matrices in a block cipher are physically implemented as an electronic circuit and the implementation cost depends on the number of
Fig. 1: XOR Gate
Exclusive-OR (XOR) logic gates used (Fig. 1). Thus, decreasing the number of logic gates will reduce the implementation cost.
In our research work, we consider a set of all square matrices whose entries are from the binary field and this forms a ring, known as matrix ring. Now, here comes the climax. We found that if MDS matrices are constructed with entries from matrix ring, the output may be involutory matrices (which was not possible over
finite fields) and also the required number of XOR gates can reduce significantly. Saurabh complained, “My head is spinning?” I assured, “Don’t worry brother, we mathematicians usually generalise things this way, since the good old days.” Using this simple idea, we kill two birds with one stone. In fact, we came up with several low-XOR matrices in comparison
The growing number of EVs, will raise the demand for an orderly charging strategy.While random charging of scale electric vehicles, in time, will increase the influence of uncertain factors in power grid operation, which will bring new challenges for the economic operation of the power grid scheduling.