Efficient implementation of arithmetic in finite fields is of primary importance for cryptography, coding theory, digital signal processing etc. (see, for example [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]). In this survey we consider only Boolean circuits for arithmetic operations in finite fields. Another term: bit-parallel circuits. Boolean circuits for multiplication and inversion in finite fields are...

The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.

Many lattice cryptographic primitives require an efficient algorithm to sample lattice points according to some Gaussian distribution. All algorithms known for this task require long-integer arithmetic at some point, which may be problematic in practice. We study how much lattice sampling can be sped up using floating-point arithmetic. First, we show that a direct floating-point implementation ...

Finite fields are widely used in constructing error-correcting codes and cryptographic algorithms. In practice, error-correcting codes use small finite fields to achieve high-throughput encoding and decoding. Conversely, cryptographic systems employ considerably larger finite fields to achieve high levels of security. We focus on developing efficient software implementations of arithmetic opera...

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

The Lenstra-Lenstra-Lovász lattice basis reduction algorithm (LLL or L) is a very popular tool in public-key cryptanalysis and in many other fields. Given an integer d-dimensional lattice basis with vectors of norm less than B in an n-dimensional space, L outputs a socalled L-reduced basis in polynomial time O(dn log B), using arithmetic operations on integers of bit-length O(d log B). This wor...

Abu Ali Hossein Ebn Abdullah Ben Ali Ben Sinna entitled as Shayhk-o-Rayeis in the East and well known in the west by the name of Avicenna was born in a place called Afsharneh near the city of Bokhara in 980 AD but resided in the city of Balkh. He was five years old when his father took him to the city of Bokhara to study Holy Quran where his extraordinary memory became apparent and he memorized...

Abu Ali Hossein Ebn Abdullah Ben Ali Ben Sinna entitled as Shayhk-o-Rayeis in the East and well known in the west by the name of Avicenna was born in a place called Afsharneh near the city of Bokhara in 980 AD but resided in the city of Balkh. He was five years old when his father took him to the city of Bokhara to study Holy Quran where his extraordinary memory became apparent and he memorized...