In the [16] has been proven that the multiplicative group Z/pZ∗ is a cyclic group. Likewise, finite subgroup of the multiplicative group of a field is a cyclic group. However, finite subgroup of the multiplicative group of a field being a cyclic group has not yet been proven. Therefore, it is of importance to prove that finite subgroup of the multiplicative group of a field is a cyclic group. M...

<p style='text-indent:20px;'>Elliptic curve cryptography is based upon elliptic curves defined over finite fields. Operations such require arithmetic the underlying field. In particular, fast implementations of multiplication and squaring field are required for performing efficient cryptography. The present work considers problem obtaining algorithms squaring. From a theoretical point vie...

In this paper we report the development of TWISTER [3][8] (Telexistence Wide-angle Immersive STEReoscope), which realize the concept of “Mutual Telexistence”. In contrast to conventional telexistence, where people in remote places can be appeared with a realistic sense of presence, in mutual telexistence, the figure of the observer him/herself can be displayed to remote users and all of the use...

In this paper, we study the symmetric and generating functions for odd even terms of second-order linear recurrence sequences. introduce a operator in order to derive new family Mersenne numbers, Lucas (p,q)- Fibonacci-like k-Pell polynomials polynomials. By making use defined give some products (p,q)-Fibonacci-like numbers with certain

Abstract The paper is concerned with the old conjecture that there are infinitely many Mersenne primes. It shown in work this true standard model of arithmetic. proof refers to general approach first–order logic based on Rasiowa-Sikorski Lemma and derived notion a Rasiowa–Sikorski set. This was developed papers [2–4]. companion piece [4].

We propose a new post-quantum key exchange algorithm based on the module learning with errors (mLWE) problem. Our ThreeBears algorithm is simple and performant, but our main goal is to suggest mLWE over a generalized Mersenne field instead of a polynomial ring. We also show how to build a public-key encryption system from the key exchange algorithm.

This contribution describes a methodology used to efficiently implement elliptic curves (EC) over GF (p) on the 16-bit TI MSP430x33x family of low-cost microcontrollers. We show that it is possible to implement EC cryptosystems in highly constrained embedded systems and still obtain acceptable performance at low cost. We modified the EC point addition and doubling formulae to reduce the number ...