Intan Muchtadi-Alamsyah

SKEW POLYNOMIAL RINGS WHICH ARE GENERALIZED ASANO PRIME RINGS

Let R be a prime Goldie ring with quotient ring Q and σ be an automorphism of R. We define (σ-) generalized Asano prime rings and prove that a skew polynomial ring R[x; σ] is a generalized Asano prime ring if and only if R is a σ-generalized Asano prime ring. This is done by giving explicitly the structure of all v-ideals of R[x; σ] in case R is a σ-Krull prime ring. We provide some examples of σ-generalized Asano prime rings which are not Krull prime rings.

Composite field multiplier based on look-up table for elliptic curve cryptography implementation

In this work we propose the use of composite field to implement finite field multiplication, which will be use in ECC implementation. We use 299-bit keylength and GF((213)23) is used instead of GF(2299). Composite field multiplier can be implemented using conventional multiplication operation or using LUT (Look-Up Table). In this paper, LUT is used for multiplication in ground field and Karatsuba Offman Algorithm for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE -2.

Codes over infinite family of rings : Equivalence and invariant ring

In this paper, we study codes over the ring Bk=𝔽pr[v1,…,vk]/(vi2=vi,∀i=1,…,k). For instance, we focus on two topics, i.e. characterization of the equivalent condition between two codes over Bk using a Gray map into codes over finite field 𝔽pr, and finding generators for invariant ring of Hamming weight enumerator for Euclidean self-dual codes over Bk.

ΘS-cyclic codes over Ak

ABSTRACT We study -cyclic codes over the family of rings . We characterize -cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is -cyclic then its Hermitian dual is also -cyclic. Finally, we give constructions of -cyclic codes.

A characterization of S-prime submodules of a free module over a principal ideal domain

In 2010 N. V. Sanh introduced the notion of S-prime submodules of a given right R−module and described their properties as generalization of prime ideals in an assosiative ring. Let M be a right R−module, S be the ring of endomorphisms of M and X be a fully invariant proper submodule of M. The submodule X is called an S-prime submodule of M if for any ideal I of S and any fully invariant submodule U of M, I(U)⊂X implies U⊂X or I(M)⊂X. In this paper we will characterize S-prime submodules of a free module over a principal ideal domain.

Construction of U-extension module

Given any R-module M, in this paper we show that the U-projective resolution of M always exists for any R - submodule U of M. This U-projective resolution is a generalization of ordinary projective resolution, that is when U is the zero submodule, the resolution is just the ordinary projective resolution. This resolution is unique up to U-homotopy and generates the U-extension module as the ordinary projective resolution generates the ordinary extension module. We also show that this U-extension module is unique up to isomorphism for every choice of the U-projective resolution.

Design of Connectivity Preserving Flocking Using Control Lyapunov Function

This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov function. As a result, we prove that our flocking protocol establishes group stabilization and the communication topology of multiagent flocking is always connected.

Implementation of Elliptic Curve Cryptography in Binary Field

Currently, there is a steadily increasing demand of information security, caused by a surge in information flow. There are many ways to create a secure information channel, one of which is to use cryptography. In this paper, we discuss the implementation of elliptic curves over the binary field for cryptography. We use the simplified version of the ECIES (Elliptic Curve Integrated Encryption Scheme). The ECIES encrypts a plaintext by masking the original message using specified points on the curve. The encryption process is done by separating the plaintext into blocks. Each block is then separately encrypted using the encryption scheme.

Braid group representation on quantum computation

There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.

Implementation of Pollard Rho attack on elliptic curve cryptography over binary fields

Elliptic Curve Cryptography (ECC) is a public key cryptosystem with a security level determined by discrete logarithm problem called Elliptic Curve Discrete Logarithm Problem (ECDLP). John M. Pollard proposed an algorithm for discrete logarithm problem based on Monte Carlo method and known as Pollard Rho algorithm. The best current brute-force attack for ECC is Pollard Rho algorithm. In this research we implement modified Pollard Rho algorithm on ECC over GF (241). As the result, the runtime of Pollard Rho algorithm increases exponentially with the increase of the ECC key length. This work also presents the estimated runtime of Pollard Rho attack on ECC over longer bits.