Construction of an Elliptic Curve over Binary Finite Fields to combine with LDPC Code in Mobile Communication
نویسندگان
چکیده
In this paper we propose the construction of an efficient cryptographic system, based on the combination of the ElGamal Elliptic Curve Algorithm and Low Density Parity Check (LDPC) codes for mobile communication. When using elliptic curves and codes for cryptography it is necessary to construct elliptic curves with a given or known number of points over a given finite field, in order to represent the input alphabet. In this paper we develop algorithms to construct efficient elliptic curves over binary finite field for combination with LDPC codes. A list of the suitable elliptic curves and the study of time to construction elliptic curves is presented.
منابع مشابه
Efficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملA Simple Architectural Enhancement for Fast and Flexible Elliptic Curve Cryptography over Binary Finite Fields GF(2m)
Mobile and wireless devices like cell phones and networkenhanced PDAs have become increasingly popular in recent years. The security of data transmitted via these devices is a topic of growing importance and methods of public-key cryptography are able to satisfy this need. Elliptic curve cryptography (ECC) is especially attractive for devices which have restrictions in terms of computing power ...
متن کاملConstruction of Full-Diversity LDPC Lattices for Block-Fading Channels
LDPC lattices were the first family of lattices which have an efficient decoding algorithm in high dimensions over an AWGN channel. Considering Construction D’ of lattices with one binary LDPC code as underlying code gives the well known Construction A LDPC lattices or 1-level LDPC lattices. Block-fading channel (BF) is a useful model for various wireless communication channels in both indoor a...
متن کاملUpper Bounds on the Rate of Ramdomly Constructed LDPC Codes for a Class of Markov Channels
We consider a class of finite-state Markov channels, in which channel behaves as a Binary Symmetric Channel (BSC) in each state. We find upper bounds on the rate of LDPC codes for reliable communication over this class of Markov channels. However, the results hold only for the construction of LDPC codes in which a code is selected randomly from a given ensemble of codes.
متن کاملAnalysis of Error Floors for Non-binary LDPC Codes over General Linear Group through q-Ary Memoryless Symmetric Channels
In this paper, we compare the decoding error rates in the error floors for non-binary low-density parity-check (LDPC) codes over general linear groups with those for non-binary LDPC codes over finite fields transmitted through the q-ary memoryless symmetric channels under belief propagation decoding. To analyze non-binary LDPC codes defined over both the general linear group GL(m, F2) and the f...
متن کامل