Elliptic Curve Cryptography (ECC) gained a lot of attention in industry. The key attraction of ECC over RSA is that it
offers equal security even for smaller bit size, thus reducing the processing complexity. ECC Encryption and Decryption methods can
only perform encrypt and decrypt operations on the curve but not on the message. This paper presents a fast mapping method based on
matrix approach for ECC, which offers high security for the encrypted message. First, the alphabetic message is mapped on to the
points on an elliptic curve. Later encode those points using Elgamal encryption method with the use of a non-singular matrix. And the
encoded message can be decrypted by Elgamal decryption technique and to get back the original message, the matrix obtained from
decoding is multiplied with the inverse of non-singular matrix. The coding is done using Verilog. The design is simulated and
synthesized using FPGA.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document discusses the implementation of Elliptic Curve Digital Signature Algorithm (ECDSA) using variable text message encryption methods. It begins with an abstract that outlines ECDSA, its advantages over other digital signature algorithms like smaller key size, and implementation of ECDSA over elliptic curves P-192 and P-256 with variable size text message, fixed size text message, and text based message encryption. It then provides details on elliptic curve cryptography, the elliptic curve discrete logarithm problem, finite fields, and domain parameters for ECDSA.
This document summarizes an academic paper presented at the International Conference on Emerging Trends in Engineering and Management in 2014. The paper proposes a design and implementation of an elliptic curve scalar multiplier on a field programmable gate array (FPGA) using the Karatsuba algorithm. It aims to reduce hardware complexity by using a polynomial basis representation of finite fields and projective coordinate representation of elliptic curves. Key mathematical concepts like finite fields, point addition, and point doubling that are important to elliptic curve cryptography are also discussed at a high level.
This presentation contains the contents pertaining to the undergraduate course on Cryptography and Network Security (UITC203) at Sri Ramakrishna Institute of Technology. This covers the Elliptic Curve Cryptography and the basis of elliptic curve arithmetics.
This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields for encryption, digital signatures, and key exchange. It provides the same security as RSA or discrete logarithm schemes but with smaller key sizes (e.g. 256-bit ECC vs. 3072-bit RSA). ECC algorithms are also faster and use less energy than other schemes. While ECC offers advantages, security relies on using cryptographically strong elliptic curves and there is no deterministic method to encode messages as curve points.
Implementation of Elliptic Curve Digital Signature Algorithm Using Variable T...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document discusses the implementation of Elliptic Curve Digital Signature Algorithm (ECDSA) using variable text message encryption methods. It begins with an abstract that outlines ECDSA, its advantages over other digital signature algorithms like smaller key size, and implementation of ECDSA over elliptic curves P-192 and P-256 with variable size text message, fixed size text message, and text based message encryption. It then provides details on elliptic curve cryptography, the elliptic curve discrete logarithm problem, finite fields, and domain parameters for ECDSA.
This document summarizes an academic paper presented at the International Conference on Emerging Trends in Engineering and Management in 2014. The paper proposes a design and implementation of an elliptic curve scalar multiplier on a field programmable gate array (FPGA) using the Karatsuba algorithm. It aims to reduce hardware complexity by using a polynomial basis representation of finite fields and projective coordinate representation of elliptic curves. Key mathematical concepts like finite fields, point addition, and point doubling that are important to elliptic curve cryptography are also discussed at a high level.
This presentation contains the contents pertaining to the undergraduate course on Cryptography and Network Security (UITC203) at Sri Ramakrishna Institute of Technology. This covers the Elliptic Curve Cryptography and the basis of elliptic curve arithmetics.
This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields for encryption, digital signatures, and key exchange. It provides the same security as RSA or discrete logarithm schemes but with smaller key sizes (e.g. 256-bit ECC vs. 3072-bit RSA). ECC algorithms are also faster and use less energy than other schemes. While ECC offers advantages, security relies on using cryptographically strong elliptic curves and there is no deterministic method to encode messages as curve points.
Implementation of Elliptic Curve Digital Signature Algorithm Using Variable T...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
A SURVEY ON ELLIPTIC CURVE DIGITAL SIGNATURE ALGORITHM AND ITS VARIANTScsandit
The Elliptic Curve Digital Signature Algorithm (ECDSA) is an elliptic curve variant of the
Digital Signature Algorithm (DSA). It gives cryptographically strong digital signatures making
use of Elliptic curve discrete logarithmic problem. It uses arithmetic with much smaller
numbers 160/256 bits instead of 1024/2048 bits in RSA and DSA and provides the same level of
security. The ECDSA was accepted in 1999 as an ANSI standard, and was accepted in 2000 as
IEEE and NIST standards. It was also accepted in 1998 as an ISO standard. Many cryptologist
have studied security aspects of ECDSA and proposed different variants. In this paper, we
discuss a detailed analysis of the original ECDSA and all its available variants in terms of the
security level and execution time of all the phases. To the best of our knowledge, this is a unique
attempt to juxtapose and compare the ECDSA with all of its variants.
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
This document provides an overview of elliptic curve cryptography (ECC). It begins with background on ECC, describing how it was independently proposed in 1985 as an approach to asymmetric cryptography. It then covers the basics of asymmetric cryptosystems and how ECC compares to RSA and Diffie-Hellman. The document goes on to explain elliptic curves over real and finite numbers, how points are added and doubled on elliptic curves, and how this relates to discrete logarithm problems. It discusses implementations of ECC for cryptography and comparisons to RSA in terms of key size and performance. Finally, it covers efficient implementations of ECC for smart cards.
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields for encryption, digital signatures, and key exchange. The key sizes are smaller than RSA for the same security level. Its security relies on the assumed hardness of solving the discrete logarithm problem over elliptic curves. ECC defines elliptic curves with parameters over Galois fields GF(p) for prime p or binary fields GF(2m). Points on the curves along with addition and doubling formulas are used to perform scalar multiplications for cryptographic operations.
Cryptography is the combination of Mathematics and Computer science. Cryptography is used for encryption and decryption of data using mathematics. Cryptography transit the information in an illegible manner such that only intended recipient will be able to decrypt the information
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields to provide public-key encryption and digital signatures. ECC requires significantly smaller key sizes than other cryptosystems like RSA to provide equivalent security. This allows for faster computations and less storage requirements, making ECC ideal for constrained environments like smartphones. ECC relies on the difficulty of solving the elliptic curve discrete logarithm problem to provide security.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Ec2203 digital electronics questions anna university by www.annaunivedu.organnaunivedu
EC2203 Digital Electronics Anna University Important Questions for 3rd Semester ECE , EC2203 Digital Electronics Important Questions, 3rd Sem Question papers,
http://www.annaunivedu.org/digital-electronics-ec-2203-previous-year-question-paper-for-3rd-sem-ece-anna-univ-question/
Data Security Using Elliptic Curve CryptographyIJCERT
Cryptography technique is used to provide data security. In existing cryptography technique the key generation takes place randomly. Key generation require shared key. If shared key is access by unauthorized user then security becomes disoriented. Hence existing problems are alleviated to give more security to data. In proposed system a algorithm called as Elliptic Curve Cryptography is used. The ECC generates the key by using the point on the curve. The ECC is used for generating the key by using point on the curve and encryption and decryption operation takes place through curve. In the proposed system the encryption and key generation process takes place rapidly.
Elliptic Curve Cryptography was presented by Ajithkumar Vyasarao. He began with an introduction to ECC, noting its advantages over RSA like smaller key sizes providing equal security. He described how ECC works using elliptic curves over real numbers and finite fields. He demonstrated point addition and scalar multiplication on curves. ECC can be used for applications like smart cards and mobile devices. For key exchange, Alice and Bob can agree on a starting point and generate secret keys by multiplying a private value with the shared point. ECC provides security through the difficulty of solving the elliptic curve discrete logarithm problem.
Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptogr...Marisa Paryasto
This document discusses implementing elliptic curve cryptography using composite fields. It proposes using a 299-bit key represented in the composite field GF((213)23) instead of the conventional GF(2299). This breaks the finite field multiplication into smaller chunks by dividing the field into a ground field and extension field. A lookup table is used for multiplication in the ground field GF(213) while a classic multiplier is used for the extension field GF(23). This composite field approach aims to provide better time and area efficiency for implementation on FPGAs compared to a single large multiplier. The document provides background on elliptic curves, finite fields, and previous work on composite field representations.
The branch-and-bound method is used to solve optimization problems by traversing a state space tree. It computes a bound at each node to determine if the node is promising. Better approaches traverse nodes breadth-first and choose the most promising node using a bounding heuristic. The traveling salesperson problem is solved using branch-and-bound by finding an initial tour, defining a bounding heuristic as the actual cost plus minimum remaining cost, and expanding promising nodes in best-first order until finding the minimal tour.
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
The document discusses Boolean algebra and logic circuits. It covers Boolean algebra, fundamental concepts like binary digits and logical operators. It discusses Boolean functions, their representation using algebraic expressions and truth tables. Methods to minimize Boolean functions by reducing literals and terms are also covered. Logic gates and how they are used to build combinational logic circuits are explained.
Improved security system using steganography and elliptic curve crypto...atanuanwesha
The main objectives of the project is to make the data safe and secure and transmit the data in such a way that it is not possible for anyone to detect the data . Steganography is concealing the secret message in non secret image. Whereas Encryption is converting data into code to prevent unauthorized access .Steganography as well as cryptography has its own disadvantage. Our objective is to implement both the procedures to enforce tight security and to prevent evesdropping etc.
Efficiency of 128-bit Encryption and Decryption Process in Elgamal Method Usi...TELKOMNIKA JOURNAL
1) The document discusses efficiency of 128-bit encryption and decryption using the Elgamal method with elliptic curve cryptography (ECC).
2) It describes how ECC can optimize encryption and decryption processes by using mathematical problems that are harder to solve than traditional cryptography methods.
3) The document outlines the process of generating a public/private key pair using ECC, and then using those keys for Elgamal encryption and decryption of plaintext data.
The document discusses the arithmetic of elliptic curves. It begins by introducing elliptic curves and their group structure under addition. It describes how points on an elliptic curve form an abelian group and that rational points form a subgroup. It then discusses points of finite order, including points of order 2 and 3. The Nagell-Lutz theorem and Mazur's theorem characterize rational points of finite order. Finally, it introduces Mordell's theorem, which states that the group of rational points on an elliptic curve is finitely generated.
This document discusses formatting bits to better implement signal processing algorithms with integer arithmetic. It begins by introducing the context and objectives, which is to develop a methodology and tools to implement embedded filter algorithms using only integer arithmetic while controlling errors. It then discusses fixed-point arithmetic and how filters can be implemented using sum-of-products operations. The objective is given a bound on the final error, to find an implementation that reduces bit usage while controlling output error. The document proposes a two-step bit formatting method that first formats the most significant bits using Jackson's rule, then determines the minimum number of least significant bits that need to be kept to ensure faithful rounding of the final result.
This document summarizes a lecture on algorithms and graph traversal techniques. It discusses:
1) Breadth-first search (BFS) and depth-first search (DFS) algorithms for traversing graphs. BFS uses a queue while DFS uses a stack.
2) Applications of BFS and DFS, including finding connected components, minimum spanning trees, and bi-connected components.
3) Identifying articulation points to determine biconnected components in a graph.
4) The 0/1 knapsack problem and approaches for solving it using greedy algorithms, backtracking, and branch and bound search.
On the Adjacency Matrix and Neighborhood Associated with Zero-divisor Graph f...Editor IJCATR
This document discusses zero-divisor graphs for direct products of finite commutative rings. Specifically, it analyzes the zero-divisor graphs, neighborhoods, and adjacency matrices for the rings Zp × Zp2, Zp × Z2p, and Zp × Zp2–2, where p is a prime number. It presents the constructions of the zero-divisor graphs for examples when p=2 and p=3. It also generalizes the results to the ring Zp × Zp2 for any prime p. The document proves properties of the adjacency matrices and neighborhoods for these zero-divisor graphs. Finally, it discusses some results on annihilators for the zero-divisor graph of the direct product of any two
Second order and Third order NLO studies of L- alanine crystals grown in aque...Editor IJCATR
Nonlinear optics is a fascinating field, which plays a vital role in the emerging field of photonics and optoelectronics. A
nonlinear optical crystal of L-alanine grown in aqueous solution of hydrofluoric acid is done by slow evaporation method. L-alanine is
an NLO material and it has a Second Harmonic Generation (SHG) efficiency of about 0.3 times that of KDP. To alter the various
properties of L-alanine, single crystals of L-alanine have been grown in the aqueous solution of hydrofluoric acid. In this work, Lalanine
was admixtured with hydrofluoric acid (LAHF) in the molar ratio of 1:1. The grown crystals were colorless and transparent
and they were subjected to various studies for characterization.The third-order nonlinearities of LAHF crystal have been investigated
by Z-scan method. The values of nonlinear refractive index (n2), the nonlinear absorption coefficient (β) and third-order nonlinear
susceptibility (χ(3)) are estimated for the sample
Cs6402 design and analysis of algorithms may june 2016 answer keyappasami
The document discusses algorithms and complexity analysis. It provides Euclid's algorithm for computing greatest common divisor, compares the orders of growth of n(n-1)/2 and n^2, and describes the general strategy of divide and conquer methods. It also defines problems like the closest pair problem, single source shortest path problem, and assignment problem. Finally, it discusses topics like state space trees, the extreme point theorem, and lower bounds.
A SURVEY ON ELLIPTIC CURVE DIGITAL SIGNATURE ALGORITHM AND ITS VARIANTScsandit
The Elliptic Curve Digital Signature Algorithm (ECDSA) is an elliptic curve variant of the
Digital Signature Algorithm (DSA). It gives cryptographically strong digital signatures making
use of Elliptic curve discrete logarithmic problem. It uses arithmetic with much smaller
numbers 160/256 bits instead of 1024/2048 bits in RSA and DSA and provides the same level of
security. The ECDSA was accepted in 1999 as an ANSI standard, and was accepted in 2000 as
IEEE and NIST standards. It was also accepted in 1998 as an ISO standard. Many cryptologist
have studied security aspects of ECDSA and proposed different variants. In this paper, we
discuss a detailed analysis of the original ECDSA and all its available variants in terms of the
security level and execution time of all the phases. To the best of our knowledge, this is a unique
attempt to juxtapose and compare the ECDSA with all of its variants.
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
This document provides an overview of elliptic curve cryptography (ECC). It begins with background on ECC, describing how it was independently proposed in 1985 as an approach to asymmetric cryptography. It then covers the basics of asymmetric cryptosystems and how ECC compares to RSA and Diffie-Hellman. The document goes on to explain elliptic curves over real and finite numbers, how points are added and doubled on elliptic curves, and how this relates to discrete logarithm problems. It discusses implementations of ECC for cryptography and comparisons to RSA in terms of key size and performance. Finally, it covers efficient implementations of ECC for smart cards.
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields for encryption, digital signatures, and key exchange. The key sizes are smaller than RSA for the same security level. Its security relies on the assumed hardness of solving the discrete logarithm problem over elliptic curves. ECC defines elliptic curves with parameters over Galois fields GF(p) for prime p or binary fields GF(2m). Points on the curves along with addition and doubling formulas are used to perform scalar multiplications for cryptographic operations.
Cryptography is the combination of Mathematics and Computer science. Cryptography is used for encryption and decryption of data using mathematics. Cryptography transit the information in an illegible manner such that only intended recipient will be able to decrypt the information
Elliptic curve cryptography (ECC) uses elliptic curves over finite fields to provide public-key encryption and digital signatures. ECC requires significantly smaller key sizes than other cryptosystems like RSA to provide equivalent security. This allows for faster computations and less storage requirements, making ECC ideal for constrained environments like smartphones. ECC relies on the difficulty of solving the elliptic curve discrete logarithm problem to provide security.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Ec2203 digital electronics questions anna university by www.annaunivedu.organnaunivedu
EC2203 Digital Electronics Anna University Important Questions for 3rd Semester ECE , EC2203 Digital Electronics Important Questions, 3rd Sem Question papers,
http://www.annaunivedu.org/digital-electronics-ec-2203-previous-year-question-paper-for-3rd-sem-ece-anna-univ-question/
Data Security Using Elliptic Curve CryptographyIJCERT
Cryptography technique is used to provide data security. In existing cryptography technique the key generation takes place randomly. Key generation require shared key. If shared key is access by unauthorized user then security becomes disoriented. Hence existing problems are alleviated to give more security to data. In proposed system a algorithm called as Elliptic Curve Cryptography is used. The ECC generates the key by using the point on the curve. The ECC is used for generating the key by using point on the curve and encryption and decryption operation takes place through curve. In the proposed system the encryption and key generation process takes place rapidly.
Elliptic Curve Cryptography was presented by Ajithkumar Vyasarao. He began with an introduction to ECC, noting its advantages over RSA like smaller key sizes providing equal security. He described how ECC works using elliptic curves over real numbers and finite fields. He demonstrated point addition and scalar multiplication on curves. ECC can be used for applications like smart cards and mobile devices. For key exchange, Alice and Bob can agree on a starting point and generate secret keys by multiplying a private value with the shared point. ECC provides security through the difficulty of solving the elliptic curve discrete logarithm problem.
Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptogr...Marisa Paryasto
This document discusses implementing elliptic curve cryptography using composite fields. It proposes using a 299-bit key represented in the composite field GF((213)23) instead of the conventional GF(2299). This breaks the finite field multiplication into smaller chunks by dividing the field into a ground field and extension field. A lookup table is used for multiplication in the ground field GF(213) while a classic multiplier is used for the extension field GF(23). This composite field approach aims to provide better time and area efficiency for implementation on FPGAs compared to a single large multiplier. The document provides background on elliptic curves, finite fields, and previous work on composite field representations.
The branch-and-bound method is used to solve optimization problems by traversing a state space tree. It computes a bound at each node to determine if the node is promising. Better approaches traverse nodes breadth-first and choose the most promising node using a bounding heuristic. The traveling salesperson problem is solved using branch-and-bound by finding an initial tour, defining a bounding heuristic as the actual cost plus minimum remaining cost, and expanding promising nodes in best-first order until finding the minimal tour.
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
The document discusses Boolean algebra and logic circuits. It covers Boolean algebra, fundamental concepts like binary digits and logical operators. It discusses Boolean functions, their representation using algebraic expressions and truth tables. Methods to minimize Boolean functions by reducing literals and terms are also covered. Logic gates and how they are used to build combinational logic circuits are explained.
Improved security system using steganography and elliptic curve crypto...atanuanwesha
The main objectives of the project is to make the data safe and secure and transmit the data in such a way that it is not possible for anyone to detect the data . Steganography is concealing the secret message in non secret image. Whereas Encryption is converting data into code to prevent unauthorized access .Steganography as well as cryptography has its own disadvantage. Our objective is to implement both the procedures to enforce tight security and to prevent evesdropping etc.
Efficiency of 128-bit Encryption and Decryption Process in Elgamal Method Usi...TELKOMNIKA JOURNAL
1) The document discusses efficiency of 128-bit encryption and decryption using the Elgamal method with elliptic curve cryptography (ECC).
2) It describes how ECC can optimize encryption and decryption processes by using mathematical problems that are harder to solve than traditional cryptography methods.
3) The document outlines the process of generating a public/private key pair using ECC, and then using those keys for Elgamal encryption and decryption of plaintext data.
The document discusses the arithmetic of elliptic curves. It begins by introducing elliptic curves and their group structure under addition. It describes how points on an elliptic curve form an abelian group and that rational points form a subgroup. It then discusses points of finite order, including points of order 2 and 3. The Nagell-Lutz theorem and Mazur's theorem characterize rational points of finite order. Finally, it introduces Mordell's theorem, which states that the group of rational points on an elliptic curve is finitely generated.
This document discusses formatting bits to better implement signal processing algorithms with integer arithmetic. It begins by introducing the context and objectives, which is to develop a methodology and tools to implement embedded filter algorithms using only integer arithmetic while controlling errors. It then discusses fixed-point arithmetic and how filters can be implemented using sum-of-products operations. The objective is given a bound on the final error, to find an implementation that reduces bit usage while controlling output error. The document proposes a two-step bit formatting method that first formats the most significant bits using Jackson's rule, then determines the minimum number of least significant bits that need to be kept to ensure faithful rounding of the final result.
This document summarizes a lecture on algorithms and graph traversal techniques. It discusses:
1) Breadth-first search (BFS) and depth-first search (DFS) algorithms for traversing graphs. BFS uses a queue while DFS uses a stack.
2) Applications of BFS and DFS, including finding connected components, minimum spanning trees, and bi-connected components.
3) Identifying articulation points to determine biconnected components in a graph.
4) The 0/1 knapsack problem and approaches for solving it using greedy algorithms, backtracking, and branch and bound search.
On the Adjacency Matrix and Neighborhood Associated with Zero-divisor Graph f...Editor IJCATR
This document discusses zero-divisor graphs for direct products of finite commutative rings. Specifically, it analyzes the zero-divisor graphs, neighborhoods, and adjacency matrices for the rings Zp × Zp2, Zp × Z2p, and Zp × Zp2–2, where p is a prime number. It presents the constructions of the zero-divisor graphs for examples when p=2 and p=3. It also generalizes the results to the ring Zp × Zp2 for any prime p. The document proves properties of the adjacency matrices and neighborhoods for these zero-divisor graphs. Finally, it discusses some results on annihilators for the zero-divisor graph of the direct product of any two
Second order and Third order NLO studies of L- alanine crystals grown in aque...Editor IJCATR
Nonlinear optics is a fascinating field, which plays a vital role in the emerging field of photonics and optoelectronics. A
nonlinear optical crystal of L-alanine grown in aqueous solution of hydrofluoric acid is done by slow evaporation method. L-alanine is
an NLO material and it has a Second Harmonic Generation (SHG) efficiency of about 0.3 times that of KDP. To alter the various
properties of L-alanine, single crystals of L-alanine have been grown in the aqueous solution of hydrofluoric acid. In this work, Lalanine
was admixtured with hydrofluoric acid (LAHF) in the molar ratio of 1:1. The grown crystals were colorless and transparent
and they were subjected to various studies for characterization.The third-order nonlinearities of LAHF crystal have been investigated
by Z-scan method. The values of nonlinear refractive index (n2), the nonlinear absorption coefficient (β) and third-order nonlinear
susceptibility (χ(3)) are estimated for the sample
A New Approach to Segmentation of On-Line Persian Cursive WordsEditor IJCATR
Segmentation approaches, as processes that divide word into smaller parts which contain one letter at most, have important
effect on cursive word recognition. While online cursive word recognition became applied technology in Latin and Chinese languages,
complex structural features in Arabic-based script made it an important field of study in Persian and Arabic languages. In this paper,
by introducing of Standard Persian Handwriting, we proposed a novel approach to segmentation online Persian cursive script based on
width of letter's body in Persian language. Results are shown 99.86% accuracy in detection of expected segmentation points, while
recognized extra points reduced 93.73% compared to our previous methods.
Successive approximation of neutral stochastic functional differential equati...Editor IJCATR
We establish results concerning the existence and uniqueness of solutions to neutral stochastic functional differential
equations with infinite delay and Poisson jumps in the phase space C((-∞,0];Rd) under non-Lipschitz condition with Lipschitz
condition being considered as a special case and a weakened linear growth condition on the coefficients by means of the successive
approximation. Compared with the previous results, the results obtained in this paper is based on a other proof and our results can
complement the earlier publications in the existing literatures.
RW-CLOSED MAPS AND RW-OPEN MAPS IN TOPOLOGICAL SPACESEditor IJCATR
In this paper we introduce rw-closed map from a topological space X to a topological space Y as the image
of every closed set is rw-closed and also we prove that the composition of two rw-closed maps need not be rw-closed
map. We also obtain some properties of rw-closed maps.
Modeling and Evaluation of Performance and Reliability of Component-based So...Editor IJCATR
Validation of software systems is very useful at the primary stages of their development cycle. Evaluation of functional
requirements is supported by clear and appropriate approaches, but there is no similar strategy for evaluation of non-functional requirements
(such as performance and reliability). Whereas establishing the non-functional requirements have significant effect on success of software
systems, therefore considerable necessities are needed for evaluation of non-functional requirements. Also, if the software performance has
been specified based on performance models, may be evaluated at the primary stages of software development cycle. Therefore, modeling
and evaluation of non-functional requirements in software architecture level, that are designed at the primary stages of software systems
development cycle and prior to implementation, will be very effective.
We propose an approach for evaluate the performance and reliability of software systems, based on formal models (hierarchical timed
colored petri nets) in software architecture level. In this approach, the software architecture is described by UML use case, activity and
component diagrams, then UML model is transformed to an executable model based on hierarchical timed colored petri nets (HTCPN) by a
proposed algorithm. Consequently, upon execution of an executive model and analysis of its results, non-functional requirements including
performance (such as response time) and reliability may be evaluated in software architecture level.
Formal Models for Context Aware ComputingEditor IJCATR
Context-aware computing refers to a general class of mobile systems that can sense their physical environment, and
adapt their behavior accordingly. In this paper we seek to develop a systematic understanding of context-aware computing by
constructing a formal model and notation for expressing context-aware computations. This discussion is followed by a
description and comparison of current context modeling and reasoning techniques.
Natural Hand Gestures Recognition System for Intelligent HCI: A SurveyEditor IJCATR
Gesture recognition is to recognizing meaningful expressions of motion by a human, involving the hands, arms, face, head,
and/or body. Hand Gestures have greater importance in designing an intelligent and efficient human–computer interface. The applications
of gesture recognition are manifold, ranging from sign language through medical rehabilitation to virtual reality. In this paper a survey on
various recent gesture recognition approaches is provided with particular emphasis on hand gestures. A review of static hand posture
methods are explained with different tools and algorithms applied on gesture recognition system, including connectionist models, hidden
Markov model, and fuzzy clustering. Challenges and future research directions are also highlighted.
Survey on Efficient and Secure Anonymous Communication in ManetsEditor IJCATR
Mobile ad-hoc networks require anonymous communications in order to thwart new wireless passive attacks; and to protect new
assets of information such as nodes locations, motion patterns, network topology and traffic patterns in addition to conventional identity and
message privacy. The transmitted routing messages and cached active routing entries leave plenty of opportunities for eavesdroppers.
Anonymity and location privacy guarantees for the deployed ad hoc networks are critical in military and real time communication systems,
otherwise the entire mission may be compromised. This poses challenging constraints on MANET routing and data forwarding. To address
the new challenges, several anonymous routing schemes have been proposed recently.
A Study of Sybil and Temporal Attacks in Vehicular Ad Hoc Networks: Types, Ch...Editor IJCATR
In recent years, the number of automobiles on the road has increased tremendously. Due to high density and mobility of vehicles,
possible threats and road accidents are increasing. Wireless communication allows sending safety and other critical information. Due to this
inherent wireless characteristic and periodic exchange of safety packets, Vehicular Ad-hoc Network (VANET) is vulnerable to number of
security threats like Sybil attack or temporal attack. In this paper, a detailed discussion has been done on both the type of attacks. With the
help of already published works, some approaches have also been studied which have proved to be of significance in detection of these
attacks.
Optical Character Recognition from Text ImageEditor IJCATR
Optical Character Recognition (OCR) is a system that provides a full alphanumeric recognition of printed or handwritten
characters by simply scanning the text image. OCR system interprets the printed or handwritten characters image and converts it into
corresponding editable text document. The text image is divided into regions by isolating each line, then individual characters with
spaces. After character extraction, the texture and topological features like corner points, features of different regions, ratio of
character area and convex area of all characters of text image are calculated. Previously features of each uppercase and lowercase
letter, digit, and symbols are stored as a template. Based on the texture and topological features, the system recognizes the exact
character using feature matching between the extracted character and the template of all characters as a measure of similarity.
Implementation of Elliptic Curve Digital Signature Algorithm Using Variable T...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Low Power FPGA Based Elliptical Curve CryptographyIOSR Journals
Abstract: Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. The development of public-key cryptography is the greatest and perhaps the only true revolution in the entire history of cryptography. Elliptic Curve Cryptography is one of the public-key cryptosystem showing up in standardization efforts, including the IEEE P1363 Standard. The principal attraction of elliptic curve cryptography compared to RSA is that it offers equal security for a smaller key-size, thereby reducing the processing overhead. As a Public-Key Cryptosystem, ECC has many advantages such as fast speed, high security and short key. It is suitable for the hardware of implementation, so ECC has been more and more focused in recent years. The hardware implementation of ECC on FPGA uses the arithmetic unit that has small area, small storage unit and fast speed, and it is an extremely suitable system which has limited computation ability and storage space.[1][2] The modular arithmetic division operations are carried out using conditional successive subtractions, thereby reducing the area. The system is implemented on Vertex-Pro XCV1000 FPGA. Index Terms – VHDL, FSM, FPGA, Elliptic Curve Cryptography.
Low Power FPGA Based Elliptical Curve CryptographyIOSR Journals
Cryptography is the study of techniques for ensuring the secrecy and authentication of the
information. The development of public-key cryptography is the greatest and perhaps the only true revolution in
the entire history of cryptography. Elliptic Curve Cryptography is one of the public-key cryptosystem showing
up in standardization efforts, including the IEEE P1363 Standard. The principal attraction of elliptic curve
cryptography compared to RSA is that it offers equal security for a smaller key-size, thereby reducing the
processing overhead. As a Public-Key Cryptosystem, ECC has many advantages such as fast speed, high
security and short key. It is suitable for the hardware of implementation, so ECC has been more and more
focused in recent years. The hardware implementation of ECC on FPGA uses the arithmetic unit that has small
area, small storage unit and fast speed, and it is an extremely suitable system which has limited computation
ability and storage space.[1][2] The modular arithmetic division operations are carried out using conditional
successive subtractions, thereby reducing the area. The system is implemented on Vertex-Pro XCV1000 FPGA
Elliptic Curves as Tool for Public Key Cryptographyinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
AUTHENTICATED PUBLIC KEY ENCRYPTION SCHEME USING ELLIPTIC CURVE CRYPTOGRAPHYijujournal
Secure transformation of data is of prime importance in today’s world. In the present paper, we propose a
double fold authenticated public key encryption scheme which helps us in securely sending the confidential
data between sender and receiver. This scheme makes the encrypted data more secure against various
cryptographic attacks.
AUTHENTICATED PUBLIC KEY ENCRYPTION SCHEME USING ELLIPTIC CURVE CRYPTOGRAPHYijujournal
The document presents an authenticated public key encryption scheme using elliptic curve cryptography. It proposes a double encryption method to securely transmit confidential data between a sender and receiver. In the scheme, the sender and receiver first agree on an elliptic curve and generator point over a finite field. They generate private/public key pairs and specific public keys for each other. The sender encrypts the message points in two stages - first generating cipher points using a random integer, and then performing XOR operations on the point coordinates with other values. The receiver decrypts the cipher text in two stages to recover the original message points and plaintext. An example is provided to illustrate the encryption and decryption process.
Elliptic curve cryptography is additional powerful than different methodology that gains countless attention within the industry and plays vital role within the world of CRYPTOGRAPHY. This paper explains the strategy of elliptic curve cryptography victimization matrix scrambling method. during this methodology of cryptography we have a tendency to initial rework the plain text to elliptic curve so victimization matrix scrambling methodology we have a tendency to encrypt/decrypt the message. This method keeps information safe from unwanted attack to our information.
SYMMETRIC BILINEAR CRYPTOGRAPHY ON ELLIPTIC CURVE AND LIE ALGEBRABRNSS Publication Hub
1) The document discusses symmetric bilinear pairings on elliptic curves and Lie algebras in the context of cryptography. It provides an overview of the theoretical foundations and applications of combining these areas.
2) Key concepts covered include the Weil pairing as a symmetric bilinear pairing on elliptic curves, its properties of bilinearity and non-degeneracy, and efficient computation. Applications of elliptic curves in cryptography like ECDH and ECDSA are also summarized.
3) The security of protocols like ECDH and ECDSA relies on the assumed difficulty of solving the elliptic curve discrete logarithm problem (ECDLP). The document proves various mathematical aspects behind symmetric bilinear pairings and their use in elliptic curve cryptography.
Novel encryption algorithm and software development ecc and rsaSoham Mondal
Awarded 2nd prize in the event Papier (scientific paper presentation) conducted by Jadavpur University Electrical Engineering Department, named Convolution, under the aegis of IET and IEEE Signal Processing Society in 2018
This document presents a block cipher that incorporates concepts from the Hill cipher and previous block ciphers developed by the authors. The cipher uses a key matrix K and encryption key bunch matrix E to encrypt plaintext P into ciphertext C. Decryption uses the inverse of K and a decryption key bunch matrix D to recover P from C. The cipher is strengthened by including Mix() and Imix() functions that diffuse bits during encryption and decryption rounds. Cryptanalysis shows the cipher is unbreakable against known attacks due to the diffusion achieved by superimposing Hill cipher and previous block cipher concepts. In 3 sentences or less, this document proposes and analyzes a block cipher combining aspects of Hill cipher and previous work, using key matrices for
The document presents a new encryption method for elliptic curve cryptography based on matrices. It begins by generating an addition table containing all possible point combinations on the elliptic curve. The plaintext is then converted to multiple points on the curve. These points are arranged in a matrix and encrypted using matrix multiplication with a non-singular matrix. The resulting cipher matrix undergoes circular shifting. The decryption process recovers the points from the cipher and performs the inverse operations to obtain the original plaintext. An example is provided to demonstrate the encryption of the word "cipher" using this method.
This document presents a dissertation on improving the baby step giant step algorithm for solving the elliptic curve discrete logarithmic problem. It begins with an overview of cryptography, symmetric and asymmetric encryption, and elliptic curve cryptography. It then discusses the elliptic curve discrete logarithmic problem and surveys existing literature. The proposed approach improves the baby step giant step algorithm by using a smaller baby step set size. Experimental results on two examples show that the proposed approach has faster runtime than the previous method. A complexity analysis is also presented.
The document discusses the objectives and concepts of cryptography. The four main objectives are confidentiality, data integrity, authentication, and non-repudiation. It describes symmetric-key cryptography which uses a single secret key for encryption and decryption, and asymmetric key cryptography which uses different keys for encryption and decryption. It also provides an overview of elliptic curve cryptography, including how it works and some benefits over RSA in providing equivalent security with smaller key sizes.
Implementation of Energy Efficient Scalar Point Multiplication Techniques for...idescitation
Elliptic curve cryptography (ECC) is mainly an
alternative to traditional public-key cryptosystems (PKCs),
such as RSA, due to its smaller key size with same security
level for resource-constrained networks. The computational
efficiency of ECC depends on the scalar point multiplication,
which consists of modular point addition and point doubling
operations. The paper emphasizes on point multiplication
techniques such as Binary, NAF, w-NAF and different
coordinate systems like Affine and Projective (Standard
Projective, Jacobian and Mixed) for point addition and doubling
operations. These operations are compared based on execution
time. The results given here are for general purpose processor
with 1:73 GH z frequency. The implementation is done over
NIST-recommended prime fields 192/224/256/384/521.
Ecc cipher processor based on knapsack algorithmAlexander Decker
This document describes a method for encrypting messages using Elliptic Curve Cryptography (ECC) combined with the knapsack algorithm. It begins by explaining the basics of ECC, including defining elliptic curves over a finite field and describing point addition and doubling operations. It then presents algorithms for the full encryption/decryption process. The process involves first transforming the message into points on an elliptic curve, then applying the knapsack algorithm to further encrypt the ECC-encrypted message before transmission. Decryption reverses these steps to recover the original message. The combination of ECC and knapsack encryption is presented as an innovation that provides increased security over traditional ECC alone.
An Introduction to ECDSA and it's use in Bitcoin (1)Hakeem Hunte
This document provides an introduction to ECDSA and its use in Bitcoin. It begins by explaining how Bitcoin uses a blockchain to record transactions and ensure their authenticity through digital signatures. ECDSA is the algorithm used to generate these signatures. The document then discusses public key cryptography and how ECDSA works. It introduces concepts like elliptic curves, finite fields, point addition/doubling, and scalar multiplication which are important to understanding how ECDSA generates public/private key pairs to digitally sign transactions on the Bitcoin blockchain.
Linear cryptanalysis is a method used to break encryption standards like DES. It involves finding linear approximations between plaintext, ciphertext, and key bits that hold with probability greater than 50%. These approximations are used to determine partial key bits using maximum likelihood algorithms on known or ciphertext-only data. For S-DES, the method finds a linear expression involving S-box inputs/outputs that predicts a key bit with 78% accuracy, allowing recovery of multiple key bits.
This document provides an overview of elliptic curve cryptography (ECC). It discusses how ECC provides stronger security than RSA with smaller key sizes. The document describes the mathematical foundations of elliptic curves over finite fields. It explains scalar multiplication, which involves adding a point on the elliptic curve to itself multiple times, as the core operation in ECC. Finally, it discusses implementations of ECC and applications for encryption and digital signatures.
The discrete logarithm problem (DLP) is the basis for elliptic curve cryptography (ECC) and differs from the integer factorization problem in RSA. In ECC over a finite field, the DLP is to find the exponent that computes one point on the elliptic curve as a multiple of another point, given the curve equation and two points. In RSA, the problem is to find the prime factors of a composite integer. While general algorithms exist to solve both, the DLP in ECC providing equivalent security to RSA requires smaller key sizes, making ECC more efficient.
This document summarizes research on using elliptic curve cryptography based on imaginary quadratic orders. It shows that for elliptic curves over a finite field Fq, if q satisfies certain conditions, the elliptic curve discrete logarithm problem can be reduced to the discrete logarithm problem over the finite field Fp2. This allows the elliptic curve discrete logarithm problem to potentially be solved faster. It then provides examples of how to construct "weak curves" that satisfy the necessary conditions.
Similar to Ijcatr03051008Implementation of Matrix based Mapping Method Using Elliptic Curve Cryptography (20)
Text Mining in Digital Libraries using OKAPI BM25 ModelEditor IJCATR
The emergence of the internet has made vast amounts of information available and easily accessible online. As a result, most libraries have digitized their content in order to remain relevant to their users and to keep pace with the advancement of the internet. However, these digital libraries have been criticized for using inefficient information retrieval models that do not perform relevance ranking to the retrieved results. This paper proposed the use of OKAPI BM25 model in text mining so as means of improving relevance ranking of digital libraries. Okapi BM25 model was selected because it is a probability-based relevance ranking algorithm. A case study research was conducted and the model design was based on information retrieval processes. The performance of Boolean, vector space, and Okapi BM25 models was compared for data retrieval. Relevant ranked documents were retrieved and displayed at the OPAC framework search page. The results revealed that Okapi BM 25 outperformed Boolean model and Vector Space model. Therefore, this paper proposes the use of Okapi BM25 model to reward terms according to their relative frequencies in a document so as to improve the performance of text mining in digital libraries.
Green Computing, eco trends, climate change, e-waste and eco-friendlyEditor IJCATR
This document discusses green computing practices and sustainable IT services. It provides an overview of factors driving adoption of green computing to reduce costs and environmental impact of data centers, such as rising energy costs and density. Green strategies discussed include improving infrastructure efficiency, power management, thermal management, efficient product design, and virtualization to optimize resource utilization. The document examines how green computing aims to lower costs and environmental footprint, and how sustainable IT services take a broader approach considering economic, environmental and social impacts.
Policies for Green Computing and E-Waste in NigeriaEditor IJCATR
Computers today are an integral part of individuals’ lives all around the world, but unfortunately these devices are toxic to the environment given the materials used, their limited battery life and technological obsolescence. Individuals are concerned about the hazardous materials ever present in computers, even if the importance of various attributes differs, and that a more environment -friendly attitude can be obtained through exposure to educational materials. In this paper, we aim to delineate the problem of e-waste in Nigeria and highlight a series of measures and the advantage they herald for our country and propose a series of action steps to develop in these areas further. It is possible for Nigeria to have an immediate economic stimulus and job creation while moving quickly to abide by the requirements of climate change legislation and energy efficiency directives. The costs of implementing energy efficiency and renewable energy measures are minimal as they are not cash expenditures but rather investments paid back by future, continuous energy savings.
Performance Evaluation of VANETs for Evaluating Node Stability in Dynamic Sce...Editor IJCATR
Vehicular ad hoc networks (VANETs) are a favorable area of exploration which empowers the interconnection amid the movable vehicles and between transportable units (vehicles) and road side units (RSU). In Vehicular Ad Hoc Networks (VANETs), mobile vehicles can be organized into assemblage to promote interconnection links. The assemblage arrangement according to dimensions and geographical extend has serious influence on attribute of interaction .Vehicular ad hoc networks (VANETs) are subclass of mobile Ad-hoc network involving more complex mobility patterns. Because of mobility the topology changes very frequently. This raises a number of technical challenges including the stability of the network .There is a need for assemblage configuration leading to more stable realistic network. The paper provides investigation of various simulation scenarios in which cluster using k-means algorithm are generated and their numbers are varied to find the more stable configuration in real scenario of road.
Optimum Location of DG Units Considering Operation ConditionsEditor IJCATR
The optimal sizing and placement of Distributed Generation units (DG) are becoming very attractive to researchers these days. In this paper a two stage approach has been used for allocation and sizing of DGs in distribution system with time varying load model. The strategic placement of DGs can help in reducing energy losses and improving voltage profile. The proposed work discusses time varying loads that can be useful for selecting the location and optimizing DG operation. The method has the potential to be used for integrating the available DGs by identifying the best locations in a power system. The proposed method has been demonstrated on 9-bus test system.
Analysis of Comparison of Fuzzy Knn, C4.5 Algorithm, and Naïve Bayes Classifi...Editor IJCATR
Early detection of diabetes mellitus (DM) can prevent or inhibit complication. There are several laboratory test that must be done to detect DM. The result of this laboratory test then converted into data training. Data training used in this study generated from UCI Pima Database with 6 attributes that were used to classify positive or negative diabetes. There are various classification methods that are commonly used, and in this study three of them were compared, which were fuzzy KNN, C4.5 algorithm and Naïve Bayes Classifier (NBC) with one identical case. The objective of this study was to create software to classify DM using tested methods and compared the three methods based on accuracy, precision, and recall. The results showed that the best method was Fuzzy KNN with average and maximum accuracy reached 96% and 98%, respectively. In second place, NBC method had respective average and maximum accuracy of 87.5% and 90%. Lastly, C4.5 algorithm had average and maximum accuracy of 79.5% and 86%, respectively.
Web Scraping for Estimating new Record from Source SiteEditor IJCATR
Study in the Competitive field of Intelligent, and studies in the field of Web Scraping, have a symbiotic relationship mutualism. In the information age today, the website serves as a main source. The research focus is on how to get data from websites and how to slow down the intensity of the download. The problem that arises is the website sources are autonomous so that vulnerable changes the structure of the content at any time. The next problem is the system intrusion detection snort installed on the server to detect bot crawler. So the researchers propose the use of the methods of Mining Data Records and the method of Exponential Smoothing so that adaptive to changes in the structure of the content and do a browse or fetch automatically follow the pattern of the occurrences of the news. The results of the tests, with the threshold 0.3 for MDR and similarity threshold score 0.65 for STM, using recall and precision values produce f-measure average 92.6%. While the results of the tests of the exponential estimation smoothing using ? = 0.5 produces MAE 18.2 datarecord duplicate. It slowed down to 3.6 datarecord from 21.8 datarecord results schedule download/fetch fix in an average time of occurrence news.
Evaluating Semantic Similarity between Biomedical Concepts/Classes through S...Editor IJCATR
Most of the existing semantic similarity measures that use ontology structure as their primary source can measure semantic similarity between concepts/classes using single ontology. The ontology-based semantic similarity techniques such as structure-based semantic similarity techniques (Path Length Measure, Wu and Palmer’s Measure, and Leacock and Chodorow’s measure), information content-based similarity techniques (Resnik’s measure, Lin’s measure), and biomedical domain ontology techniques (Al-Mubaid and Nguyen’s measure (SimDist)) were evaluated relative to human experts’ ratings, and compared on sets of concepts using the ICD-10 “V1.0” terminology within the UMLS. The experimental results validate the efficiency of the SemDist technique in single ontology, and demonstrate that SemDist semantic similarity techniques, compared with the existing techniques, gives the best overall results of correlation with experts’ ratings.
Semantic Similarity Measures between Terms in the Biomedical Domain within f...Editor IJCATR
The techniques and tests are tools used to define how measure the goodness of ontology or its resources. The similarity between biomedical classes/concepts is an important task for the biomedical information extraction and knowledge discovery. However, most of the semantic similarity techniques can be adopted to be used in the biomedical domain (UMLS). Many experiments have been conducted to check the applicability of these measures. In this paper, we investigate to measure semantic similarity between two terms within single ontology or multiple ontologies in ICD-10 “V1.0” as primary source, and compare my results to human experts score by correlation coefficient.
A Strategy for Improving the Performance of Small Files in Openstack Swift Editor IJCATR
This is an effective way to improve the storage access performance of small files in Openstack Swift by adding an aggregate storage module. Because Swift will lead to too much disk operation when querying metadata, the transfer performance of plenty of small files is low. In this paper, we propose an aggregated storage strategy (ASS), and implement it in Swift. ASS comprises two parts which include merge storage and index storage. At the first stage, ASS arranges the write request queue in chronological order, and then stores objects in volumes. These volumes are large files that are stored in Swift actually. During the short encounter time, the object-to-volume mapping information is stored in Key-Value store at the second stage. The experimental results show that the ASS can effectively improve Swift's small file transfer performance.
Integrated System for Vehicle Clearance and RegistrationEditor IJCATR
Efficient management and control of government's cash resources rely on government banking arrangements. Nigeria, like many low income countries, employed fragmented systems in handling government receipts and payments. Later in 2016, Nigeria implemented a unified structure as recommended by the IMF, where all government funds are collected in one account would reduce borrowing costs, extend credit and improve government's fiscal policy among other benefits to government. This situation motivated us to embark on this research to design and implement an integrated system for vehicle clearance and registration. This system complies with the new Treasury Single Account policy to enable proper interaction and collaboration among five different level agencies (NCS, FRSC, SBIR, VIO and NPF) saddled with vehicular administration and activities in Nigeria. Since the system is web based, Object Oriented Hypermedia Design Methodology (OOHDM) is used. Tools such as Php, JavaScript, css, html, AJAX and other web development technologies were used. The result is a web based system that gives proper information about a vehicle starting from the exact date of importation to registration and renewal of licensing. Vehicle owner information, custom duty information, plate number registration details, etc. will also be efficiently retrieved from the system by any of the agencies without contacting the other agency at any point in time. Also number plate will no longer be the only means of vehicle identification as it is presently the case in Nigeria, because the unified system will automatically generate and assigned a Unique Vehicle Identification Pin Number (UVIPN) on payment of duty in the system to the vehicle and the UVIPN will be linked to the various agencies in the management information system.
Assessment of the Efficiency of Customer Order Management System: A Case Stu...Editor IJCATR
The Supermarket Management System deals with the automation of buying and selling of good and services. It includes both sales and purchase of items. The project Supermarket Management System is to be developed with the objective of making the system reliable, easier, fast, and more informative.
Energy-Aware Routing in Wireless Sensor Network Using Modified Bi-Directional A*Editor IJCATR
Energy is a key component in the Wireless Sensor Network (WSN)[1]. The system will not be able to run according to its function without the availability of adequate power units. One of the characteristics of wireless sensor network is Limitation energy[2]. A lot of research has been done to develop strategies to overcome this problem. One of them is clustering technique. The popular clustering technique is Low Energy Adaptive Clustering Hierarchy (LEACH)[3]. In LEACH, clustering techniques are used to determine Cluster Head (CH), which will then be assigned to forward packets to Base Station (BS). In this research, we propose other clustering techniques, which utilize the Social Network Analysis approach theory of Betweeness Centrality (BC) which will then be implemented in the Setup phase. While in the Steady-State phase, one of the heuristic searching algorithms, Modified Bi-Directional A* (MBDA *) is implemented. The experiment was performed deploy 100 nodes statically in the 100x100 area, with one Base Station at coordinates (50,50). To find out the reliability of the system, the experiment to do in 5000 rounds. The performance of the designed routing protocol strategy will be tested based on network lifetime, throughput, and residual energy. The results show that BC-MBDA * is better than LEACH. This is influenced by the ways of working LEACH in determining the CH that is dynamic, which is always changing in every data transmission process. This will result in the use of energy, because they always doing any computation to determine CH in every transmission process. In contrast to BC-MBDA *, CH is statically determined, so it can decrease energy usage.
Security in Software Defined Networks (SDN): Challenges and Research Opportun...Editor IJCATR
In networks, the rapidly changing traffic patterns of search engines, Internet of Things (IoT) devices, Big Data and data centers has thrown up new challenges for legacy; existing networks; and prompted the need for a more intelligent and innovative way to dynamically manage traffic and allocate limited network resources. Software Defined Network (SDN) which decouples the control plane from the data plane through network vitalizations aims to address these challenges. This paper has explored the SDN architecture and its implementation with the OpenFlow protocol. It has also assessed some of its benefits over traditional network architectures, security concerns and how it can be addressed in future research and related works in emerging economies such as Nigeria.
Measure the Similarity of Complaint Document Using Cosine Similarity Based on...Editor IJCATR
Report handling on "LAPOR!" (Laporan, Aspirasi dan Pengaduan Online Rakyat) system depending on the system administrator who manually reads every incoming report [3]. Read manually can lead to errors in handling complaints [4] if the data flow is huge and grows rapidly, it needs at least three days to prepare a confirmation and it sensitive to inconsistencies [3]. In this study, the authors propose a model that can measure the identities of the Query (Incoming) with Document (Archive). The authors employed Class-Based Indexing term weighting scheme, and Cosine Similarities to analyse document similarities. CoSimTFIDF, CoSimTFICF and CoSimTFIDFICF values used in classification as feature for K-Nearest Neighbour (K-NN) classifier. The optimum result evaluation is pre-processing employ 75% of training data ratio and 25% of test data with CoSimTFIDF feature. It deliver a high accuracy 84%. The k = 5 value obtain high accuracy 84.12%
Hangul Recognition Using Support Vector MachineEditor IJCATR
The recognition of Hangul Image is more difficult compared with that of Latin. It could be recognized from the structural arrangement. Hangul is arranged from two dimensions while Latin is only from the left to the right. The current research creates a system to convert Hangul image into Latin text in order to use it as a learning material on reading Hangul. In general, image recognition system is divided into three steps. The first step is preprocessing, which includes binarization, segmentation through connected component-labeling method, and thinning with Zhang Suen to decrease some pattern information. The second is receiving the feature from every single image, whose identification process is done through chain code method. The third is recognizing the process using Support Vector Machine (SVM) with some kernels. It works through letter image and Hangul word recognition. It consists of 34 letters, each of which has 15 different patterns. The whole patterns are 510, divided into 3 data scenarios. The highest result achieved is 94,7% using SVM kernel polynomial and radial basis function. The level of recognition result is influenced by many trained data. Whilst the recognition process of Hangul word applies to the type 2 Hangul word with 6 different patterns. The difference of these patterns appears from the change of the font type. The chosen fonts for data training are such as Batang, Dotum, Gaeul, Gulim, Malgun Gothic. Arial Unicode MS is used to test the data. The lowest accuracy is achieved through the use of SVM kernel radial basis function, which is 69%. The same result, 72 %, is given by the SVM kernel linear and polynomial.
Application of 3D Printing in EducationEditor IJCATR
This paper provides a review of literature concerning the application of 3D printing in the education system. The review identifies that 3D Printing is being applied across the Educational levels [1] as well as in Libraries, Laboratories, and Distance education systems. The review also finds that 3D Printing is being used to teach both students and trainers about 3D Printing and to develop 3D Printing skills.
Survey on Energy-Efficient Routing Algorithms for Underwater Wireless Sensor ...Editor IJCATR
In underwater environment, for retrieval of information the routing mechanism is used. In routing mechanism there are three to four types of nodes are used, one is sink node which is deployed on the water surface and can collect the information, courier/super/AUV or dolphin powerful nodes are deployed in the middle of the water for forwarding the packets, ordinary nodes are also forwarder nodes which can be deployed from bottom to surface of the water and source nodes are deployed at the seabed which can extract the valuable information from the bottom of the sea. In underwater environment the battery power of the nodes is limited and that power can be enhanced through better selection of the routing algorithm. This paper focuses the energy-efficient routing algorithms for their routing mechanisms to prolong the battery power of the nodes. This paper also focuses the performance analysis of the energy-efficient algorithms under which we can examine the better performance of the route selection mechanism which can prolong the battery power of the node
Comparative analysis on Void Node Removal Routing algorithms for Underwater W...Editor IJCATR
The designing of routing algorithms faces many challenges in underwater environment like: propagation delay, acoustic channel behaviour, limited bandwidth, high bit error rate, limited battery power, underwater pressure, node mobility, localization 3D deployment, and underwater obstacles (voids). This paper focuses the underwater voids which affects the overall performance of the entire network. The majority of the researchers have used the better approaches for removal of voids through alternate path selection mechanism but still research needs improvement. This paper also focuses the architecture and its operation through merits and demerits of the existing algorithms. This research article further focuses the analytical method of the performance analysis of existing algorithms through which we found the better approach for removal of voids
Decay Property for Solutions to Plate Type Equations with Variable CoefficientsEditor IJCATR
In this paper we consider the initial value problem for a plate type equation with variable coefficients and memory in
1 n R n ), which is of regularity-loss property. By using spectrally resolution, we study the pointwise estimates in the spectral
space of the fundamental solution to the corresponding linear problem. Appealing to this pointwise estimates, we obtain the global
existence and the decay estimates of solutions to the semilinear problem by employing the fixed point theorem
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
UiPath Test Automation using UiPath Test Suite series, part 6DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
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Ijcatr03051008Implementation of Matrix based Mapping Method Using Elliptic Curve Cryptography
1. International Journal of Computer Applications Technology and Research
Volume 3– Issue 5, 312 - 317, 2014
www.ijcat.com 312
Implementation of Matrix based Mapping Method Using
Elliptic Curve Cryptography
Geetha G
Dept. of Electronics and Communication
BNM Institute of Technology
Bangalore, India
Padmaja Jain
Dept. of Electronics and Communication
BNM Institute of Technology
Bangalore, India
Abstract: Elliptic Curve Cryptography (ECC) gained a lot of attention in industry. The key attraction of ECC over RSA is that it
offers equal security even for smaller bit size, thus reducing the processing complexity. ECC Encryption and Decryption methods can
only perform encrypt and decrypt operations on the curve but not on the message. This paper presents a fast mapping method based on
matrix approach for ECC, which offers high security for the encrypted message. First, the alphabetic message is mapped on to the
points on an elliptic curve. Later encode those points using Elgamal encryption method with the use of a non-singular matrix. And the
encoded message can be decrypted by Elgamal decryption technique and to get back the original message, the matrix obtained from
decoding is multiplied with the inverse of non-singular matrix. The coding is done using Verilog. The design is simulated and
synthesized using FPGA.
Keywords: Cryptography; Elliptic Curve; Finite Field; Mapping; Non-singular matrix; Elgamal Encryption; Elgamal Decryption
1. INTRODUCTION
With the rapid development of technology, people find
various methods to hack information. For secured data
communication, Cryptography is one of the techniques. It
basically deals with encryption and decryption of a given data.
The two types of cryptography being Public and Private key
cryptography, where in two types of keys are used in former
and a single key is used in later case. The advantage of public
key cryptography is that it is more secure than private key
cryptography. ECC is one such method of public key
cryptography along with RSA. The key attraction of ECC
over RSA is that it offers equal security even for smaller bit
size, thus reducing the band width, processing complexity [1].
In ECC, the operations such as point inverse, point addition,
point subtraction, scalar multiplication are performed on the
points obtained from an elliptic curve. These point operations
are useful in performing encryption and decryption
operations.
In paper [2], Static (One to One) and dynamic (One to N)
mapping methods are explained. In static, though it is a simple
technique, the same alphanumeric characters from the
different words are always mapped onto the same x-y
coordinates of the elliptic curve points. When encrypted,
points obtained will also be same. So, an intruder can easily
interpret data with trial and error method. Hence the secrecy
of data transmission by using this methodology is very low. In
dynamic mapping, the alphanumeric characters are mapped
dynamically on to the points of EC. Thus it is difficult for an
intruder to guess which particular character is mapped to
which point on EC. But mapping method using matrix method
as in paper [3], guarantees the security for the data. And no
intruder can hack it. Since this method avoids the regularity in
the resultant encrypted text. Thus strengthens the crypto
systems and provides better performance.
This paper is organized as follows. The brief introduction to
cryptography is given in section 1, cryptography using elliptic
curves followed by the point operations, encryption and
decryption operations is given in section 2, section 3 describes
the proposed method, and the mapping technique followed by
illustration and results in section 4, section 5 is about the future
enhancements, section 6 gives conclusion and section 7 is
about the acknowledgement followed by references.
2. CRYTOGRAPHY USING ELLIPTIC
CURVES
2.1. Elliptic Curve
In elliptic curve cryptography, a restricted form of elliptic curve
defined over a finite field Fp is considered. One particular
interest for cryptography is referred to elliptic group mod p,
where p is prime number. Eq.1 defines the condition for
choosing the elliptic curve.
4a3
+27b2
(mod p) ≠ 0 (1)
Where „a‟ and „b‟ are two nonnegative integers less than p.
Then Ep(a, b) indicates the elliptic group mod p whose
elements (x, y) are pairs of nonnegative integers less than p.
Eq. 2 refers to the general form of elliptic curve.
y2
=x3
+ax+b (2)
2.2. Modular Arithmetic
Modular arithmetic is the principal mathematical concept in
Cryptography. Here for every operation, modulus is taken
w.r.t the prime number. Eg: Prime number considered in this
work is 31.
2.3. ECC Point Operations
2.3.1. Point Inverse
If J = (x, y) E (Fp), then (x, y) + (x, – y) = ∞. The point (x, –
y) E (Fp) and is called the inverse of J.
Given a point J(x1, y1) on an elliptic curve, -J(x1, y1)
represents its inverse. The inverse of a given point can be
computed using Eq. 3.
-J(x1, y1) = J(x1, p- y1) (3)
Fig.1 shows the graphical representation of point inverse.
2. International Journal of Computer Applications Technology and Research
Volume 3– Issue 5, 312 - 317, 2014
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Fig.1. Point Inverse operation on elliptic curve
2.3.2. Point Addition
The Addition operator is defined over E (Fp) and it can be
seen that E (Fp) forms an abelian group under addition.
The addition operation in E (Fp) is given by Eq.4.
J + ∞ = ∞ + J = J, J Є E (Fp) (4)
If J = (x1, y1) Є E (Fp) and K = (x2, y2) Є E (Fp) and J ≠ K,
then L = J + K = (x3, y3) Є E (Fp).
Given two points on an elliptic curve, J(x1, y1) and K(x2, y2),
then the addition of those points results in L(x3, y3) which lies
on the same curve. The graphical representation of point
addition is shown in Fig.2. It is computed using Eq. 5, Eq. 6
and Eq. 7 as given in [4] and [5].
λ= (y2-y1)/(x2-x1) (5)
x3= λ2
-x1-x (6)
y3= λ(x1-x3)-y1 (7)
Fig.2. Point addition operation on elliptic curve
2.3.3. Point Doubling
If J = (x1, y1) E (Fp), then L = 2J = (x3, y3) E (Fp). Let
J(x1, y1) be a point on the elliptic curve, then point doubling
yields L(x3, y3) which lies on that curve. The graphical
representation of point doubling is shown in Fig. 3. It is
computed using Eq.8, Eq.9 and Eq.10 as given in [4] and [5].
λ = (3x1
2
+ a) / (2y1) (8)
x3= λ2
-2x1 (9)
y3=λ(x1-x3)-y1 (10)
Fig.3. Point doubling operation on elliptic curve
2.3.4. Scalar Multiplication
Given a point P(x1, y1) on the curve, to find k* P(x1, y1),
where k is any integer, it needs repeated computations of
point additions and point doublings.
The reason for choosing prime fields is that distinct additive
and multiplicative inverses exist for each number i.e. 0 to (P-
1) in the field of the prime number P.
2.4. ECC encryption and decryption
Let E be an elliptic curve defined over a finite field Fp. Now
map the plain text on to the points Pm on an elliptic curve. Then
the matrix mapping is used for higher security. Later, these
points are encrypted which again represents the points on the
curve. Then decryption operation is performed.
Elgamal method of encryption consists of following steps:
Step 1: Receiver selects a random integer k, and computes the
point kP („k‟ remains secret).
Step 2: Sender selects a random integer l, and sends the pair of
points, (lP, Q+l (kP)) to receiver, here P refers to the generator
point.
Step 3: To decrypt the message, receiver finds k(lP) from the
first part of the pair, later subtracts it from the second part to
get, Q + l(kP) - k(lP) = Q + lkP - klP = Q.
Step 4: Reverse the mapping to get back the original data sent
in terms of level I mapped points.
3. PROPOSED METHOD
3.1 To obtain points on an elliptic curve
The elliptic curve y2
=(x3
+x+13) mod 31 is employed in this
work. i.e. by choosing a=1, b=13 and p=31in the general form
of elliptic curve given in Eg.2.
The following steps are used to find out the points on an
elliptic curve
Step1: Compute y2
mod 31 for y= 0 to 31.
Step 2: For x= 0 to 31, compute y2
=(x3
+x+13) mod 31.
Step 3: Match the value of y2
in step 2 with that in step 1.
Step 4: If match is found, then the corresponding x and y
becomes a point on an elliptic curve.
Step 5: For any point on an elliptic curve, its inverse will also
be present.
For the above curve choosen, 34 points can be obtained
including point at ∞. Here, the group is said to be cyclic, since
the points repeat after 34 points.
The Table 1 gives the set of points on an elliptic curve. Let P
be the generator point of the group. Now, the preliminary
mapping is performed. I.e. the alphabet in the given message is
mapped initially on to the points on an elliptic curve. Thus the
alphabet „a‟ can be mapped as P = (9, 10), „b‟ can be mapped
as 2P = (18, 29), „c‟ can be mapped as 3P = (23, 19), and so
on. Finally the alphabet „z‟ can be mapped as 26P = (24, 2).
Remaining 8 points can be used for mapping special characters
or numbers.
Table 1: A set of points on EC
(9,10) (18,29) (23,19) (4,22) (25,16)
(17,18) (6,24) (24,29) (16,8) (20,2)
(22,22) (28,13) (27,10) (26,21) (5,9)
(19,3) (10,0) (19,28) (5,22) (26,10)
(27,21) (28,18) (22,9) (20,29) (16,23)
(24,2) (6,7) (17,13) (25,15) (4,9)
(23,12) (18,2) (9,21) ∞
3.2. Matrix mapping methodology
In this section, a mapping method based on matrices is
discussed. The alphabetic characters are mapped on to the
points on an elliptic curve. Here, both the sender and receiver
agree upon few common relationships among them.
Some of the parameters are defined as follows:-
E (Fp): The set of points on an elliptic curve.
P: Generator point of the curve with order N.
S: Set of the mapping points generated by the proposed
algorithm.
3. International Journal of Computer Applications Technology and Research
Volume 3– Issue 5, 312 - 317, 2014
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A: Non singular matrix, i.e. |A| ± 1 which has only integer
entries.
A-1
: Inverse of matrix A.
l: Senders private key.
k: Receivers private key.
The following steps are given for matrix mapping method:-
Step 1: Transform the alphabetic characters into points on
elliptic curve.
[P1(x1,y1), P2(x2,y2),…….., Pn(xn,yn)]
Let m be the original message of length n. If n is divided by 3,
then the points have to be padded with ∞, which represents
space.
Step 2: Create the matrix of 3*r with entries as points on EC.
Here, take r =n/3 and s = 2n/3. The matrix M is given as
Step 3: A non singular matrix of 3*3 such that |A| ±1 is
selected. Using addition and doubling of points, find Q =
AM.
Where, matrix A is given as
Step 4: The result is set of points S.
S = [Q1(x1,y1), Q2(x2,y2),…….., Qn(xn,yn)]
4. ILLUSTRATION AND RESULTS
Choosing non-singular matrix A as
Then, the inverse matrix of A is given by
Let sender‟s private key l be 25 and receiver‟s private key k
be 13. Now Q = AM yields matrix mapping points, Encrypted
points as (C1, C2) = (lP, Q+l(kP)), Decrypted points D as (C2-
kC1). The original message can be obtained from decrypted
points (D) using the formula M = A-1
D.
4.1. Simulation results using Xilinx
The coding is done in Verilog with Xilinx ISE 13.2 simulator.
Fig.4 shows the simulation set up.
Fig.4. Simulation set up
Fig.5. RTL schematic of ECC Top module
The Fig. 5 gives the RTL schematic of the Top module
consisting of level I, level II mappings, encryption,
decryption along with decoding.
4.1.1. Addressing letters by its ASCII values
The letters in the given word are addressed by its ASCII
values. For the example word “experimenter”, level I mapping
block is given by Fig.6 with its ASCII values shown in Fig.7
and Fig.8 shows the level I mapping is as discussed in
Table 1.
Fig.6. Level I mapping block.
Fig.7. Showing the ASCII values for the word “experimenter”
Fig.8. Respective points for the letters in the chosen word on an
elliptic curve
4.1.2. Basic point operations
4.1.2.1. Point Inverse
The point inverse of a point say J = (9, 10) is given by L = (9,
31-10) = (9, 21). Here Fig.9 shows the RTL schematic of
Point Inverse and Fig.10 gives its simulation waveform.
Fig.9. Block diagram of Point Inverse operation
4. International Journal of Computer Applications Technology and Research
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Fig.10. Point Inverse operation on elliptic curve
4.1.2.2. Point Addition
The point addition of two points say J= (16, 8) and K= (19,
28) yields x3 = 6 and y3 = 7. Fig.11 shows the RTL schematic
of point addition and Fig.12 gives its simulation waveform
Fig.11. Block diagram of Point addition operation
Fig.12. Point addition operation on elliptic curve
4.1.2.3. Point Doubling
When a point is doubled say J = (18, 29) yields x3 = 4 and y3 =
22. Fig.13 shows the RTL schematic of point doubling and
Fig.14 gives its simulation waveform.
Fig.13. Block diagram of point doubling operation
Fig.14. Point doubling operation on elliptic curve
4.1.3. Matrix mapping (level II mapping)
After preliminary mapping, the points are again mapped using
matrix based mapping approach for high security. Fig.15
refers to the level II mapping block and Fig.16 refers to the
matrix mapped points.
Fig.15. Level II (Matrix) mapping block
Fig.16. Matrix mapped points
4.1.4. ECC Encryption
The matrix mapped points are encrypted using the encryption
formula given in section II. The Fig.17 refers to ECC
encryption block and Fig.18 and Fig.19 refers to its simulation
waveform of encrypted points for the example word
experimenter.
Fig.17. ECC encryption block
Fig.18. Encrypted points
Fig.19. Encrypted points
4.1.5. ECC Decryption
The encrypted points are decrypted using the decryption
formula discussed in section II. Fig.20 shows the decryption
block and Fig.21 refers to the simulation waveform of
decrypted points.
Fig.20. ECC decryption block
Fig.21. Decrypted points
4.1.6. Decoding
After decryption, the original message can be obtained using
the formula given in section IV. Fig.22 shows the block
diagram of decoding part and Fig. 23 shows the simulation
waveform for the same.
Fig.22. Decoding block
5. International Journal of Computer Applications Technology and Research
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Fig.23. Decoded points
4.2. Results from CADENCE
The design is analysed using Cadence tool. Fig 24 refers to
the ECC block, Fig 25 shows level I mapping, Fig 26 gives
level II or matrix mapping block, followed by encryption
block in Fig 27, decryption block in Fig 28 and Fig 29 refers
to the decoding block, point addition block is given by Fig 30
and point doubling block is given by Fig 31.
Fig.24. ECC Block using cadence
Fig.25. Level I mapping using Cadence
Fig.26. Level II (Matrix) mapping using Cadence
Fig.27.ECC Encryption using Cadence
Fig.28.ECC Decryption using Cadence
Fig.29.ECC Decoding using Cadence
Fig.30.Point addition using Cadence
Fig.31.Point doubling using Cadence
4.3. Analysis
In Table 2, the number of point additions, point doublings
and point inverses are given for respective blocks.
Table 2: Number of PA, PD and PI‟s required for each block
Blocks Point
Addition
(PA)
Point
Doubling
(PD)
Point
Inverse
(PI)
Matrix mapping 40 24 12
Encryption 17 9 0
Decryption 36 36 12
Decoding 60 48 16
TOTAL 153 117 40
The Table 3 gives the area report for point addition and point
doubling blocks using Cadence. The Table 4 gives the power
report for point addition and point doubling blocks using
Cadence. The Table 5 gives the power report for point
addition and point doubling blocks using Cadence.
6. International Journal of Computer Applications Technology and Research
Volume 3– Issue 5, 312 - 317, 2014
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Table 3: Area report using Cadence
Instance Cells Cell
Area
Net
Area
Technology
library
Point
addition
1597 8755 0 Wireload
Point
doubling
1692 8534 0 Wireload
Table 4: Power report using Cadence
Instance Cells Leakage
power
(nW)
Dynamic
power
(nW)
Technology
library
Point
addition
1597 27140.155 79593.237 Wireload
Point
doubling
1692 25157.323 130700.945 Wireload
Table 5: Timing report using Cadence
Instance Fan
out
Load
(fF)
Slew
(ps)
Delay
(ps)
Arrival(ps)
Point
addition
15 18.8 0 +90 20520 R
Point
doubling
18 23.5 0 +90 30014 R
5. FUTURE WORK
Optimizing the design in terms of Area, Power and Speed and
extending the work so that the numerals, capital letters etc
also can be encoded.
6. CONCLUSION
In this work, a method of mapping alphabetic characters to an
elliptic curve points by using a non-singular matrix is
described. The mapping points are encrypted and decrypted
using ECC technique. The obtained results show that the
chosen method avoids the regularity in the resultant encrypted
points. The Table 6 gives the encrypted and decrypted points
for the example word “experimenter”.
Table 6: Encrypted and decrypted points for the word “experimenter”
.
Char
Point
Pm
Matrix
Mapped
points Q
Encrypted points
(C1,C2)
Decrypted
points D
e (25,16) (23,19) ((16,23),(28,18)) (23,19)
x (20,29) (9,10) ((16,23),(26,10)) (9,10)
p (19,3) (20,2) ((16,23),(25,15)) (20,2)
e (25,16) (18,29) ((16,23),(27,21)) (18,29)
r (19,28) (26,21) ((16,23),(9,21)) (26,21)
i (16,8) (27,21) ((16,23),(17,18)) (27,21)
m (27,10) (20,2) ((16,23),(25,15)) (20,2)
e (25,16) (9,10) ((16,23),(26,10)) (9,10)
n (26,21) (22,22) ((16,23),(4,9)) (22,22)
t (26,10) (5,22) ((16,23),(4,22)) (5,22)
e (25,16) (25,15) ((16,23),(26,21)) (25,15)
r (19,28) (19,3) ((16,23),(9,10)) (19,3)
In the paper [2], an intruder can easily guess the repeating
letter since the mapping methods discussed shows regularity
in the encrypted points. The mapping method employed in
this paper does not show any regularity. Hence it would be
difficult to guess the word. Thus it is concluded that the
proposed mapping method can not only strengthen the crypto
system but it also guarantee the confidentiality of messages
hence providing better performance in this regard.
7. ACKNOWLEDGMENTS
Our thanks to the BNMIT management who have contributed
towards this paper.
8. REFERENCES
[1] A Comparative Study of Public Key Cryptosystem based
on ECC and RSA, Arun kumar, Dr. S.S. Tyagi, Manisha
Rana, Neha Aggarwal, Pawan Bhadana, Manav Rachna
International University, Faridabad, India, International
Journal on Computer Science and Engineering (IJCSE),
2011.
[2] Efficient Mapping methods for Elliptic Curve
Cryptosystems, O.Srinivasa Rao, Prof. S. Pallam Setty,
Andhra Pradesh, India, International Journal of
Engineering Science and Technology, 2010.
[3] Fast Mapping Method based on Matrix Approach for
Elliptic Curve Cryptography, F. Amounas and E.H. El
Kinani, Moulay Ismaïl University, Morocco,
International Journal of Information & Network Security
(IJINS), Vol.1, No.2, June 2012, pp. 54~59, ISSN: 2089-
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[4] William Stallings, “Cryptography and network security
principles and practice” , Prentice Hall,5th
Edition, 2011
[5] Darrel R. Hankerson, A. Menezes and A. Vanstone,
“Guide to Elliptic Curve Cryptography”, Springer, 2004.
[6] http://en.wikipedia.org/wiki/Elliptic_curve_cryptography
[7] http://www.certicom.com/index.php/ecc-tutorial
[8] http://www.eccworkshop.org/Engineering,UK, 2009