Elliptic Curve Cryptography Research Papers (original) (raw)

In an increasingly connected world, security is a top concern for Internet of Things (IoT). These IoT devices have to be inexpensive implying that they will be constrained in storage and computing resources. In order to secure such devices, highly efficient public key cryptosystems (PKC) are critical. Elliptic Curve Cryptography (ECC) is the most commonly implemented PKC in use today. In this paper, an alternate and a more efficient PKC, called the PEC (Pells Equation Cryptography) has been proposed based on Pells equation: x 2 − D * y 2 ≡ 1 (mod p). It is shown that scalar multiplication in PEC is significantly more efficient compared to ECC. It is also shown that the Discrete Logarithm Problem-computing the private key from the public key-in PEC is at least as hard as that of ECC.

- by Berta István
- •
- Java Card, Public key cryptography, Smart Card, Elliptic Curve Cryptography
- by julio cesar
- •
- Computer Science, Elliptic Curve Cryptography, Finite Field, Public Key
- by Saeideh Kabirirad
- •
- Computer Science, Distributed Computing, Public Information, Secret Sharing
- by Muhammad Zulkifli
- •
- Electrical Engineering, Finite Element Methods, FPGA, Finite element method
- by C Gebotys
- •
- Processor Architecture, High Speed, Elliptic Curve Cryptography, Bottom Up
- by Ahmad Abusukhon
- •
- Encryption, Algorithm, Network, Encoding
- by Elsayed Mohamed
- •
- Elliptic Curve Cryptography, Finite Field
- by Refik Molva
- •
- Computer Science, Distributed Computing, Decision Making, Digital Signature
- by Andrew Hone
- •
- Number Theory, Pure Mathematics, Recurrence Relation, Second Order
- by Gerardo Vega
- •
- Pure Mathematics, Finite Fields, Linear Code, Elliptic Curve Cryptography

In this work, we propose an algorithm to produce the double-base chain that optimizes the time used for computing an elliptic curve scalar multiplication, i.e. the bottleneck operation of the elliptic curve cryptosystem. The double-base number system and its subclass, double-base chain, are the representation that combines the binary and ternary representations. The time is measured as the weighted sum in terms of the point double, triple, and addition, as used in evaluating the performance of existing greedy-type algorithms, and our algorithm is the first to attain the minimum time by means of dynamic programming. Compared with greedy-type algorithm, the experiments show that our algorithm reduces the time for computing the scalar multiplication by 3.88-3.95% with almost the same average running time for the method itself. We also extend our idea, and propose an algorithm to optimize multi-scalar multiplication. By that extension, we can improve a computation time of the operation by 3.2-11.3%.

- by SDIWC Organization
- •
- Computer Science, Information Technology, Internet Security, Cryptography

We discuss irreducible polynomials that can be used to speed up square root extraction in fields of characteristic two. We call such polynomials square root friendly. The obvious applications are to point halving methods for elliptic curves and divisor halving methods for hyperelliptic curves. Irreducible polynomials P (X) such that the square root ζ of a zero x of P (X) is a sparse polynomial are considered and those for which ζ has minimal degree are characterized. We reveal a surprising connection between the minimality of this degree and the extremality of the the number of trace one elements in the polynomial base associated to P (X). We also show how to improve the speed of solving quadratic equations and that the increase in the time required to perform modular reduction is marginal and does not affect performance adversely. Experimental results confirm that the new polynomials mantain their promises; These results generalize work by Fong et al. to polynomials other than trin...

- by Roberto Avanzi
- •
- Mathematics, Computer Science, Hyperelliptic Curve, Elliptic Curve Cryptography
- by Opeyemi Enoch
- •
- Pure Mathematics, riemann Hypothesis, Elliptic Curve Cryptography, Finite Field
- by Mirza Maulana and +3
- •
- Cryptography, Elliptic Curve Cryptography, Finite Field

With the advent of the World Wide Web and the emergence of e-commerce applications and social networks, organizations across the world generate a large amount of data daily. Data security is the utmost critical issue in ensuring safe transmission of information through the internet. Also network security issues are now becoming important as society is moving towards digital information age. As more and more users connect to the internet it attracts a lot of cyber-criminals. It comprises authorization of access to information in a network, controlled by the network administrator. The task of network security not only requires ensuring the security of end systems but of the entire network. In this paper, an attempt has been made to review the various Network Security and Cryptographic concepts. This paper discusses the state of the art for a broad range of cryptographic algorithms that are used in networking applications.

With the advancement of technology, devices, which are considered non-traditional in terms of internet capabilities, are now being embedded in microprocessors to communicate and these devices are known as IoT devices. This technology has enabled household devices to have the ability to communicate with the internet and a network comprising of such device can create a home IoT network. Such IoT devices are resource constrained and lack high-level security protocols. Thus, security becomes a major issue for such network systems. One way to secure the networks is through reliable authentication protocols and data transfer mechanism. As the household devices are controllable by the users remotely, they are accessed over the internet. Therefore, there should also be a method to make the communication over the internet between IoT devices and the users more secured. This paper proposes a two-phase authentication protocol for authentication purposes and a VPN based secure channel creation ...

- by Kuspriyanto Kuspriyanto and +1
- •
- Electrical, Algorithm Design, Look up Table, Elliptic Curve Cryptography

We consider the geometrical addition law on the elliptic curve in Tate coordinates. It corresponds to the general formal group law over the ring of polynomials with integer coefficients of the parametra of the curve. We study the structure of this law and the differential equation that determines its exponent. We describe a 5-parametric family of Hirzebruch genera with integer

- by Victor M Buchstaber
- •
- Elliptic Curve Cryptography, Differential equation
- by Marco Baldi
- •
- Cryptography, Cryptanalysis, IT adoption, Public key cryptography

ABSTRACT Mobile Instant Messenger is an IM application that need communication fastly and in a secured manner. A good level security with strong autentication must be applied to ensure data transmission between IM sender and IM recipient over public network is valid. This paper propose a new method for securing message IM with an efficient autentication method. In this research, an efficient autentication method will implement Hyper Elliptic Curve Cryptosystem (HECC) algorithm in generating and verifiying the message sign while occur data transaction. The main function of signing message is to autenticate data to ensure validation of data. Then, the sign method used to ensure unauthorized person cannot change the original data or information that sent through the network. This method developed to give auntentication user with key pair per session and using it while communication running between sender and receiver.it is a novel approach in IM auntentication method to elevate the security level of data.

- by Putra Wanda
- •
- Elliptic Curve Cryptography
- by Berna Ors Yalcin
- •
- FPGA, Field-Programmable Gate Arrays, Parallel & Distributed Computing, Hardware

This paper aims to give researchers an approachable introduction to the Supersingular Isogeny Diffie-Hellman key exchange (SIDH-KEX). SIDH is one of the few post-quantum key exchange algorithms based on elliptic curves that has shown potential due to its small key sizes and quick timing. This paper will briefly describe the history and motivation of SIDH. Furthermore, we will present a simple construction of the algorithm along with the mathematical background needed to understand it. Lastly, we will present the recommended parameters to use for potential implementations.

In these days communication technology is very advanced. Digital communication has become very important to secure transmission of information between the sender and the receiver. Security for exchange is a very important feature because it protects information from interloper. In this paper we present a hierarchy of network security technologies such as privacy, authentication, non-rejection and honesty control. There are two popular security mechanisms, namely cryptography and steganography. Both are well known and widely used techniques. Cryptography is used to send data in an encrypted form using the encryption key. Encrypted data is transmitted through unsafe public media. Decryption algorithms are also used to decrypt messages when using decryption keys. Steganography is used to hide data in other cover media.

— Nowadays, the usage of resource constrained devices is increasing and these devices are primarily working with sensitive data. Consequently, data security has become crucial for both producers and users. Limitation of resources is deemed as the major issue that makes these devices vulnerable. Attackers might exploit these limitations to get access to the valuable data. Therefore, carefully chosen and practically tested encryption algorithm must be applied to increase the device efficiency and mitigate the risk of sensitive data loss. This study will compare elliptic curve cryptography (ECC) algorithm with Key size of 160-bit and Rivest-Shamir-Adleman (RSA) algorithm with Key size of 1024-bit. As a result of this study utilizing ECC in resource constrained devices has advantages over RSA but ECC needs continues enhancement to satisfy the limitations of newly designed chips.

- by Mohsen Bafandehkar and +1
- •
- Network Security, Wireless Sensor Networks, Cryptography, Elliptical Curve Cryptography for Wirless Sensor Networks

Elliptic Curve Cryptography (ECC) has a big role in Information Security. Pollard’s Rho
Attack is the only real life threat against elliptic curve based cryptosystems.
Pollard’s
Rho attack solves the so-called Elliptic Curve Discrete Logarithm Problem upon which the
conjectured security is claimed for ECC.
In the context of this thesis, the algorithm realizing Pollard’s Rho attack is initially coded in
Magma programming language as a high level prototype, and then it’s coded in C programming
language for full performance and parallelism. The final code can now run on a TCP/IP
network using n processors(n = 16 in experiments) at their peak to speed-up the attack by a sqrt(n).

- by N. Gamze Orhon Kılıç and +1
- •
- Cryptography, Public Key Crypto systems, Elliptic Curve Cryptography, PARALLEL POLLARD’S

Elliptic curves were introduced to the ancient science of cryptography in the mid 1980s, and Elliptic Curve Cryptography (ECC) has since been growing rapidly. However, owing to the incompleteness of the Weierstrass addition law, elliptic curve cryptosystems based on the Weierstrass model are vulnerable to side-channel attacks. New addition algorithms and elliptic curve models have been proposed to take elliptic curve cryptosystems resistant to side-channel attacks. A promising model in this regard is the Edwards model introduced in 2007. The Edwards addition law is both complete and has the fastest known implementations for elliptic curve operations like addition and doubling. As a part of this work we study the Edwards model in relation to ECC with an emphasis on its computational aspects. We also study two encoding schemes, Elligator and Elligator Square, for representing elliptic curve points as bit strings indistinguishable from uniform random bit strings, both of which have formulations over Edwards curves. We also study isogenies and their computation using analogues of V ́elu’s and Kohel’s formulas for the Edwards model, which turn out to be simpler and more efficient than those for the Weierstrass model. We implement an hitherto unavailable library for Edwards curves, and two ECC algorithms using the implemented Edwards curves, in the mathematical software Sage.

- by Adarsh Saraf
- •
- Elliptic curves, Elliptic Curve Cryptography, Isogenies

Abstract: A Computer Network is an interconnected group of autonomous computing nodes, which use a well defined, mutually agreed set of rules and conventions known as protocols, interact with one-another meaningfully and allow resource sharing preferably in a predictable and controllable manner. Communication has a major impact on today’s business. It is desired to communicate data with high security. Security Attacks compromises the security and hence various Symmetric and Asymmetric cryptographic algorithms have been proposed to achieve the security services such as Authentication, Confidentiality, Integrity, Non-Repudiation and Availability. At present, various types of cryptographic algorithms provide high security to information on controlled networks. These algorithms are required to provide data security and users authenticity. To improve the strength of these security algorithms, a new security protocol for on line transaction can be designed using combination of both symmetric and asymmetric cryptographic techniques. This protocol provides three cryptographic primitives such as integrity, confidentiality and authentication. These three primitives can be achieved with the help of Elliptic Curve Cryptography, Dual-RSA algorithm and Message Digest MD5. That is it uses Elliptic Curve Cryptography for encryption, Dual-RSA algorithm for authentication and MD-5 for integrity. This new security protocol has been designed for better security with integrity using a combination of both symmetric and asymmetric cryptographic techniques.
Keywords: Network Security, Elliptic Curve Cryptography, Dual-RSA, Message Digest-5.
Title: A Hybrid Security Protocol Using Python
Author: Devi.V.Kumar
International Journal of Computer Science and Information Technology Research
ISSN 2348-120X (online), ISSN 2348-1196 (print)
Research publish Journals

In crittografia i pairing sono stati inizialmente
utilizzati nell’analisi crittografica per attaccare alcuni sistemi
basati sul problema del logaritmo discreto. Negli ultimi anni,
però, sono stati impiegati anche per progettare nuovi potenti
sistemi crittografici come i protocolli per il one-round three-party
key agreement e gli schemi di identity-based encryption.
La sicurezza dei pairing-based cryptosystems è basata in gran
parte sull’intrattabilità del Bilinear Diffie-Hellman problem in
determinati gruppi.
Nel presente lavoro, dopo un’introduzione alle curve ellittiche,
vengono trattati i pairing più diffusi, ossia il Weil pairing e
il Tate pairing. Infine sono presentati alcuni protocolli per lo
scambio delle chiavi basati sui pairing.

- by Usha Vyas
- •
- Electrical Engineering, Biomedical Engineering, Computer Security, Cryptography
- by Ann Koblitz and +1
- •
- Number Theory, Social Construction of Technology, Pure Mathematics, Paradigm Shift

In terms of identifying the attacker, the Big Data environment helps resolving cyber security problems. There are big data security concerns as well as safety issues that the analyst must understand. The security of confidential data has long been a serious concern, and as a result, data security is in huge demand. Data is considered an important aspect of an asset and must be protected. Data Protection comprises data integrity, data authenticity, data confidentiality, and then some. Data is prone to possible security risks despite several measures for protecting data including encryption, decryption, and compression. Cryptography is an art and science that encodes messages to make them unreadable in order to achieve secrecy. The data is translated from a readable format known as plain text to an unreadable format known as cypher text, and vice versa. Based on various techniques, there are different types of cryptographic algorithms proposed over the years. These methods use different techniques to implement cryptography's fundamental features, i.e. to conceal the data from unauthorised users. A hybrid cryptographic technique is proposed in this paper to enhance data protection during network transmission, and its implementation and results are published. The proposed secure cryptographic technique promises to use the Enhanced ECC and AES technologies to include the highly secure cypher generation technique. Using JAVA technology, the implementation of the proposed technique is given and its efficiency in terms of space and time complexity is calculated and compared with conventional ECC cryptography. During comparative performance analysis, the proposed cryptographic technique established the successful and enhanced cypher text.

- by IJCSMC Journal
- •
- Mathematics, Computer Science, Information Technology, Technology

The cryptography is the branch of Cryptology. It is a combination of mathematics and computer Science. It is the study of obscuring information in cyberspace. Cipher is a set of algorithm which comprise of encryption and decryption. The cipher paly important role in modern technology. The technologies involving communication including the Internet, Mobile Phones, Digital Television, and ATM machine rely on cipher in order to maintain security and privacy. Thinking about aforesaid importance of cipher in cryptography, in this article, we have designed a smallest cipher which may be efficient in RFID chips. The smallest cipher has been comprised of five mathematical operation: Exponentiation, Multiplication, Addition, Subtraction and Division based on systematic study of classical cipher. The proposed cipher is a keyless cipher, but it is very efficient in secret information passing.

- by Thành Phạm HN and +1
- •
- Cryptography, Elliptic Curve Cryptography

Elliptic Curve Discrete Logarithm (ECDL) are most popular choice Elliptic Curve Cryptography (ECC),which gives provision for shorter key lengths as compared to as compared to its counterpart public key cryptosystems, and it can be used for security in embedded systems,wirless communications and personal communication systems. In this paper Elliptic Curve Discrete Logarithm code has been written in Verilog Hardware Description Language (HDL) and implemented on Xilinx Spartan3E Field Programmable Gate Array (FPGA),has taken 403 encoders, decoders with minimum period of 5.043 ns,maximum frequency 198.295 MHz and with a total memory usage of 269824 Kilobytes respectively. The performance of the crypto system is much faster than the software implementation of the same system. Keywords: Elliptic Curve Discrete Logarithm (ECDL),VerilogHardware Description Language (HDL), Elliptic Curve Cryptography (ECC),Field Programmable Gate Array (FPGA),Finite Fields.

- by GJESR Journal
- •
- Field Programmable Gate Array, Ecdl, Elliptic Curve Cryptography, HDL

- by Carmen Sánchez Ávila
- •
- Digital Signature, Java Programming, Java Card, Smart Card

En els darrers anys, la criptografia amb corbes el.líptiques ha adquirit una importància creixent, fins a arribar a formar part en la actualitat de diferents estàndards industrials. Tot i que s'han dissenyat variants amb corbes el.líptiques de criptosistemes clàssics, com el RSA, el seu màxim interès rau en la seva aplicació en criptosistemes basats en el Problema del Logaritme Discret,

- by Jordi Pujolàs
- •
- Elliptic Curve Cryptography, Contributions

Let F q [ε] := F q [X]/(X 4 − X 3) be a finite quotient ring where ε 4 = ε 3 , with F q is a finite field of order q such that q is a power of a prime number p greater than or equal to 5. In this work, we will study the elliptic curve over F q [ε], ε 4 = ε 3 of characteristic p = 2, 3 given by homogeneous Weierstrass equation of the form Y 2 Z = X 3 + aXZ 2 + bZ 3 where a and b are parameters taken in F q [ε]. Firstly, we study the arithmetic operation of this ring. In addition, we define the elliptic curve E a,b (F q [ε]) and we will show that E π0(a),π0(b) (F q) and E π1(a),π1(b) (F q) are two elliptic curves over the finite field F q , such that π 0 is a canonical projection and π 1 is a sum projection of coordinate of element in F q [ε]. Precisely, we give a classification of elements in elliptic curve over the finite ring F q [ε].

- by Bilel Selikh
- •
- Ring Theory, Elliptic curves, Elliptic Curve Cryptography, Finite Field