Elliptic Curve Algorithm Research Articles

Pollard Rho Algorithm for Elliptic Curves Over with Negation and Frobenius Map

Pollard Rho Algorithm for Elliptic Curves Over with Negation and Frobenius Map

Fast Elliptic Curve Algorithm of Embedded Mobile Equipment

Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the embedded system in the security situation goes through invariable situation causes the embedded system to realize a fast elliptic curve realization method, which enhances the efficiency of embedded system.

Improving Efficiency of Basic Encryption and Authentication Technique using Elliptic Curve with Parameterized Hash Algorithm

In present era, mostly data sends via the internet for sharing, so the reliability on data is decreased. To maintain reliability, several kinds of security and authentication is mechanisms needed, less security increase the liability of attacks on data. Digital Signature of the data is a solution to this security problem which provides the reliability, authenticity and accuracy. Most basic algorithm for security and authentication is RSA, DSA, ECDSA algorithms which uses the different key of different sizes. This paper presents elliptic curve algorithm to encrypt the data and use parameterized hash algorithm to authenticate the data.

Asymmetric cryptosystem and software design based on two-step phase-shifting interferometry and elliptic curve algorithm

We propose an asymmetric cryptosystem based on two-step phase-shifting interferometry (PSI) and elliptic curve (EC) public-key cryptographic algorithm, in which one image is encrypted to two interferograms by double random-phase encoding (DRPE) in Fresnel domain and two-step PSI, and the session keys such as geometrical parameters and pseudo-random seeds, are asymmetrically encoded and decoded with the aid of EC algorithm. The receiver, who possesses the corresponding private key generated by EC algorithm, can successfully decipher the transmitted data using the extracted session keys. The utilization of EC asymmetric cryptosystem solves the problem of key management and dispatch, which is inevitable in the conventional optical symmetric cryptosystems. Not only computer simulation, but also software design and development are carried out to verify the feasibility of the proposed cryptosystem.

Implementation of Embedded Mobile Device Elliptic Curve Algorithm Fast Generating Algorithm

Elliptic curve cryptosystem is used in the process of embedded systems, the selection and generation algorithm of the elliptic curve will directly affect the efficiency of systems. From Elliptic Curve's selection, Elliptic Curve's structure, Elliptic Curve's generation, this paper discussed the realization of a random elliptic curve method of Embedded Mobile Device, the SEA algorithm and its improved algorithm. The results show that this method can achieve a quick implementation of the elliptic curve method to improve the operating efficiency of embedded systems in the same security guarantees.

Prioritized WAVE-based Parking Assistance with Security and User Anonymity

We present a secure, privacy-preserving car parking assistance application using priority-based vehicular communications. The proposed technique utilizes two modified Elliptic Curve algorithms for vehicular message authentication between parking vehicles and corresponding infrastructure. We address the major challenges associated with VANET security and user privacy. The standard Wireless Access in Vehicular Environment (WAVE) protocol suite has been used to construct our signature mechanism, application data secrecy, and message integrity. Security analysis proves the resilience of the scheme against all known attacks. We also investigate network performances in order to justify the effectiveness of the scheme for practical use.

실수체 기반 타원곡선 암호시스템의 연산항 연구

Abstract Recently, as communication is evolved by leaps and bounds through wired/wireless networks, variety of services are routinely made through communication networks. Accordingly, technology that is for protecting data and personal information is required essentially, and study of security technology is actively being make progress to solve these information protection problems. In this paper, to expand selection scope of the key of elliptic curve cryptography, arithmetic items of real number based elliptic curve algorithm among various cryptographic algorithms was studied. The result of an experiment, we could know that elliptic curve cryptography using the real number can choose more various keys than existing elliptic curve cryptography using integer and implement securer cryptographic system. Key Words : Elliptic Curve, Real Number, Information Security, Encryption, ECC 본 논문은 2011년도 서일대학 학술연구비에 의해 연구되었음. * 교신저자 : 우찬일(ciwoo@seoil.ac.kr)접수일 11년 12월 15일 수정일 12년 01월 19일 게재확정일 12년 02월 10일

Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation

Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((2 13 ) 23 ) instead of in GF(2 299 ). Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.

A Mobile Ad Hoc Network Public Key Encryption Algorithm Based on Hash-Chain

In this algorithm, we can choose different public key encryption algorithm, elliptic curve algorithm, different hash algorithm, such as MD5, SHA-1. Based on the public key management algorithm to Hash-chain mobile AD hoc network not only the solution to the problem of public key distribution management, also can be as a addible safety equipment connected in the current network terminal used in network environment is the need for security.

A novel research of confidential communication based on the elliptic curve and the combined chaotic mapping

This letter presents a new type of chaotic encryption system based on combined chaotic mapping pseudo-random number generator, Hash table, and elliptic curve. In this program, the elliptic curve algorithm is used for the key distribution. After the linear transformation, the original chaotic sequence generated by drive system will be combined to chaotic mapping, converted to an encryption key sequence and constructed as Hash table for message authentication. The communication experiment used in the letter proves that the combination of combined chaotic encryption and conventional encryption is safe, feasible, and easy to implement by software.

Security Considerations and Key Negotiation Techniques for Power Constrained Sensor Networks

Sensor networks are becoming increasingly important for a wide variety of applications including environmental monitoring, building safety and emergency relief services. A typical sensor network consists of a large number of small, low-power, low-cost nodes that form a self-organized network using wireless peer-to-peer communication. Because sensor networks pose unique constraints on their operation, traditional security techniques used by conventional networks cannot be applied. In this paper we consider the operational issues and security threats to sensor networks. We discuss the state of the art in terms of sensor network security and we examine the practicality of using efficient elliptic curve algorithms and identity based encryption to deploy a secure sensor network infrastructure. We evaluate the potential for realizing this on low-power, long-life devices by measuring power consumption of the operations needed for key management in a sensor network and thus provide further evidencefor the feasibility of the approach.

Construction of an elliptic curve over finite fields to combine with convolutional code for cryptography

The construction of an efficient cryptographic system, based on the combination of the ElGamal elliptic curve algorithm and convolutional codes using the Viterbi decoding algorithm over the Gaussian channel, is proposed. The originality is based on the construction of the mapping of encryption and coding at the channel level and the constraints imposed on the construction of the elliptic curve. When using elliptic curves and codes for cryptography it is necessary to construct elliptic curves with a given or known number of points over a given finite field with a range of constraint lengths, in order to represent the input alphabet and produce channel gain, respectively. The results show that the benefit of coding with encryption increases the security and coding gain and reduces the expansion factor, but at the expense of higher complexity.

A [formula omitted]-adic point counting algorithm for elliptic curves on legendre form

In 2000 T. Satoh gave the first p - adic point counting algorithm for elliptic curves over finite fields. Satoh' s algorithm was followed by the Satoh–Skjernaa–Taguchi algorithm and furthermore by the arithmetic–geometric mean and modified SST algorithms for characteristic two only. All four algorithms are important to Elliptic Curve Cryptography. In this paper, we present the general framework for p -adic point counting and we apply it to elliptic curves on Legendre form. We show how the λ - modular polynomial can be used for lifting the curve and Frobenius isogeny to characteristic zero and we show how the associated multiplier gives the action of the lifted Frobenius isogeny on the invariant differential. The result is a point counting algorithm for elliptic curves on Legendre form. The algorithm runs in a time complexity of O ( n 2 μ + 1 / ( μ + 1 ) ) for fixed p and a space complexity of O ( n 2 ) where p n is the field size. We include results from experimeriments in characteristic p = 3 , 5 , … , 19 .

FPGA based hardware acceleration for elliptic curve public key cryptosystems

This paper addresses public key cryptosystems based on elliptic curves, which are aimed to high-performance digital signature schemes. Elliptic curve algorithms are characterized by the fact that one can work with considerably shorter keys compared to the RSA approach at the same level of security. A general and highly efficient method for mapping the most time-critical operations to a configurable co-processor is proposed. By means of real-time measurements the resulting performance values are compared to previously published state of the art hardware implementations. A generator based approach is advocated for that purpose which supports application specific co-processor configurations in a flexible and straight forward way. Such a configurable CryptoProcessor has been integrated into a Java-based digital signature environment resulting in a considerable increase of its performance. The outlined approach combines in an unique way the advantages of mapping functionality to either hardware or software and it results in high-speed cryptosystems which are both portable and easy to update according to future security requirements.

Shor's discrete logarithm quantum algorithm for elliptic curves

We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further beyond current computing than for integer factorisation. A 160 bit elliptic curve cryptographic key could be broken on a quantum computer using around 1000 qubits while factoring the security-wise equivalent 1024 bit RSA modulus would require about 2000 qubits. In this paper we only consider elliptic curves over GF(p) and not yet the equally important ones over GF(2^n) or other finite fields. The main technical difficulty is to implement Euclid's gcd algorithm to compute multiplicative inverses modulo p. As the runtime of Euclid's algorithm depends on the input, one difficulty encountered is the ``quantum halting problem''.

On the reduction theory of binary forms

Cremona developed a reduction theory for binary forms of degree 3 and 4 with integer coefficients, the motivation in the case of quartics being to improve 2-descent algorithms for elliptic curves over Q. In this paper we extend some of these results to forms of higher degree. One application of this is to the study of hyperelliptic curves.

The enumerative geometry of rational and elliptic curves in projective space

We study the geometry of varieties parametrizing degree d rational and elliptic curves in P^n intersecting fixed general linear spaces and tangent to a fixed hyperplane H with fixed multiplicities along fixed general linear subspaces of H. As an application, we derive recursive formulas for the number of such curves when the number is finite. These recursive formulas require as ``seed data'' only one input: there is one line in P^1 through two points. These numbers can be seen as top intersection products of various cycles on the Hilbert scheme of degree d rational or elliptic curves in P^n, or on certain components of $\mbar_0(P^n,d)$ or $\mbar_1(P^n,d)$, and as such give information about the Chow ring (and hence the topology) of these objects. The formula can also be interpreted as an equality in the Chow ring (not necessarily at the top level) of the appropriate Hilbert scheme or space of stable maps. In particular, this gives an algorithm for counting rational and elliptic curves in P^n intersecting various fixed general linear spaces. (The genus 0 numbers were found earlier by Kontsevich-Manin, and the genus 1 numbers were found for n=2 by Ran and Caporaso-Harris, and independently by Getzler for n=3.)

Algorithms for modular elliptic curves, by J. E. Cremona. Pp. 343. 1992. SBN 0-521-41813-5 (Cambridge University Press)

Algorithms for modular elliptic curves, by J. E. Cremona. Pp. 343. 1992. SBN 0-521-41813-5 (Cambridge University Press)

A practical analysis of the elliptic curve factoring algorithm

Much asymptotic analysis has been devoted to factoring algorithms. We present a practical analysis of the complexity of the elliptic curve algorithm, suggesting optimal parameter selection and run-time guidelines. The parameter selection is aided by a novel use of Bayesian statistical decision techniques as applied to random algorithms. We discuss how frequently the elliptic curve algorithm succeeds in practice and compare it with the quadratic sieve algorithm.

Construction of Elliptic Curves with Large Rank

We describe an algorithm for finding elliptic curves over Q with large rank and nontrivial torsion group. In particular, an example of a curve of rank exactly 10 with a point of order 2 is given. This method seems to suggest that the rank may be large independently of the torsion group.