Elliptic curves

Xem 1-20 trên 36 kết quả Elliptic curves
  • Let E be an elliptic curve over Q, let p be an ordinary prime for E, and let K be an imaginary quadratic field. Write K∞/K for the anticyclotomic Zp-extension of K and set G∞ = Gal(K∞/K). Following a construction of Section 2 of [BD1] which is recalled in Section 1, one attaches to the data (E,K, p) an anticyclotomic p-adic L-function Lp(E,K) which belongs to the Iwasawa algebra Λ := Zp[[G∞]]. This element, whose construction was inspired by a formula proved in [Gr1], is known, thanks to work of Zhang ([Zh, §1.

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  • This paper presents an approach related to authenticate mutually a RFID (Radio Frequency Identification) tag from a RFID reader by using the cryptography based on Elliptic curve. Our proposal mutual authentication lies on the Elliptic curve discrete logarithm problem, which is considered the core in order to fight against all of attacks like replay attack, forgery attack and man-in-the-middle attack. Scientifically, we prove not only the accuracy and the security of our approach, but also its performance in the mutual authentication between a RFID tag and a reader. ...

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  • Abstract Elliptic curve cryptosystems offer security comparable to that of traditional asymmetric cryptosystems, such as those based on the RSA encryption and digital signature algorithms, with smaller keys and computationally more efficient algorithms.

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  • This document includes: Introduction to Elliptic Curves, Elliptic Curve Cryptosystems (ECC), Implementation of ECC in Binary Fields.

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  • A Hardware Architecture for Elliptic Curve Cryptography and Lossless Data Compression. We present a hardware architecture that combines Elliptic Curve Cryptography (ECC) and lossless data compression in a single chip.

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  • This work proposes a processor architecture for elliptic curves cryptosystems over fields GF (2m ). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields.

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  • The paper gives an introduction to elliptic curve cryptography (ECC) and how it is used in the implementation of digital signature (ECDSA) and key agreement (ECDH) Algorithms. The paper discusses the implementation of ECC on two finite fields, prime field and binary field.

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  • This paper describes elliptic curve cryptosystems (ECCs), which are expected to be-come the next-generation public key cryptosystems, and also describes Fujitsu Labo-ratories’ study of ECCs.

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  • In the underlying finite field arithmetic of an elliptic curve cryptosystem, field multiplication is the next computational costly operation other than field inversion. We present two novel algorithms for efficient implementation of field multiplication and modular reduction used frequently in an elliptic curve cryptosystem defined over GF (2n ).

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  • This thesis describes how an elliptic curve cryptosystem can be implemented on low cost microprocessors without coprocessors with reasonable performance. We focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other cost-sensitive devices, and on the Motorola Dragonball, found in the Palm Computing Platform.

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  • Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincar´e upper half-plane, provide us with a rich source of arithmetic questions and insights. They allow the analytic construction of abelian extensions of imaginary quadratic fields, encode special values of zeta functions through the Kronecker limit formula, and are a prototype for Stark’s conjectural construction of units in abelian extensions of number fields.

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  • At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is similar in structure to the ordinary case. Namely, Kobayashi’s conjecture relates modified Selmer groups, which he defined, with modified padic L-functions defined by the first author.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Supporting Symmetric 128-bit AES in Networked Embedded Systems: An Elliptic Curve Key Establishment Protocol-on-Chip

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  • The paper discusses the implementation of ECC on two finite fields, prime field and binary field. It also gives an overview of ECC implementation on different coordinate systems called the projective coordinate systems.

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  • In this paper, we present the results of our implementation of elliptic curve cryptography (ECC) over the field GF (p) on an 80-MHz, 32-bit ARM microprocessor. We have produced a practical software library which supports variable length implementation of the elliptic curve digital signature algorithm (ECDSA).

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  • Objectives of Chapter 13: To define a digital signature; to define security services provided by a digital signature; to define attacks on digital signatures; to discuss some digital signature schemes, including RSA, ElGamal, Schnorr, DSS, and elliptic curve; to describe some applications of digital signatures.

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  • Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides significantly higher performance than the implementation of the EC-based algorithms, in which the ECs are defined over the ground fields and extension finite fields of polynomials.

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  • During the last few years, a considerable effort has been devoted to the development of reconfigurable computers, machines that are based on the close interoperation of traditional microprocessors and Field Programmable Gate Arrays (FPGAs).

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  • We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus.

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  • The Elliptic Curve Cryptography (ECC) is evolving as an important cryptography, and shows a promise to be an alternative of RSA. Small size, high security and other features characterize ECC. Based on the theory of ECC, this paper analyzes its advantages over other cryptographies and focuses on its principle.

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