49 research outputs found
Algorithms and cryptographic protocols using elliptic curves
En els darrers anys, la criptografia amb corbes el.lĂptiques ha
adquirit una importĂ ncia creixent, fins a arribar a formar part en
la actualitat de diferents estĂ ndards industrials. Tot i que s'han
dissenyat variants amb corbes el.lĂptiques de criptosistemes
clà ssics, com el RSA, el seu mà xim interès rau en la seva
aplicaciĂł en criptosistemes basats en el Problema del Logaritme
Discret, com els de tipus ElGamal. En aquest cas, els
criptosistemes el.lĂptics garanteixen la mateixa seguretat que els
construïts sobre el grup multiplicatiu d'un cos finit primer, però
amb longituds de clau molt menor.
Mostrarem, doncs, les bones propietats d'aquests criptosistemes,
aixĂ com els requeriments bĂ sics per a que una corba
sigui criptogrĂ ficament Ăştil, estretament relacionat amb la seva
cardinalitat. Revisarem alguns mètodes que permetin descartar
corbes no criptogrĂ ficament Ăştils, aixĂ com altres que permetin
obtenir corbes bones a partir d'una de donada. Finalment,
descriurem algunes aplicacions, com sĂłn el seu Ăşs en Targes
Intel.ligents i sistemes RFID, per concloure amb alguns avenços
recents en aquest camp.The relevance of elliptic curve cryptography has grown in recent
years, and today represents a cornerstone in many industrial
standards. Although elliptic curve variants of classical
cryptosystems such as RSA exist, the full potential of elliptic
curve cryptography is displayed in cryptosystems based on the
Discrete Logarithm Problem, such as ElGamal. For these, elliptic
curve cryptosystems guarantee the same security levels as their
finite field analogues, with the additional advantage of using
significantly smaller key sizes.
In this report we show the positive properties of elliptic curve
cryptosystems, and the requirements a curve must meet to be
useful in this context, closely related to the number of points.
We survey methods to discard cryptographically uninteresting
curves as well as methods to obtain other useful curves from
a given one. We then describe some real world applications
such as Smart Cards and RFID systems and conclude with a
snapshot of recent developments in the field
NTRU software implementation for constrained devices
The NTRUEncrypt is a public-key cryptosystem based on the shortest vector problem. Its main
characteristics are the low memory and computational requirements while providing a high
security level.
This document presents an implementation and optimization of the NTRU public-key cryptosys-
tem for constrained devices. Speci cally the NTRU cryptosystem has been implemented on the
ATMega128 and the ATMega163 microcontrollers.
This has turned in a major e ort in order to reduce the consumption of memory and op-
timize the computational resources. The di erent resulting optimizations have been compared
and evaluated throught the AVR Studio 4 [1]. The nal outcome has also been compared
with other published public-key cryptosystems as RSA or ECC showing the great performance
NTRUEncrypt is able to deliver at a surprising very low cost
Elliptic Curve Cryptography: The Serpentine Course of a Paradigm Shift
Over a period of sixteen years elliptic curve cryptography went from being an approach that many people mistrusted or misunderstood to being a public key technology that enjoys almost unquestioned acceptance. We describe the sometimes surprising twists and turns in this paradigm shift, and compare this story with the commonly accepted Ideal Model
of how research and development function in cryptography. We also
discuss to what extent the ideas in the literature on social
construction of technology can contribute to a better understanding
of this history
A double large prime variation for small genus hyperelliptic index calculus
International audienceIn this article, we examine how the index calculus approach for computing discrete logarithms in small genus hyperelliptic curves can be improved by introducing a double large prime variation. Two algorithms are presented. The first algorithm is a rather natural adaptation of the double large prime variation to the intended context. On heuristic and experimental grounds, it seems to perform quite well but lacks a complete and precise analysis. Our second algorithm is a considerably simplified variant, which can be analyzed easily. The resulting complexity improves on the fastest known algorithms. Computer experiments show that for hyperelliptic curves of genus three, our first algorithm surpasses Pollard's Rho method even for rather small field sizes
Cryptography Through the Lens of Group Theory
Cryptography has been around for many years, and mathematics has been around even longer. When the two subjects were combined, however, both the improvements and attacks on cryptography were prevalent. This paper introduces and performs a comparative analysis of two versions of the ElGamal cryptosystem, both of which use the specific field of mathematics known as group theory