27 research outputs found
A new attack on the KMOVcryptosystem
In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring where is the product of two large unknown primes of equal bit-size. We consider KMOV with a public key where the exponent satisfies an equation , with unknown parameters , , . Using Diophantine approximations and lattice reduction techniques, we show that KMOV is insecure when , , are suitably small
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
clĂ ssics, com el RSA, el seu mĂ xim interĂšs 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
construĂŻts sobre el grup multiplicatiu d'un cos finit primer, perĂČ
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 Ăștil, estretament relacionat amb la seva
cardinalitat. Revisarem alguns mĂštodes que permetin descartar
corbes no criptogrĂ ficament Ăștils, aixĂ com altres que permetin
obtenir corbes bones a partir d'una de donada. Finalment,
descriurem algunes aplicacions, com sĂłn el seu Ășs 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
A cryptanalytic attack on the LUC cryptosystem using continued fractions
The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences.
In this paper we extend the Verheul - van Tilborg and Dujella variants
of the Wiener attack on RSA to the LUC cryptosystem. We describe an
algorithm for finding a secret key of the form , for some and nonnegative integers and , using continued fractions.
We derive bounds for and using results on Diophantine approximations
An efficient probabilistic public-key cryptosystem over quadratic fields quotients
AbstractWe present a new probabilistic cryptosystem working in quadratic fields quotients. Computation in such objects can be done efficiently with Lucas sequences which help to design a fast system. The security of the scheme is based on the LUC problem and its semantic security on a new decisional problem. This system appears to be an alternative to schemes based on the RSA primitive and has a full computational cost smaller than the El Gamal EC cryptosystem
A cryptanalytic attack on the LUC cryptosystem using continued fractions
The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences.
In this paper we extend the Verheul - van Tilborg and Dujella variants
of the Wiener attack on RSA to the LUC cryptosystem. We describe an
algorithm for finding a secret key of the form , for some and nonnegative integers and , using continued fractions.
We derive bounds for and using results on Diophantine approximations
A KEY EXCHANGE PROTOCOL USING CONJUGACY PROBLEM IN THE DIVISION SEMIRINGS
In this article, we present a new key exchange protocol which works in the division semiring. We prove that the protocol meets the security of key establishment based on the conjugacy search problem and security attribute also discussed
A new encryption algorithm over elliptic curve
Various public key encryption systems have been proposed in modern information techology. Some of them have also been used in various applications, such as E-commerce and mobile database. This paper proposes two secure receipt oriented encryption systems. The decryptioner's private keys could be changed with the different time periods. This case would be very useful in some practical scenarios, for instance, in a mobile database environment. Besides the semantic security, the proposed schemes have the backward-and-future security, a new security requirement for semantically secure encryption schemes. In terms of construction, the two schemes are based on the pairings over elliptic curves. Also, this paper provides a heuristic security analysis for the underlying system