8 research outputs found
Algorithms and cryptographic protocols using elliptic curves
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, com els de tipus ElGamal. En aquest cas, els
criptosistemes el.líptics 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,
així com els requeriments bàsics per a que una corba
sigui criptogràficament útil, estretament relacionat amb la seva
cardinalitat. Revisarem alguns mètodes que permetin descartar
corbes no criptogràficament útils, així com altres que permetin
obtenir corbes bones a partir d'una de donada. Finalment,
descriurem algunes aplicacions, com són el seu ús 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
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
Pairing-based public-key encryption schemes with backward-and-forward security
Identity-based cryptosystems utilize some arbitrary strings as the participants' public key in the underlying system. The encryptioner will not need to obtain the decryptioner's certificate. That will simplify the certificate management. Therefore, it is still interesting to propose some new identity-based encryption schemes. In this paper we will propose two new different constructions, i.e. receiptor-oriented encryption schemes. They are both identity-based encryption schemes and also based on pairings. The proposed encryption schemes have a new advantage, i.e. backward-and-forward security. In addition, we provide the security analysis for the proposed schemes
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
A Public Key Cryptosystem Based on Singular Cubic Curve
An efficient and semantically secure public key cryptosystem based on singular cubic curve is proposed in this paper. It is about two times faster than the cryptosystem of David at the same security label and more efficient than the Koyama scheme at high security level. Further, the partially known plaintext attack and the linearly related plaintext attacks are analyzed and concluded that those are not possible in the proposed scheme
Efficient cryptosystem for universally verifiable mixnets
Projecte final de carrera realitzat en col.laboració amb Scytl Secure Electronic Votin
An efficient semantically secure elliptic curve cryptosystem based on KMOV scheme
We propose an elliptic curve scheme over the ring Z n 2, which is efficient and semantically secure in the standard model. There appears to be no previous elliptic curve cryptosystem based on factoring that enjoys both of these properties. KMOV scheme has been used as an underlying primitive to obtain efficiency and probabilistic encryption. Semantic security of the scheme is based on a new decisional assumption, namely, the Decisional Small-x e-Multiples Assumption. Confidence on this assumption is also discussed