Articles de revista
http://hdl.handle.net/2117/3529
Mon, 24 Apr 2017 23:15:12 GMT
20170424T23:15:12Z

Efficient cryptosystems from 2kth power residue symbols
http://hdl.handle.net/2117/103661
Efficient cryptosystems from 2kth power residue symbols
Herranz Sotoca, Javier; Libert, Benoit; Joye, Marc; Benhamouda, Fabrice
Goldwasser and Micali (J Comput Syst Sci 28(2):270–299, 1984) highlighted the importance of randomizing the plaintext for publickey encryption and introduced the notion of semantic security. They also realized a cryptosystem meeting this security notion under the standard complexity assumption of deciding quadratic residuosity modulo a composite number. The Goldwasser–Micali cryptosystem is simple and elegant but is quite wasteful in bandwidth when encrypting large messages. A number of works followed to address this issue and proposed various modifications. This paper revisits the original Goldwasser–Micali cryptosystem using 2kth power residue symbols. The soobtained cryptosystems appear as a very natural generalization for k=2 (the case k=1 corresponds exactly to the Goldwasser–Micali cryptosystem). Advantageously, they are efficient in both bandwidth and speed; in particular, they allow for fast decryption. Further, the cryptosystems described in this paper inherit the useful features of the original cryptosystem (like its homomorphic property) and are shown to be secure under a similar complexity assumption. As a prominent application, this paper describes an efficient lossy trapdoor functionbased thereon.
Mon, 24 Apr 2017 10:25:48 GMT
http://hdl.handle.net/2117/103661
20170424T10:25:48Z
Herranz Sotoca, Javier
Libert, Benoit
Joye, Marc
Benhamouda, Fabrice
Goldwasser and Micali (J Comput Syst Sci 28(2):270–299, 1984) highlighted the importance of randomizing the plaintext for publickey encryption and introduced the notion of semantic security. They also realized a cryptosystem meeting this security notion under the standard complexity assumption of deciding quadratic residuosity modulo a composite number. The Goldwasser–Micali cryptosystem is simple and elegant but is quite wasteful in bandwidth when encrypting large messages. A number of works followed to address this issue and proposed various modifications. This paper revisits the original Goldwasser–Micali cryptosystem using 2kth power residue symbols. The soobtained cryptosystems appear as a very natural generalization for k=2 (the case k=1 corresponds exactly to the Goldwasser–Micali cryptosystem). Advantageously, they are efficient in both bandwidth and speed; in particular, they allow for fast decryption. Further, the cryptosystems described in this paper inherit the useful features of the original cryptosystem (like its homomorphic property) and are shown to be secure under a similar complexity assumption. As a prominent application, this paper describes an efficient lossy trapdoor functionbased thereon.

The Kernel Matrix DiffieHellman Assumption
http://hdl.handle.net/2117/102936
The Kernel Matrix DiffieHellman Assumption
Morillo Bosch, M. Paz; Rafols Salvador, Carla; Villar Santos, Jorge Luis
We put forward a new family of computational assumptions, the Kernel Matrix DiffieHellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional DiffieHellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The kDecisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some blackbox reductions between flexible problems (i.e., computational problems with a non unique solution).
The final publication is available at link.springer.com
Tue, 28 Mar 2017 09:12:06 GMT
http://hdl.handle.net/2117/102936
20170328T09:12:06Z
Morillo Bosch, M. Paz
Rafols Salvador, Carla
Villar Santos, Jorge Luis
We put forward a new family of computational assumptions, the Kernel Matrix DiffieHellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional DiffieHellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The kDecisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some blackbox reductions between flexible problems (i.e., computational problems with a non unique solution).

Natural generalizations of threshold secret sharing
http://hdl.handle.net/2117/100003
Natural generalizations of threshold secret sharing
Farràs Ventura, Oriol; Padró Laimon, Carles; Xing, Chaoping; Yang, An
We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.
© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Wed, 25 Jan 2017 10:11:40 GMT
http://hdl.handle.net/2117/100003
20170125T10:11:40Z
Farràs Ventura, Oriol
Padró Laimon, Carles
Xing, Chaoping
Yang, An
We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.

Soft and hard modelling methods for decovolution of mixtures of Raman spectra for pigment analysis: a qualitative and quantitative approach
http://hdl.handle.net/2117/98513
Soft and hard modelling methods for decovolution of mixtures of Raman spectra for pigment analysis: a qualitative and quantitative approach
Coma, L; Breitman Mansilla, Mónica Celia; Ruiz Moreno, Sergio
Raman spectroscopy provides a means for the detection and identification of pictorial materials on artworks. As a nondestructive, applicable in situ and nonambiguous technique, it is one of the most preferred to analyse the pigmentation of any kind of artwork: from paintings [1] and papyrus [2] to polychromes on woods [3]. A common problem, however, is lack of spatial resolution on some systems due to large focal distances, which degrades the theoretical high resolution of the system, which involves the resolution of mixtures of individual Raman spectra. In this work, we will present the advantages and disadvantages of two methods for the separation of mixtures of Raman spectra [4] and [5], and we present a new solution to overcome the problems of the above. To such an end, we will provide qualitative (identification of the species) and quantitative (determine their concentration profiles) results of the methods. The experimental analyses have been carried out in two steps: first we calibrate the methods with known mixtures of two compounds prepared in the laboratory. Second, we test the methods with a real artwork supposed to be from ‘El Greco’. Procedures to minimise problems, such as extreme fluorescence and noise, that arise on real artworks are also presented.
Fri, 16 Dec 2016 18:07:04 GMT
http://hdl.handle.net/2117/98513
20161216T18:07:04Z
Coma, L
Breitman Mansilla, Mónica Celia
Ruiz Moreno, Sergio
Raman spectroscopy provides a means for the detection and identification of pictorial materials on artworks. As a nondestructive, applicable in situ and nonambiguous technique, it is one of the most preferred to analyse the pigmentation of any kind of artwork: from paintings [1] and papyrus [2] to polychromes on woods [3]. A common problem, however, is lack of spatial resolution on some systems due to large focal distances, which degrades the theoretical high resolution of the system, which involves the resolution of mixtures of individual Raman spectra. In this work, we will present the advantages and disadvantages of two methods for the separation of mixtures of Raman spectra [4] and [5], and we present a new solution to overcome the problems of the above. To such an end, we will provide qualitative (identification of the species) and quantitative (determine their concentration profiles) results of the methods. The experimental analyses have been carried out in two steps: first we calibrate the methods with known mixtures of two compounds prepared in the laboratory. Second, we test the methods with a real artwork supposed to be from ‘El Greco’. Procedures to minimise problems, such as extreme fluorescence and noise, that arise on real artworks are also presented.

La espectroscopía raman aplicada a la identificación de materiales pictóricos
http://hdl.handle.net/2117/97876
La espectroscopía raman aplicada a la identificación de materiales pictóricos
Ruiz Moreno, Sergio; Yúfera Gomez, José Manuel; Soneira Ferrando, M. José; Breitman Mansilla, Mónica Celia; Morillo Bosch, M. Paz; Gràcia Rivas, Ignacio
Wed, 07 Dec 2016 14:46:16 GMT
http://hdl.handle.net/2117/97876
20161207T14:46:16Z
Ruiz Moreno, Sergio
Yúfera Gomez, José Manuel
Soneira Ferrando, M. José
Breitman Mansilla, Mónica Celia
Morillo Bosch, M. Paz
Gràcia Rivas, Ignacio

An algebraic framework for Diffie–Hellman assumptions
http://hdl.handle.net/2117/91050
An algebraic framework for Diffie–Hellman assumptions
Escala Ribas, Alex; Herold, Gottfried; Kiltz, Eike; Ràfols Salvador, Carla; Villar Santos, Jorge Luis
We put forward a new algebraic framework to generalize and analyze DiffieHellman like Decisional Assumptions which allows us to argue about security and applications by considering only algebraic properties. Our D`,kMDDH assumption states that it is hard to decide whether a vector in ¿ìs linearly dependent of the columns of some matrix in ¿`×k sampled according to distribution D`,k. It covers known assumptions such as DDH, 2Lin (linear assumption), and kLin (the klinear assumption). Using our algebraic viewpoint, we can relate the generic hardness of our assumptions in mlinear groups to the irreducibility of certain polynomials which describe the output of D`,k. We use the hardness results to find new distributions for which the D`,kMDDHAssumption holds generically in mlinear groups. In particular, our new assumptions 2SCasc and 2ILin are generically hard in bilinear groups and, compared to 2Lin, have shorter description size, which is a relevant parameter for efficiency in many applications. These results support using our new assumptions as natural replacements for the 2Lin Assumption which was already used in a large number of applications. To illustrate the conceptual advantages of our algebraic framework, we construct several fundamental primitives based on any MDDHAssumption. In particular, we can give many instantiations of a primitive in a compact way, including publickey encryption, hashproof systems, pseudorandom functions, and GrothSahai NIZK and NIWI proofs. As an independent contribution we give more efficient NIZK and NIWI proofs for membership in a subgroup of ¿` . The results imply very significant efficiency improvements for a large number of schemes.
Tue, 25 Oct 2016 09:11:30 GMT
http://hdl.handle.net/2117/91050
20161025T09:11:30Z
Escala Ribas, Alex
Herold, Gottfried
Kiltz, Eike
Ràfols Salvador, Carla
Villar Santos, Jorge Luis
We put forward a new algebraic framework to generalize and analyze DiffieHellman like Decisional Assumptions which allows us to argue about security and applications by considering only algebraic properties. Our D`,kMDDH assumption states that it is hard to decide whether a vector in ¿ìs linearly dependent of the columns of some matrix in ¿`×k sampled according to distribution D`,k. It covers known assumptions such as DDH, 2Lin (linear assumption), and kLin (the klinear assumption). Using our algebraic viewpoint, we can relate the generic hardness of our assumptions in mlinear groups to the irreducibility of certain polynomials which describe the output of D`,k. We use the hardness results to find new distributions for which the D`,kMDDHAssumption holds generically in mlinear groups. In particular, our new assumptions 2SCasc and 2ILin are generically hard in bilinear groups and, compared to 2Lin, have shorter description size, which is a relevant parameter for efficiency in many applications. These results support using our new assumptions as natural replacements for the 2Lin Assumption which was already used in a large number of applications. To illustrate the conceptual advantages of our algebraic framework, we construct several fundamental primitives based on any MDDHAssumption. In particular, we can give many instantiations of a primitive in a compact way, including publickey encryption, hashproof systems, pseudorandom functions, and GrothSahai NIZK and NIWI proofs. As an independent contribution we give more efficient NIZK and NIWI proofs for membership in a subgroup of ¿` . The results imply very significant efficiency improvements for a large number of schemes.

Extending BrickellDavenport theorem to nonperfect secret sharing schemes
http://hdl.handle.net/2117/86923
Extending BrickellDavenport theorem to nonperfect secret sharing schemes
Farràs Ventura, Oriol; Padró Laimon, Carles
One important result in secret sharing is the BrickellDavenport Theorem: every ideal perfect secret sharing scheme de nes a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory de nition of ideal secret sharing scheme for the general case, in which nonperfect schemes are considered as well. Without providing another unsatisfactory de nition of ideal nonperfect secret sharing scheme, we present a generalization of the BrickellDavenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.
Wed, 11 May 2016 10:34:11 GMT
http://hdl.handle.net/2117/86923
20160511T10:34:11Z
Farràs Ventura, Oriol
Padró Laimon, Carles
One important result in secret sharing is the BrickellDavenport Theorem: every ideal perfect secret sharing scheme de nes a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory de nition of ideal secret sharing scheme for the general case, in which nonperfect schemes are considered as well. Without providing another unsatisfactory de nition of ideal nonperfect secret sharing scheme, we present a generalization of the BrickellDavenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.

On secret sharing with nonlinear product reconstruction
http://hdl.handle.net/2117/86921
On secret sharing with nonlinear product reconstruction
Cascudo, Ignacio; Cramer, Ronald; Mirandola, Diego; Padró Laimon, Carles; Xing, Chaoping
Multiplicative linear secret sharing is a fundamental notion in the area of secure multi party computation (MPC) and, since recently, in the area of twoparty cryptography as well. In a nutshell, this notion guarantees that \the product of two secrets is obtained as a linear function of the vector consisting of the coordinatewise product of two respective sharevectors
Wed, 11 May 2016 10:22:41 GMT
http://hdl.handle.net/2117/86921
20160511T10:22:41Z
Cascudo, Ignacio
Cramer, Ronald
Mirandola, Diego
Padró Laimon, Carles
Xing, Chaoping
Multiplicative linear secret sharing is a fundamental notion in the area of secure multi party computation (MPC) and, since recently, in the area of twoparty cryptography as well. In a nutshell, this notion guarantees that \the product of two secrets is obtained as a linear function of the vector consisting of the coordinatewise product of two respective sharevectors

Attributebased versions of Schnorr and ElGamal
http://hdl.handle.net/2117/86060
Attributebased versions of Schnorr and ElGamal
Herranz Sotoca, Javier
We design in this paper the first attributebased cryptosystems that work in the classical discrete logarithm, pairingfree, setting. The attributebased signature scheme can be seen as an extension of Schnorr signatures, with adaptive security relying on the discrete logarithm assumption, in the random oracle model. The attributebased encryption schemes can be seen as extensions of ElGamal cryptosystem, with adaptive security relying on the decisional Diffie–Hellman assumption, in the standard model. The proposed schemes are secure only in a bounded model: the systems admit L secret keys, at most, for a bound L that must be fixed in the setup of the systems. The efficiency of the cryptosystems, later, depends on this bound L. Although this is an important drawback that can limit the applicability of the proposed schemes in some reallife applications, it turns out that the bounded security of our keypolicy attributebased encryption scheme (in particular, with L=1L=1) is enough to implement the generic transformation of Parno, Raykova and Vaikuntanathan at TCC’2012. As a direct result, we obtain a protocol for the verifiable delegation of computation of boolean functions, which does not employ pairings or lattices, and whose adaptive security relies on the decisional Diffie–Hellman assumption.
The final publication is available at Springer via http://dx.doi.org/10.1007/s0020001502707
Thu, 21 Apr 2016 12:03:25 GMT
http://hdl.handle.net/2117/86060
20160421T12:03:25Z
Herranz Sotoca, Javier
We design in this paper the first attributebased cryptosystems that work in the classical discrete logarithm, pairingfree, setting. The attributebased signature scheme can be seen as an extension of Schnorr signatures, with adaptive security relying on the discrete logarithm assumption, in the random oracle model. The attributebased encryption schemes can be seen as extensions of ElGamal cryptosystem, with adaptive security relying on the decisional Diffie–Hellman assumption, in the standard model. The proposed schemes are secure only in a bounded model: the systems admit L secret keys, at most, for a bound L that must be fixed in the setup of the systems. The efficiency of the cryptosystems, later, depends on this bound L. Although this is an important drawback that can limit the applicability of the proposed schemes in some reallife applications, it turns out that the bounded security of our keypolicy attributebased encryption scheme (in particular, with L=1L=1) is enough to implement the generic transformation of Parno, Raykova and Vaikuntanathan at TCC’2012. As a direct result, we obtain a protocol for the verifiable delegation of computation of boolean functions, which does not employ pairings or lattices, and whose adaptive security relies on the decisional Diffie–Hellman assumption.

Secret sharing, rank inequalities, and information inequalities
http://hdl.handle.net/2117/86051
Secret sharing, rank inequalities, and information inequalities
Martín Mollevi, Sebastià; Padró Laimon, Carles; Yang, An
Beimel and Orlov proved that all information
inequalities on four or five variables, together with all information
inequalities on more than five variables that are known to date,
provide lower bounds on the size of the shares in secret sharing
schemes that are at most linear on the number of participants.
We present here another two negative results about the power of
information inequalities in the search for lower bounds in secret
sharing. First, we prove that all information inequalities on a
bounded number of variables can only provide lower bounds that
are polynomial on the number of participants. Second, we prove
that the rank inequalities that are derived from the existence of
two common informations can provide only lower bounds that
are at most cubic in the number of participants.
© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Thu, 21 Apr 2016 11:07:34 GMT
http://hdl.handle.net/2117/86051
20160421T11:07:34Z
Martín Mollevi, Sebastià
Padró Laimon, Carles
Yang, An
Beimel and Orlov proved that all information
inequalities on four or five variables, together with all information
inequalities on more than five variables that are known to date,
provide lower bounds on the size of the shares in secret sharing
schemes that are at most linear on the number of participants.
We present here another two negative results about the power of
information inequalities in the search for lower bounds in secret
sharing. First, we prove that all information inequalities on a
bounded number of variables can only provide lower bounds that
are polynomial on the number of participants. Second, we prove
that the rank inequalities that are derived from the existence of
two common informations can provide only lower bounds that
are at most cubic in the number of participants.