Articles de revista
http://hdl.handle.net/2117/3529
20171017T22:41:48Z

On the optimization of bipartite secret sharing schemes
http://hdl.handle.net/2117/105969
On the optimization of bipartite secret sharing schemes
Farràs Ventura, Oriol; MetcalfBurton, Jessica Ruth; Padró Laimon, Carles; Vázquez González, Leonor
Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and longstanding open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.
20170629T08:25:56Z
Farràs Ventura, Oriol
MetcalfBurton, Jessica Ruth
Padró Laimon, Carles
Vázquez González, Leonor
Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and longstanding open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.

Ideal hierarchical secret sharing schemes
http://hdl.handle.net/2117/105968
Ideal hierarchical secret sharing schemes
Farràs Ventura, Oriol; Padró Laimon, Carles
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.
20170629T08:18:46Z
Farràs Ventura, Oriol
Padró Laimon, Carles
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.

Finding lower bounds on the complexity of secret sharing schemes by linear programming
http://hdl.handle.net/2117/105967
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Padró Laimon, Carles; Vázquez González, Leonor; Yang, An
Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and longstanding open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants.
By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program nonShannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of nonrepresentable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme
20170629T07:37:30Z
Padró Laimon, Carles
Vázquez González, Leonor
Yang, An
Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and longstanding open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants.
By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program nonShannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of nonrepresentable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme

Signcryption schemes with threshold unsigncryption, and applications
http://hdl.handle.net/2117/105873
Signcryption schemes with threshold unsigncryption, and applications
Herranz Sotoca, Javier; Ruiz, Alexandre; Sáez Moreno, Germán
The goal of a signcryption scheme is to achieve the same functionalities as encryption and signature together, but in a more efficient way than encrypting and signing separately. To increase security and reliability in some applications, the unsigncryption phase can be distributed among a group of users, through a (t, n)threshold process. In this work we consider this task of threshold unsigncryption, which has received very few attention from the cryptographic literature up to now (maybe surprisingly, due to its potential applications). First we describe in detail the security requirements that a scheme for such a task should satisfy: existential unforgeability and indistinguishability, under insider chosen message/ciphertext attacks, in a multiuser setting. Then we show that generic constructions of signcryption schemes (by combining encryption and signature schemes) do not offer this level of security in the scenario of threshold unsigncryption. For this reason, we propose two new protocols for threshold unsigncryption, which we prove to be secure, one in the random oracle model and one in the standard model. The two proposed schemes enjoy an additional property that can be very useful. Namely, the unsigncryption protocol can be divided in two phases: a first one where the authenticity of the ciphertext is verified, maybe by a single party; and a second one where the ciphertext is decrypted by a subset of t receivers, without using the identity of the sender. As a consequence, the schemes can be used in applications requiring some level of anonymity, such as electronic auctions.
The final publication is available at link.springer.com
20170626T15:08:46Z
Herranz Sotoca, Javier
Ruiz, Alexandre
Sáez Moreno, Germán
The goal of a signcryption scheme is to achieve the same functionalities as encryption and signature together, but in a more efficient way than encrypting and signing separately. To increase security and reliability in some applications, the unsigncryption phase can be distributed among a group of users, through a (t, n)threshold process. In this work we consider this task of threshold unsigncryption, which has received very few attention from the cryptographic literature up to now (maybe surprisingly, due to its potential applications). First we describe in detail the security requirements that a scheme for such a task should satisfy: existential unforgeability and indistinguishability, under insider chosen message/ciphertext attacks, in a multiuser setting. Then we show that generic constructions of signcryption schemes (by combining encryption and signature schemes) do not offer this level of security in the scenario of threshold unsigncryption. For this reason, we propose two new protocols for threshold unsigncryption, which we prove to be secure, one in the random oracle model and one in the standard model. The two proposed schemes enjoy an additional property that can be very useful. Namely, the unsigncryption protocol can be divided in two phases: a first one where the authenticity of the ciphertext is verified, maybe by a single party; and a second one where the ciphertext is decrypted by a subset of t receivers, without using the identity of the sender. As a consequence, the schemes can be used in applications requiring some level of anonymity, such as electronic auctions.

On the efficiency of revocation in RSAbased anonymous systems
http://hdl.handle.net/2117/104254
On the efficiency of revocation in RSAbased anonymous systems
Fueyo, María; Herranz Sotoca, Javier
The problem of revocation in anonymous authentication systems is subtle and has motivated a lot of work. One of the preferable solutions consists in maintaining either a whitelist LW of nonrevoked users or a blacklist LB of revoked users, and then requiring users to additionally prove, when authenticating themselves, that they are in LW (membership proof) or that they are not in LB (nonmembership proof). Of course, these additional proofs must not break the anonymity properties of the system, so they must be zeroknowledge proofs, revealing nothing about the identity of the users. In this paper, we focus on the RSAbased setting, and we consider the case of nonmembership proofs to blacklists L = LB. The existing solutions for this setting rely on the use of universal dynamic accumulators; the underlying zeroknowledge proofs are bit complicated, and thus their efficiency; although being independent from the size of the blacklist L, seems to be improvable. Peng and Bao already tried to propose simpler and more efficient zeroknowledge proofs for this setting, but we prove in this paper that their protocol is not secure. We fix the problem by designing a new protocol, and formally proving its security properties. We then compare the efficiency of the new zeroknowledge nonmembership protocol with that of the protocol, when they are integrated with anonymous authentication systems based on RSA (notably, the IBM product Idemix for anonymous credentials). We discuss for which values of the size k of the blacklist L, one protocol is preferable to the other one, and we propose different ways to combine and implement the two protocols.
c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works."
20170510T09:52:33Z
Fueyo, María
Herranz Sotoca, Javier
The problem of revocation in anonymous authentication systems is subtle and has motivated a lot of work. One of the preferable solutions consists in maintaining either a whitelist LW of nonrevoked users or a blacklist LB of revoked users, and then requiring users to additionally prove, when authenticating themselves, that they are in LW (membership proof) or that they are not in LB (nonmembership proof). Of course, these additional proofs must not break the anonymity properties of the system, so they must be zeroknowledge proofs, revealing nothing about the identity of the users. In this paper, we focus on the RSAbased setting, and we consider the case of nonmembership proofs to blacklists L = LB. The existing solutions for this setting rely on the use of universal dynamic accumulators; the underlying zeroknowledge proofs are bit complicated, and thus their efficiency; although being independent from the size of the blacklist L, seems to be improvable. Peng and Bao already tried to propose simpler and more efficient zeroknowledge proofs for this setting, but we prove in this paper that their protocol is not secure. We fix the problem by designing a new protocol, and formally proving its security properties. We then compare the efficiency of the new zeroknowledge nonmembership protocol with that of the protocol, when they are integrated with anonymous authentication systems based on RSA (notably, the IBM product Idemix for anonymous credentials). We discuss for which values of the size k of the blacklist L, one protocol is preferable to the other one, and we propose different ways to combine and implement the two protocols.

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.
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
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.
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.
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
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