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AG Codes and Kryptographie Show image information

AG Codes and Kryptographie

Pairing-based Cryptography

Pairings are bilinear maps that enable the realization of several cryptographic primitives. Hence pairing-based cryptography offers approaches for numerous interesting problems, such as

Pairing-based cryptography was first known and utilized in the field of identity-based cryptography. Identity-based cryptography deals with special asymmetric encryption and signature schemes. In identity-based schemes, the public key can be directly derived from the owner's identity. For example, this would allow you to encrypt an email using a key locally derived from the recipient's email address. Hence there is no need for the usual process of contacting a central key authority to retrieve the recipient's public key. Instead, the key authority is used to generate the private keys, with the added benefit that it only has be contacted once by every user. Since the key authority generates all private keys in such a system, it represents an especially lucrative target for malicious attacks.

In our group, we develop new schemes in the field of pairing-based cryptography. Furthermore, we analyze implementations of such schemes with respect to efficiency and security.

Attribute-based Cryptography

Development of the so-called functional encryption schemes is one of the main visions of modern cryptography. These encryption schemes should overcome the main disadvantages of the conventional encryption schemes, namely that the data are encrypted for a certain addressee and the access to the encrypted data is all or nothing. In the context of functional encryption schemes every user receives a secret key which is provided with certain function according to the access rights of the user. The data are encrypted only once and the user learn only the evaluation of their function on data and not necessarily the data themselves. Whereas in general it is not even clear how to define the security requirements for this kind of encryption schemes, efficient encryption schemes for different restricted classes of functions are known. Attribute-based encryption (ABE) is a special case of functional encryption.

An attribute-based system requires a central authority which sets the system up and provides the user with their secret keys. In the key-policy ABE (KP-ABE), the owner of data defines a subset of predefined attributes for each data and encrypts it once using this set. In order to provide access to the encrypted data, every user in the system receives a user secret key provided with an access policy according to the rights of the user. The key policies are Boolean formulas over the predefined attributes. A user will be able to decrypt a ciphertext if and only if the attributes of the ciphertext satisfy the policy of his/her key. In the ciphertext-policy ABE (CP-ABE) the roles of attributes and policies are reversed. That is, the data are encrypted under the access policies and the keys are provided with sets of attributes. Systems based on ABE have to model the access rights of the user in terms of attributes and access policies depending on concrete scenarios and concrete access pattern.

In our example, the manager of Map Data Center wants to ensure a fine-grained access control to the road maps for its customers (routing services). Therefore, restricting access to the full data base, to the maps of continents, and to the maps of each single country will be realized. Each map is encrypted once with an appropriate policy. For example, the map of Germany's roads is encrypted with the policy "World OR Europe OR Germany". Every customer who gets a key with one of the attributes "World", "Europe", or "Germany" will be able to decrypt the appropriate ciphertext and obtain access to Germany's road maps. Thus, the access control is managed by the encryption itself.

Anonymous Group Signatures and Reputation Systems

In standard signature schemes, the sender computes a signature on his message using his secret key. The receiver can check, using the signature and the sender's public key, that the message was indeed composed by the sender and that it was not modified in transit. To achieve this, the public key must uniquely identify the sender. However, in many scenarios this strict identification is not necessary or even desirable. Whenever an application only needs assurance that the sender belongs to a certain group of possible senders, anonymous group signatures can be used.

Anonymous group signatures allow each member of a group to sign messages without disclosing their identity. For this, each group member gets their own private key that is associated to the group's public key. In contrast to standard digital signature schemes, the message receiver can only check whether some group member signed the message, but not which specific member did it. The actual signer can only be determined by a special entity in the system (the group manager).

Besides anonymity, other properties of group signatures play an important role in some applications. For example, it may be useful to restrict the number of messages that each group member can sign. Furthermore, techniques for revoking group membership are important. In particular, these and other extensions of group signatures can be used to construct anonymous reputation systems.

Reputation systems are an important tool to allow customers and providers of goods and services to gather useful information about past transactions. In order to receive trustworthy, reliable, and honest ratings, a reputation system should guarantee the customer anonymity and at the same ensure that no customer can submit more than one rating. Of course the ratings should be publicly verifiable by third parties.

Some of the required properties for reputation systems are already known for group signatures. Some, however, are not. For example, a reputation system does not consist of a single group, but rather there is a group for each rateable product (or service). For the security of reputation systems these different groups cannot be analyzed in isolation.

The goal of this research area is the extension of group signature schemes and the construction of anonymous reputation system on the basis of group signatures.

Anonymous Credential Systems

Wie können wir einem Apotheker die Rezeptbesitzerlaubnis eines Patienten versichern ohne die Identität des Patienten zu nennen? Wie können wir als Autofahrer unsere Fahrlizens beweisen, ohne unseren Namen Preis zu geben? Für die Umsetzung dieser Szenarien benötigen wir anonyme Zugangsberechtigungssysteme. In Zugangsberechtigungssystemen erwerben Nutzer attribut-zertifizierte Zugangsberechtigungen. Diese Zugangsberechtigungen werden von Nutzern verwendet, um Zugriff auf bestimmte Ressourcen bzw. Services zu erhalten. Von besonderem Interesse sind Zugangsberechtigungssysteme, in denen Nutzern Attribute und Ressourcen-Policies über diesen Attributen zugewiesen werden. Der Nutzer kann auf eine Ressource zugreifen, wenn er nachweisen kann, dass seine Attribute die Policy der Ressource erfüllen. Wir interessieren uns für anonyme Zugangsberechtigungssysteme, deren Ressourcen-Policies besonders komplexe Strukturen besitzen, sogenannte feingranulare Zugangsberechtigungssysteme.

Damit ein Zugangsberechtigungssystem sicher ist, soll der Ressourcenzugriff eines Nutzers möglich sein, ohne die Identität dieses Nutzers zu erkennen. Neben der Anonymität der Nutzer soll auch garantiert werden, dass verschiedene Nutzer ihre Attribute nicht kombinieren können, um Zugriff auf eine Ressource zu bekommen. Für die Konstruktion sicherer Zugangsberechtigungssysteme, werden u.a. auf Paarungen basierte digitale Signaturverfahren verwendet.

Das Ziel dieses Forschungsbereichs ist die mathematisch-beweisbare Konstruktion sicherer feingranularer Zugangsberechtigungssysteme.

Secure and Efficient Implementations

In den vergangenen Jahren wurden aufgrund der vielzähligen Anwendungsmöglichkeiten immer effizientere Algorithmen für die Berechnung von Paarungen entwickelt. Mittlerweile lassen sich Paarungen sogar in vertretbarer Zeit auf in ihren Ressourcen beschränkten Systemen, wie zum Beispiel Chipkarten berechnen. Dies ist besonders dann interessant, wenn die geheimen Schlüssel der Verfahren physikalisch gegen Angreifer geschütz werden müssen. Einem Angreifer mit physikalischem Zugriff auf die ausführende Hardware eines Verfahrens bieten sich zahlreiche Angriffspunkte, die in den Sicherheitsbeweisen der Verfahren normalerweise nicht berücksichtigt werden. Ein solcher, sogenannter Seitenkanalangreifer könnte zum Beispiel versuchen Informationen über den geheimen Schlüssel zu erlangen, indem er aktiv die Ausführung des Algorithmus manipuliert oder passiv Messgrößen wie Energieverbrauch und Ausführungszeit beobachtet.

Der Definitionsbereich einer Paarung sind Untergruppen einer elliptischen Kurve über einem endlichen Körper. Diese Strukturen bilden auch die Grundlagen für die Elliptische Kurven Kryptographie. Auf dem Gebiet der Seitenkanalresistenz Elliptischer Kurven Kryptographie gibt es bereits viele theoretische als auch praktische Ergebnisse. Teilweise lassen diese sich auch auf die paarungsbasierte Kryptographie übertragen. So können für aktive Angriffe die Fehlermechanismen, um die Ausführung eines Algorithmus zu manipulieren aus der Elliptischen Kurven Kryptographie auch hier angewandt werden. Für passive Angriffe lassen sich ebenfalls Analysemethoden übertragen, die aus Messwerten wie beispielsweise dem Energieverbrauch interessante Informationen extrahieren. Welche Manipulationen für einen Angreifer nützlich sind, und wie man aus den gewonnenen Informationen schließlich den geheimen Schlüssel eines Verfahrens extrahiert ist jedoch nicht einfach übertragbar. Dies liegt unter anderem an der komplizierteren Struktur der verwendeten Algorithmen und an der Rolle des geheimen Schlüssels für die Berechnung.

Ziel dieses Forschungsgebiets ist es die Sicherheit von paarungsbasierten Implementierungen zu verbessern und dazu relevante Seitenkanäle zu identifizieren und durch geeignete effiziente Gegenmaßnahmen zu schließen.

Publications


Open list in Research Information System

2018

Cloud Architectures for Searchable Encryption

J. Blömer, N. Löken, in: Proceedings of the 13th International Conference on Availability, Reliability and Security - ARES '18, ACM Press, 2018


Delegatable Attribute-based Anonymous Credentials from Dynamically Malleable Signatures

J. Blömer, J. Bobolz, in: ACNS 2018 Applied Cryptography & Network security, 2018

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Abstract

In this paper, we introduce the notion of delegatable attribute-based anonymous credentials (DAAC). Such systems offer fine-grained anonymous access control and they give the credential holder the ability to issue more restricted credentials to other users. In our model, credentials are parameterized with attributes that (1) express what the credential holder himself has been certified and (2) define which attributes he may issue to others. Furthermore, we present a practical construction of DAAC. For this construction, we deviate from the usual approach of embedding a certificate chain in the credential. Instead, we introduce a novel approach for which we identify a new primitive we call dynamically malleable signatures (DMS) as the main ingredient. This primitive may be of independent interest. We also give a first instantiation of DMS with efficient protocols.


Fully-Featured Anonymous Credentials with Reputation System

K. Bemmann, J. Blömer, J. Bobolz, H. Bröcher, D. Diemert, F. Eidens, L. Eilers, J. Haltermann, J. Juhnke, B. Otour, L. Porzenheim, S. Pukrop, E. Schilling, M. Schlichtig, M. Stienemeier, in: Proceedings of the 13th International Conference on Availability, Reliability and Security - ARES '18, ACM Press, 2018


Practical, Anonymous, and Publicly Linkable Universally-Composable Reputation Systems

J. Blömer, F. Eidens, J. Juhnke, in: Topics in Cryptology - {CT-RSA} 2018 - The Cryptographers' Track at the {RSA} Conference 2018, Proceedings, Springer International Publishing, 2018, pp. 470-490


Voronoi Cells of Lattices with Respect to Arbitrary Norms

J. Blömer, K. Kohn, SIAM Journal on Applied Algebra and Geometry. (2018), pp. 314-338

DOI

2017

Attribute-Based Encryption as a Service for Access Control in Large-Scale Organizations

J. Blömer, P. Günther, V. Krummel, N. Löken, in: Foundations and Practice of Security, Springer International Publishing, 2017, pp. 3-17

DOI

Attribute-based Signatures using Structure Preserving Signatures

P. Bemmann. Attribute-based Signatures using Structure Preserving Signatures. 2017.


CCA-Security for Predicate Encryption Schemes

G. Liske, Universität Paderborn, 2017


EAX - An Authenticated Encryption Mode for Block Ciphers

D. Diemert, Universität Paderborn, 2017


Instantiating a Predicate Encryption Scheme via Pair Encodings

A. Ganesh Athreya, Universität Paderborn, 2017



Semantically Secure Attribute-based Searchable Encryption

D. Niehus. Semantically Secure Attribute-based Searchable Encryption. 2017.


Subtleties in Security Definitions for Predicate Encryption with Public Index

J. Blömer, G. Liske, in: Mathematical Aspects of Computer and Information Sciences, Springer International Publishing, 2017, pp. 438-453


2016

Commitment Schemes - Definitions, Variants, and Security

K.S. Bemmann, Universität Paderborn, 2016



Construction of Fully CCA-Secure Predicate Encryptions from Pair Encoding Schemes

J. Blömer, G. Liske, in: Proceedings of the CT-RSA 2016, 2016, pp. 431-447

DOI
Abstract

This paper presents a new framework for constructing fully CCA-secure predicate encryption schemes from pair encoding schemes. Our construction is the first in the context of predicate encryption which uses the technique of well-formedness proofs known from public key encryption. The resulting constructions are simpler and more efficient compared to the schemes achieved using known generic transformations from CPA-secure to CCA-secure schemes. The reduction costs of our framework are comparable to the reduction costs of the underlying CPA-secure framework. We achieve this last result by applying the dual system encryption methodology in a novel way.


Physical attacks on pairing-based cryptography

P. Günther, Universität Paderborn, 2016



Symmetric Anonymous Credentials with Protocols for Relations on Attributes

J. Hamm. Symmetric Anonymous Credentials with Protocols for Relations on Attributes. 2016.


2015

A group signature scheme based on the LSRW assumption

F. Heihoff, Universität Paderborn, 2015


A Group Signature Scheme with Distributed Group Management - An Application of Threshold Encryption

N. Löken. A Group Signature Scheme with Distributed Group Management - An Application of Threshold Encryption. 2015.


Anonymous and Publicly Linkable Reputation Systems

J. Blömer, J. Juhnke, C. Kolb, in: Proceedings of the 18th International Conference on Financial Cryptography and Data Security (FC), 2015, pp. 478--488

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Abstract

Reputation systems are used to compute and publish reputation scores for services or products. We consider reputation systems where users are allowed to rate products that they purchased previously. To obtain trustworthy reputations, they are allowed to rate these products only once. As long as users rate products once, they stay anonymous. Everybody is able to detect users deviating from the rate-products-only-once policy and the anonymity of such dishonest users can be revoked by a system manager. In this paper we present formal models for such reputation systems and their security. Based on group signatures presented by Boneh, Boyen, and Shacham we design an efficient reputation system that meets all our requirements.


Anonymous credential system based on q-Strong Diffie-Hellman Assumption

F. Eidens. Anonymous credential system based on q-Strong Diffie-Hellman Assumption. 2015.


Constructions of Fully Secure Predicate Encryption Schemes

P. Schleiter. Constructions of Fully Secure Predicate Encryption Schemes. 2015.


Efficient Attributes for Pairing-Based Anonymous Credentials

C. Stroh. Efficient Attributes for Pairing-Based Anonymous Credentials. 2015.


Efficient Verifier-Local Revocation for Anonymous Credentials

J. Bobolz. Efficient Verifier-Local Revocation for Anonymous Credentials. 2015.


Elektromagnetische Seitenkanalangriffe auf paarungsbasierte Kryptographie

B. Gerken. Elektromagnetische Seitenkanalangriffe auf paarungsbasierte Kryptographie. 2015.


Evaluation of Pairing Optimization for Embedded Platforms

M. Sosniak. Evaluation of Pairing Optimization for Embedded Platforms. 2015.



Number of Voronoi-relevant vectors in lattices with respect to arbitrary norms

K. Kohn. Number of Voronoi-relevant vectors in lattices with respect to arbitrary norms. 2015.


Protokolle zur authentifizierten Schüsselvereinbarung

T. Eisenhofer, Universität Paderborn, 2015


Short Group Signatures with Distributed Traceability

J. Blömer, J. Juhnke, N. Löken, in: Proceedings of the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS), 2015, pp. 166-180

DOI
Abstract

Group signatures, introduced by Chaum and van Heyst [15], are an important primitive in cryptography. In group signature schemes every group member can anonymously sign messages on behalf of the group. In case of disputes a dedicated opening manager is able to trace signatures - he can extract the identity of the producer of a given signature. A formal model for static group signatures schemes and their security is defined by Bellare, Micciancio, and Warinschi [4], the case of dynamic groups is considered by Bellare, Shi, and Zhang [5]. Both models define group signature schemes with a single opening manager. The main difference between these models is that the number of group members in static schemes is fixed, while in dynamic schemes group members can join the group over time.


Voronoi Cells of Lattices with Respect to Arbitrary Norms

J. Blömer, K. Kohn, Universität Paderborn, 2015

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Abstract

Motivated by the deterministic single exponential time algorithm of Micciancio and Voulgaris for solving the shortest and closest vector problem for the Euclidean norm, we study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms.On the positive side, we show that for strictly convex and smooth norms the geometry of Voronoi cells of lattices in any dimension is similar to the Euclidean case, i.e., the Voronoi cells are defined by the so-called Voronoi-relevant vectors and the facets of a Voronoi cell are in one-to-one correspondence with these vectors. On the negative side, we show that combinatorially Voronoi cells for arbitrary strictly convex and smooth norms are much more complicated than in the Euclidean case.In particular, we construct a family of three-dimensional lattices whose number of Voronoi-relevant vectors with respect to the l_3-norm is unbounded.Since the algorithm of Micciancio and Voulgaris and its run time analysis crucially dependonthefactthatfortheEuclidean normthenumber of Voronoi-relevant vectors is single exponential in the lattice dimension, this indicates that the techniques of Micciancio and Voulgaris cannot be extended to achieve deterministic single exponential time algorithms for lattice problems with respect to arbitrary l_p-norms.


2014

A Practical Second-Order Fault Attack against a Real-World Pairing Implementation

J. Blömer, R. Gomes da Silva, P. Günther, J. Krämer, J. Seifert, in: Proceedings of Fault Tolerance and Diagnosis in Cryptography(FDTC), 2014, pp. 123--136

DOI
Abstract

Several fault attacks against pairing-based cryptography have been described theoretically in recent years. Interestingly, none of these have been practically evaluated. We accomplished this task and prove that fault attacks against pairing-based cryptography are indeed possible and are even practical — thus posing a serious threat. Moreover, we successfully conducted a second-order fault attack against an open source implementation of the eta pairing on an AVR XMEGA A1. We injected the first fault into the computation of the Miller Algorithm and applied the second fault to skip the final exponentiation completely. We introduce a low-cost setup that allowed us to generate multiple independent faults in one computation. The setup implements these faults by clock glitches which induce instruction skips. With this setup we conducted the first practical fault attack against a complete pairing computation.


Constructing CCA-secure predicate encapsulation schemes from CPA-secure schemes and universal one-way hash functions

J. Blömer, G. Liske, 2014

Abstract

We present a new transformation of chosen-plaintext secure predicate encryption schemes with public index into chosen-ciphertext secure schemes. Our construction requires only a universal one-way hash function and is selectively secure in the standard model. The transformation is not generic but can be applied to various existing schemes constructed from bilinear groups. Using common structural properties of these schemes we provide an efficient and simple transformation without overhead in form of one-time signatures or message authentication codes as required in the known generic transformations.

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Abstract

We present a new transformation of chosen-plaintext secure predicate encryption schemes with public index into chosen-ciphertext secure schemes. Our construction requires only a universal one-way hash function and is selectively secure in the standard model. The transformation is not generic but can be applied to various existing schemes constructed from bilinear groups. Using common structural properties of these schemes we provide an efficient and simple transformation without overhead in form of one-time signatures or message authentication codes as required in the known generic transformations.


Fujisaki-Okamoto Transformation

J. Lippert, Universität Paderborn, 2014


Group Signature Schemes with Strong Exculpability

P. Bemmann, Universität Paderborn, 2014


Hiding software components using functional encryption

J. Jochheim. Hiding software components using functional encryption. 2014.


RSA-Full Domain Hash Revisited

T. Rath, Universität Paderborn, 2014

Abstract

RSA Full Domain Hash ist im Zufallsorakelmodell ein EUF-CMA sicheres Signaturverfahren (existentially unforgeable under chosen-message attacks). Der Sicherheitsbeweis wird unter anderem in der Vorlesung Einf{\"u}hrung in die Kryptographie vorgestellt. Auch bei einer genaueren Analyse verliert man bei der Reduktion einen Faktor \nicefrac{1}{q_{s}}(wobei q_{s}die Anzahl der Anfragen an das Signaturorakel darstellt), was f{\"u}r die Praxis in relativ großen Systemparametern (RSA-Modul) resultiert [1].Seit der Ver{\"o}ffentlichung von [2] wurde geglaubt, dass der Faktor \nicefrac{1}{q_{s}}optimal ist. Erst zehn Jahre sp{\"a}ter offenbarten die Autoren von [3] einen Fehler in [2] und zeigten eine bessere Reduktion allerdings unter einer etwas st{\"a}rkeren Sicherheitsannahme.Die Ergebnisse aus [3] lassen sich auf PSS-Verfahren (Probabilistic Signature Scheme), das z.B. in PKCS #1 benutzt wird, {\"u}bertragen und sind somit von großer Bedeutung f{\"u}r die Praxis. Weiterhin sind die in den Beweisen verwendete Techniken n{\"u}tzlich auch bei anderen kryptographischen Verfahren.In Rahmen dieser Arbeit sollen die entsprechenden Sicherheitsbeweise aufgearbeitet und dessen Auswirkungen f{\"u}r die Praxis analysiert werden.[1] J.S. Coron, “On the Exact Security of Full Domain Hash”, CRYPTO 2000. LNCS 1880, pp. 229-235, 2000.[2] J.S. Coron, “Optimal security proofs for PPS and other signature schemes”, EUROCRYPT 2002. LNCS 2332, pp 272-287, 2002.[3] S.A. Kakvi and E. Kiltz, “Optimal Security Proofs for Full Domain Hash, Revisited”, in EUROCRYPT 2012. LNCS 7237, pp 537-553, 2012.


Tampering attacks in pairing-based cryptography

J. Blömer, P. Günther, G. Liske, in: Proceedings of Fault Tolerance and Diagnosis in Cryptography(FDTC), 2014, pp. 1--7

DOI
Abstract

In the last decade pairings have become an important, and often indispensable, ingredient in the construction of identity-based and attribute-based cryptosystems, as well as group signatures and credential systems. Consequently, the applicability of timing, power, or fault attacks to implementations of pairings is an important research topic. We will review some of the known results in this area.


2013


Direct Chosen-Ciphertext Secure Attribute-Based Key Encapsulations without Random Oracles

J. Blömer, G. Liske, 2013

Abstract

We present a new technique to realize attribute-based encryption (ABE) schemes secure in the standard model against chosen-ciphertext attacks (CCA-secure). Our approach is to extend certain concrete chosen-plaintext secure (CPA-secure) ABE schemes to achieve more efficient constructions than the known generic constructions of CCA-secure ABE schemes. We restrict ourselves to the construction of attribute-based key encapsulation mechanisms (KEMs) and present two concrete CCA-secure schemes: a key-policy attribute-based KEM that is based on Goyal's key-policy ABE and a ciphertext-policy attribute-based KEM that is based on Waters' ciphertext-policy ABE. To achieve our goals, we use an appropriate hash function and need to extend the public parameters and the ciphertexts of the underlying CPA-secure encryption schemes only by a single group element. Moreover, we use the same hardness assumptions as the underlying CPA-secure encryption schemes.

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Abstract

We present a new technique to realize attribute-based encryption (ABE) schemes secure in the standard model against chosen-ciphertext attacks (CCA-secure). Our approach is to extend certain concrete chosen-plaintext secure (CPA-secure) ABE schemes to achieve more efficient constructions than the known generic constructions of CCA-secure ABE schemes. We restrict ourselves to the construction of attribute-based key encapsulation mechanisms (KEMs) and present two concrete CCA-secure schemes: a key-policy attribute-based KEM that is based on Goyal's key-policy ABE and a ciphertext-policy attribute-based KEM that is based on Waters' ciphertext-policy ABE. To achieve our goals, we use an appropriate hash function and need to extend the public parameters and the ciphertexts of the underlying CPA-secure encryption schemes only by a single group element. Moreover, we use the same hardness assumptions as the underlying CPA-secure encryption schemes.


Securing Critical Unattended Systems with Identity Based Cryptography - A Case Study

J. Blömer, P. Günther, V. Krummel, in: Proceedings of the 5th International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS), 2013, pp. 98-105

Abstract

Unattended systems are key ingredients of various critical infrastruc-tures like networks of self service terminals or automated teller machines.For cost and efficiency reasons they should mostly run autonomously.Unattended systems are attractive and lucrative targets for various kindsof attacks, including attacks on the integrity of their components and thecommunication between components. In this paper, we propose a gen-eral cryptographic framework to protect unattended systems. We alsodemonstrate that instantiating the framework with techniques from iden-tity based cryptography is particularly well-suited to efficiently secureunattended systems.



Seitenkanalresistenz paarungsbasierter Kryptographie

O. Otte, Universität Paderborn, 2013



2012

Attribute-basierte Verschlüsselung

P. Schleiter, Universität Paderborn, 2012



2011

Fault attacks in pairing-based cryptography

G. Liske. Fault attacks in pairing-based cryptography. 2011.


2009


Open list in Research Information System

The University for the Information Society