458 research outputs found

    Improvements and New Constructions of Digital Signatures

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    Ein digitales Signaturverfahren, oft auch nur digitale Signatur genannt, ist ein wichtiger und nicht mehr wegzudenkender Baustein in der Kryptographie. Es stellt das digitale Äquivalent zur klassischen handschriftlichen Signatur dar und liefert darüber hinaus noch weitere wünschenswerte Eigenschaften. Mit solch einem Verfahren kann man einen öffentlichen und einen geheimen Schlüssel erzeugen. Der geheime Schlüssel dient zur Erstellung von Signaturen zu beliebigen Nachrichten. Diese können mit Hilfe des öffentlichen Schlüssels von jedem überprüft und somit verifiziert werden. Desweiteren fordert man, dass das Verfahren "sicher" sein soll. Dazu gibt es in der Literatur viele verschiedene Begriffe und Definitionen, je nachdem welche konkreten Vorstellungen beziehungsweise Anwendungsgebiete man hat. Vereinfacht gesagt, sollte es für einen Angreifer ohne Kenntnis des geheimen Schlüssels nicht möglich sein eine gültige Signatur zu einer beliebigen Nachricht zu fälschen. Ein sicheres Signaturverfahren kann somit verwendet werden um die folgenden Ziele zu realisieren: - Authentizität: Jeder Empfänger kann überprüfen, ob die Nachricht von einem bestimmten Absender kommt. - Integrität der Nachricht: Jeder Empfänger kann feststellen, ob die Nachricht bei der Übertragung verändert wurde. - Nicht-Abstreitbarkeit: Der Absender kann nicht abstreiten die Signatur erstellt zu haben. Damit ist der Einsatz von digitalen Signaturen für viele Anwendungen in der Praxis sehr wichtig. Überall da, wo es wichtig ist die Authentizität und Integrität einer Nachricht sicherzustellen, wie beim elektronischen Zahlungsverkehr, Softwareupdates oder digitalen Zertifikaten im Internet, kommen digitale Signaturen zum Einsatz. Aber auch für die kryptographische Theorie sind digitale Signaturen ein unverzichtbares Hilfsmittel. Sie ermöglichen zum Beispiel die Konstruktion von stark sicheren Verschlüsselungsverfahren. Eigener Beitrag: Wie bereits erwähnt gibt es unterschiedliche Sicherheitsbegriffe im Rahmen von digitalen Signaturen. Ein Standardbegriff von Sicherheit, der eine recht starke Form von Sicherheit beschreibt, wird in dieser Arbeit näher betrachtet. Die Konstruktion von Verfahren, die diese Form der Sicherheit erfüllen, ist ein vielschichtiges Forschungsthema. Dazu existieren unterschiedliche Strategien in unterschiedlichen Modellen. In dieser Arbeit konzentrieren wir uns daher auf folgende Punkte. - Ausgehend von vergleichsweise realistischen Annahmen konstruieren wir ein stark sicheres Signaturverfahren im sogenannten Standardmodell, welches das realistischste Modell für Sicherheitsbeweise darstellt. Unser Verfahren ist das bis dahin effizienteste Verfahren in seiner Kategorie. Es erstellt sehr kurze Signaturen und verwendet kurze Schlüssel, beides unverzichtbar für die Praxis. - Wir verbessern die Qualität eines Sicherheitsbeweises von einem verwandten Baustein, der identitätsbasierten Verschlüsselung. Dies hat unter anderem Auswirkung auf dessen Effizienz bezüglich der empfohlenen Schlüssellängen für den sicheren Einsatz in der Praxis. Da jedes identitätsbasierte Verschlüsselungsverfahren generisch in ein digitales Signaturverfahren umgewandelt werden kann ist dies auch im Kontext digitaler Signaturen interessant. - Wir betrachten Varianten von digitalen Signaturen mit zusätzlichen Eigenschaften, sogenannte aggregierbare Signaturverfahren. Diese ermöglichen es mehrere Signaturen effizient zu einer zusammenzufassen und dabei trotzdem alle zugehörigen verschiedenen Nachrichten zu verifizieren. Wir geben eine neue Konstruktion von solch einem aggregierbaren Signaturverfahren an, bei der das Verfahren eine Liste aller korrekt signierten Nachrichten in einer aggregierten Signatur ausgibt anstatt, wie bisher üblich, nur gültig oder ungültig. Wenn eine aggregierte Signatur aus vielen Einzelsignaturen besteht wird somit das erneute Berechnen und eventuell erneute Senden hinfällig und dadurch der Aufwand erheblich reduziert

    Short Group Signatures via Structure-Preserving Signatures: Standard Model Security from Simple Assumptions

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    International audienceGroup signatures are a central cryptographic primitive which allows users to sign messages while hiding their identity within a crowd of group members. In the standard model (without the random oracle idealization), the most efficient constructions rely on the Groth-Sahai proof systems (Euro-crypt'08). The structure-preserving signatures of Abe et al. (Asiacrypt'12) make it possible to design group signatures based on well-established, constant-size number theoretic assumptions (a.k.a. " simple assumptions ") like the Symmetric eXternal Diffie-Hellman or Decision Linear assumptions. While much more efficient than group signatures built on general assumptions, these constructions incur a significant overhead w.r.t. constructions secure in the idealized random oracle model. Indeed, the best known solution based on simple assumptions requires 2.8 kB per signature for currently recommended parameters. Reducing this size and presenting techniques for shorter signatures are thus natural questions. In this paper, our first contribution is to significantly reduce this overhead. Namely, we obtain the first fully anonymous group signatures based on simple assumptions with signatures shorter than 2 kB at the 128-bit security level. In dynamic (resp. static) groups, our signature length drops to 1.8 kB (resp. 1 kB). This improvement is enabled by two technical tools. As a result of independent interest, we first construct a new structure-preserving signature based on simple assumptions which shortens the best previous scheme by 25%. Our second tool is a new method for attaining anonymity in the strongest sense using a new CCA2-secure encryption scheme which is simultaneously a Groth-Sahai commitment

    Encryptor Combiners: A Unified Approach to Multiparty NIKE, (H)IBE, and Broadcast Encryption

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    We define the concept of an encryptor combiner. Roughly, such a combiner takes as input n public keys for a public key encryption scheme, and produces a new combined public key. Anyone knowing a secret key for one of the input public keys can learn the secret key for the combined public key, but an outsider who just knows the input public keys (who can therefore compute the combined public key for himself) cannot decrypt ciphertexts from the combined public key. We actually think of public keys more generally as encryption procedures, which can correspond to, say, encrypting to a particular identity under an IBE scheme or encrypting to a set of attributes under an ABE scheme. We show that encryptor combiners satisfying certain natural properties can give natural constructions of multi-party non-interactive key exchange, low-overhead broadcast encryption, and hierarchical identity-based encryption. We then show how to construct two different encryptor combiners. Our first is built from universal samplers (which can in turn be built from indistinguishability obfuscation) and is sufficient for each application above, in some cases improving on existing obfuscation-based constructions. Our second is built from lattices, and is sufficient for hierarchical identity-based encryption. Thus, encryptor combiners serve as a new abstraction that (1) is a useful tool for designing cryptosystems, (2) unifies constructing hierarchical IBE from vastly different assumptions, and (3) provides a target for instantiating obfuscation applications from better tools

    Tightly Secure Hierarchical Identity-Based Encryption

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    We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation

    Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE and Compact Garbled Circuits

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    We construct the first (key-policy) attribute-based encryption (ABE) system with short secret keys: the size of keys in our system depends only on the depth of the policy circuit, not its size. Our constructions extend naturally to arithmetic circuits with arbitrary fan-in gates thereby further reducing the circuit depth. Building on this ABE system we obtain the first reusable circuit garbling scheme that produces garbled circuits whose size is the same as the original circuit plus an additive poly(λ,d) bits, where λ is the security parameter and d is the circuit depth. All previous constructions incurred a multiplicative poly(λ) blowup. We construct our ABE using a new mechanism we call fully key-homomorphic encryption, a public-key system that lets anyone translate a ciphertext encrypted under a public-key x into a ciphertext encrypted under the public-key (f(x),f) of the same plaintext, for any efficiently computable f. We show that this mechanism gives an ABE with short keys. Security of our construction relies on the subexponential hardness of the learning with errors problem. We also present a second (key-policy) ABE, using multilinear maps, with short ciphertexts: an encryption to an attribute vector x is the size of x plus poly(λ,d) additional bits. This gives a reusable circuit garbling scheme where the garbled input is short.United States. Defense Advanced Research Projects Agency (Grant FA8750-11-2-0225)Alfred P. Sloan Foundation (Sloan Research Fellowship

    Adaptively Secure Revocable Hierarchical IBE from kk-linear Assumption

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    Revocable identity-based encryption (RIBE) is an extension of IBE with an efficient key revocation mechanism. Revocable hierarchical IBE (RHIBE) is its further extension with key delegation functionality. Although there are various adaptively secure pairing-based RIBE schemes, all known hierarchical analogs only satisfy selective security. In addition, the currently known most efficient adaptively secure RIBE and selectively secure RHIBE schemes rely on non-standard assumptions, which are referred to as the augmented DDH assumption and qq-type assumptions, respectively. In this paper, we propose a simple but effective design methodology for RHIBE schemes. We provide a generic design framework for RHIBE based on an HIBE scheme with a few properties. Fortunately, several state-of-the-art pairing-based HIBE schemes have the properties. In addition, our construction preserves the sizes of master public keys, ciphertexts, and decryption keys, as well as the complexity assumptions of the underlying HIBE scheme. Thus, we obtain the first RHIBE schemes with adaptive security under the standard kk-linear assumption. We prove adaptive security by developing a new proof technique for RHIBE. Due to the compactness-preserving construction, the proposed R(H)IBE schemes have similar efficiencies to the most efficient existing schemes

    Efficient Identity-Based Encryption with Hierarchical Key-Insulation from HIBE

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    Hierarchical key-insulated identity-based encryption (HKIBE) is identity-based encryption (IBE) that allows users to update their secret keys to achieve (hierarchical) key-exposure resilience, which is an important notion in practice. However, existing HKIBE constructions have limitations in efficiency: sizes of ciphertexts and secret keys depend on the hierarchical depth. In this paper, we first triumph over the barrier by proposing simple but effective design methodologies to construct efficient HKIBE schemes. First, we show a generic construction from any hierarchical IBE (HIBE) scheme that satisfies a special requirement, called MSK evaluatability introduced by Emura et al. (Designs, Codes and Cryptography, 2021). It provides several new and efficient instantiations since most pairing-based HIBE schemes satisfy the requirement. It is worth noting that it preserves all parameters\u27 sizes of the underlying HIBE scheme, and hence we obtain several efficient HKIBE schemes under the kk-linear assumption in the standard model. Since MSK evaluatability is dedicated to pairing-based HIBE schemes, the first construction restricts pairing-based instantiations. To realize efficient instantiation from various assumptions, we next propose a generic construction of an HKIBE scheme from any plain HIBE scheme. It is based on Hanaoka et al.\u27s HKIBE scheme (Asiacrypt 2005), and does not need any special properties. Therefore, we obtain new efficient instantiations from various assumptions other than pairing-oriented ones. Though the sizes of secret keys and ciphertexts are larger than those of the first construction, it is more efficient than Hanaoka et al.\u27s scheme in the sense of the sizes of master public/secret keys

    Shorter Decentralized Attribute-Based Encryption via Extended Dual System Groups

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    Decentralized attribute-based encryption (ABE) is a special form of multiauthority ABE systems, in which no central authority and global coordination are required other than creating the common reference parameters. In this paper, we propose a new decentralized ABE in prime-order groups by using extended dual system groups. We formulate some assumptions used to prove the security of our scheme. Our proposed scheme is fully secure under the standard k-Lin assumption in random oracle model and can support any monotone access structures. Compared with existing fully secure decentralized ABE systems, our construction has shorter ciphertexts and secret keys. Moreover, fast decryption is achieved in our system, in which ciphertexts can be decrypted with a constant number of pairings

    Extended Nested Dual System Groups, Revisited

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    The notion of extended nested dual system groups (ENDSG) was recently proposed by Hofheinz et al. [PKC 2015] for constructing almost-tight identity based encryptions (IBE) in the multi-instance, multi-ciphertext (MIMC) setting. However only a composite-order instantiation was proposed and more efficient prime-order instantiations are absent. The paper fills the blank by presenting two constructions. We revise the definition of ENDSG and realize it using prime-order bilinear groups based on Chen and Wee\u27s prime-order instantiation of nested dual system groups [CRYPTO 2013]. This yields the first almost-tight IBE in the prime-order setting achieving weak adaptive security in MIMC scenario under the dd-linear (dd-Lin) assumption. We further enhanced the revised ENDSG to capture stronger security notions for IBE, including BB-weak adaptive security and full adaptive security. We show that our prime-order instantiation is readily BB-weak adaptive secure and full adaptive secure without introducing extra assumption. We then try to find better solution by fine-tuning ENDSG again and realizing it using the technique of Chen, Gay, and Wee [EUROCRYPT 2015]. This leads to an almost-tight secure IBE in the same setting with better performance than our first result, but the security relies on a non-standard assumption, dd-linear assumption with auxiliary input (dd-LinAI) for an even positive integer dd. However we note that, the 22-LinAI assumption is implied by the external decisional linear (XDLIN) assumption. This concrete instantiation could also be realized using symmetric bilinear groups under standard decisional linear assumption

    Almost-tight Identity Based Encryption against Selective Opening Attack

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    The paper presented an identity based encryption (IBE) under selective opening attack (SOA) whose security is almost-tightly related to a set of computational assumptions. Our result is a combination of Bellare, Waters, and Yilek\u27s method [TCC, 2011] for constructing (not tightly) SOA secure IBE and Hofheinz, Koch, and Striecks\u27 technique [PKC, 2015] on building almost-tightly secure IBE in the multi-ciphertext setting. In particular, we first tuned Bellare et al.\u27s generic construction for SOA secure IBE to show that a one-bit IBE achieving ciphertext indistinguishability under chosen plaintext attack in the multi-ciphertext setting (with one-sided publicly openability) tightly implies a multi-bit IBE secure under selective opening attack. Next, we almost-tightly reduced such a one-bit IBE to static assumptions in the composite-order bilinear groups employing the technique of Hofheinz et al. This yielded the first SOA secure IBE with almost-tight reduction
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