Towards Tightly Secure Short Signature and IBE

Constructing short signatures with tight security from standard assumptions is a long-standing open problem. We present an adaptively secure, short (and stateless) signature scheme, featuring a constant security loss relative to a conservative hardness assumption, Short Integer Solution (SIS), and the security of a concretely instantiated pseudorandom function (PRF). This gives a class of tightly secure short lattice signature schemes whose security is based on SIS and the underlying assumption of the instantiated PRF. Our signature construction further extends to give a class of tightly and adaptively secure ``compact Identity-Based Encryption (IBE) schemes, reducible with constant security loss from Regev\u27s vanilla Learning With Errors (LWE) hardness assumption and the security of a concretely instantiated PRF. Our approach is a novel combination of a number of techniques, including Katz and Wang signature, Agrawal et al.\ lattice-based secure IBE, and Boneh et al.\ key-homomorphic encryption. Our results, at the first time, eliminate the dependency between the number of adversary\u27s queries and the security of short signature/IBE schemes in the context of lattice-based cryptography. They also indicate that tightly secure PRFs (with constant security loss) would imply tightly, adaptively secure short signature and IBE schemes (with constant security loss)

Improvements and New Constructions of Digital Signatures

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

On Cryptographic Building Blocks and Transformations

Cryptographic building blocks play a central role in cryptography, e.g., encryption or digital signatures with their security notions. Further, cryptographic building blocks might be constructed modularly, i.e., emerge out of other cryptographic building blocks. Essentially, one cryptographically transforms the underlying block(s) and their (security) properties into the emerged block and its properties. This thesis considers cryptographic building blocks and new cryptographic transformations

Tightly Secure IBE under Constant-size Master Public Key

International audienceChen and Wee [CRYPTO, 2013] proposed the first almost tightly and adaptively secure IBE in the standard model and left two open problems which called for a tightly secure IBE with (1) constant-size master public key and/or (2) constant security loss. In this paper, we propose an IBE scheme with constant-size master public key and tighter security reduction. This (partially) solves Chen and Wee's first open problem and makes progress on the second one. Technically, our IBE scheme is built based on Wee's petit IBE scheme [TCC, 2016] in the composite-order bilinear group whose order is product of four primes. The sizes of master public key, ciphertexts, and secret keys are not only constant but also nearly optimal as Wee's petit IBE. We can prove its adaptive security in the multi-instance, multi-ciphertext setting [PKC, 2015] based on the decisional subgroup assumption and a subgroup variant of DBDH assumption. The security loss is O(log q) where q is the upper bound of the total number of secret keys and challenge ciphertexts revealed to adversary in each single IBE instance. It's much smaller than those for all known adaptively secure IBE schemes in a concrete sense

Efficient IBE with Tight Reduction to Standard Assumption in the Multi-challenge Setting

In 2015, Hofheinz et al. [PKC, 2015] extended Chen and Wee\u27s almost-tight reduction technique for identity based encryptions (IBE) [CRYPTO, 2013] to the multi-instance, multi-ciphertext (MIMC, or multi-challenge) setting, where the adversary is allowed to obtain multiple challenge ciphertexts from multiple IBE instances, and gave the first almost-tightly secure IBE in this setting using composite-order bilinear groups. Several prime-order realizations were proposed lately. However there seems to be a dilemma of high system performance (involving ciphertext/key size and encryption/decryption cost) or weak/standard security assumptions. A natural question is: can we achieve high performance without relying on stronger/non-standard assumptions? In this paper, we answer the question in the affirmative by describing a prime-order IBE scheme with the same performance as the most efficient solutions so far but whose security still relies on the standard k-linear (k-Lin) assumption. Our technical start point is Blazy et al.\u27s almost-tightly secure IBE [CRYPTO, 2014]. We revisit their concrete IBE scheme and associate it with the framework of nested dual system group. This allows us to extend Blazy et al.\u27s almost-tightly secure IBE to the MIMC setting using Gong et al.\u27s method [PKC, 2016]. We emphasize that, when instantiating our construction by the Symmetric eXternal Diffie-Hellman assumption (SXDH = 1-Lin), we obtain the most efficient concrete IBE scheme with almost-tight reduction in the MIMC setting, whose performance is even comparable to the most efficient IBE in the classical model (i.e., the single-instance, single-ciphertext setting). Besides pursuing high performance, our IBE scheme also achieves a weaker form of anonymity pointed out by Attrapadung et al. [AsiaCrypt, 2015]

Tighter Security Proofs for GPV-IBE in the Quantum Random Oracle Model

In (STOC, 2008), Gentry, Peikert, and Vaikuntanathan proposed the first identity-based encryption (GPV-IBE) scheme based on a post-quantum assumption, namely, the learning with errors (LWE) assumption. Since their proof was only made in the random oracle model (ROM) instead of the quantum random oracle model (QROM), it remained unclear whether the scheme was truly post-quantum or not. In (CRYPTO, 2012), Zhandry developed new techniques to be used in the QROM and proved the security of GPV-IBE in the QROM, hence answering in the affirmative that GPV-IBE is indeed post-quantum. However, since the general technique developed by Zhandry incurred a large reduction loss, there was a wide gap between the concrete efficiency and security level provided by GPV-IBE in the ROM and QROM. Furthermore, regardless of being in the ROM or QROM, GPV-IBE is not known to have a tight reduction in the multi-challenge setting. Considering that in the real-world an adversary can obtain many ciphertexts, it is desirable to have a security proof that does not degrade with the number of challenge ciphertext. In this paper, we provide a much tighter proof for the GPV-IBE in the QROM in the single-challenge setting. In addition, we also show that a slight variant of the GPV-IBE has an almost tight reduction in the multi-challenge setting both in the ROM and QROM, where the reduction loss is independent of the number of challenge ciphertext. Our proof departs from the traditional partitioning technique and resembles the approach used in the public key encryption scheme of Cramer and Shoup (CRYPTO, 1998). Our proof strategy allows the reduction algorithm to program the random oracle the same way for all identities and naturally fits the QROM setting where an adversary may query a superposition of all identities in one random oracle query. Notably, our proofs are much simpler than the one by Zhandry and conceptually much easier to follow for cryptographers not familiar with quantum computation. Although at a high level, the techniques used for the single and multi-challenge setting are similar, the technical details are quite different. For the multi-challenge setting, we rely on the Katz-Wang technique (CCS, 2003) to overcome some obstacles regarding the leftover hash lemma

Advances in Functional Encryption

Functional encryption is a novel paradigm for public-key encryption that enables both fine-grained access control and selective computation on encrypted data, as is necessary to protect big, complex data in the cloud. In this thesis, I provide a brief introduction to functional encryption, and an overview of my contributions to the area

Ring Signature from Bonsai Tree: How to Preserve the Long-Term Anonymity

Signer-anonymity is the central feature of ring signatures, which enable a user to sign messages on behalf of an arbitrary set of users, called the ring, without revealing exactly which member of the ring actually generated the signature. Strong and long-term signer-anonymity is a reassuring guarantee for users who are hesitant to leak a secret, especially if the consequences of identification are dire in certain scenarios such as whistleblowing. The notion of \textit{unconditional anonymity}, which protects signer-anonymity even against an infinitely powerful adversary, is considered for ring signatures that aim to achieve long-term signer-anonymity. However, the existing lattice-based works that consider the unconditional anonymity notion did not strictly capture the security requirements imposed in practice, this leads to a realistic attack on signer-anonymity. In this paper, we present a realistic attack on the unconditional anonymity of ring signatures, and formalize the unconditional anonymity model to strictly capture it. We then propose a lattice-based ring signature construction with unconditional anonymity by leveraging bonsai tree mechanism. Finally, we prove the security in the standard model and demonstrate the unconditional anonymity through both theoretical proof and practical experiments

Theory and Applications of Outsider Anonymity in Broadcast Encryption

Broadcast Encryption (BE) allows efficient one-to-many secret communication of data over a broadcast channel. In the standard setting of BE, information about receivers is transmitted in the clear together with ciphertexts. This could be a serious violation of recipient privacy since the identities of the users authorized to access the secret content in certain broadcast scenarios are as sensitive as the content itself. Anonymous Broadcast Encryption (AnoBe) prevents this leakage of recipient identities from ciphertexts but at a cost of a linear lower bound (in the number of receivers) on the length of ciphertexts. A linear ciphertext length is a highly undesirable bottleneck in any large-scale broadcast application. In this thesis, we propose a less stringent yet very meaningful notion of anonymity for anonymous broadcast encryption called Outsider-Anonymous Broadcast Encryption (oABE) that allows the creation of ciphertexts that are sublinear in the number of receivers. We construct several oABE schemes with varying security guarantees and levels of efficiency. We also present two very interesting cryptographic applications afforded by the efficiency of our oABE schemes. The first is Broadcast Steganography (BS), the extension of the state of the art setting of point-to-point steganography to the multi-recipient setting. The second is Oblivious Group Storage (OGS), the introduction of fine-grained data access control policies to the setting of multi-client oblivious cloud storage protocols