Improved Signature Schemes for Secure Multi-Party Computation with Certified Inputs

The motivation for this work comes from the need to strengthen security of secure multi-party protocols with the ability to guarantee that the participants provide their truthful inputs in the computation. This is outside the traditional security models even in the presence of malicious participants, but input manipulation can often lead to privacy and result correctness violations. Thus, in this work we treat the problem of combining secure multi-party computation (SMC) techniques based on secret sharing with signatures to enforce input correctness in the form of certification. We modify two currently available signature schemes to achieve private verification and efficiency of batch verification and show how to integrate them with two prominent SMC protocols

SoK: Oblivious Pseudorandom Functions

In recent years, oblivious pseudorandom functions (OPRFs) have become a ubiquitous primitive used in cryptographic protocols and privacy-preserving technologies. The growing interest in OPRFs, both theoretical and applied, has produced a vast number of different constructions and functionality variations. In this paper, we provide a systematic overview of how to build and use OPRFs. We first categorize existing OPRFs into essentially four families based on their underlying PRF (Naor-Reingold, Dodis-Yampolskiy, Hashed Diffie-Hellman, and generic constructions). This categorization allows us to give a unified presentation of all oblivious evaluation methods in the literature, and to understand which properties OPRFs can (or cannot) have. We further demonstrate the theoretical and practical power of OPRFs by visualizing them in the landscape of cryptographic primitives, and by providing a comprehensive overview of how OPRFs are leveraged for improving the privacy of internet users. Our work systematizes 15 years of research on OPRFs and provides inspiration for new OPRF constructions and applications thereof

Universally Composable Verifiable Random Oracles

Random Oracles werden häufig in der Kryptographie eingesetzt um sehr effiziente Instanziierungen mächtiger kryptographischer Primitive zu konstruieren. Jedoch ist diese Praxis im Allgemeinen nicht zulässig wie verschiedene Nicht-Instanziierungs-Ergebnisse für Random Oracles mittels lokal berechenbarer Familien von Funktionen durch Halevi et al. (JACM ’04) zeigt. Die Random Oracle Modell kann sicher eingesetzt werden, indem Random Oracles nicht mit einer lokal berechenbaren Hashfunktion, sondern stattdessen mit einem interaktiven Protokoll instanziiert werden. In der realen Welt könnte solch ein interaktives Protokoll beispielsweise aus einem vertrauenswürdigen Server, welcher über das Internet erreichbar ist, bestehen. Dieser Server würde sodann eine der bekannten Techniken wie lazy sampling oder das Auswerten einer Pseudo-Zufälligen Funktion verwenden, um die Funktionalität eines Random Oracle bereitzustellen. Ein klarer Nachteil dieses Ansatzes ist die große Menge an Interaktion, die bei jeder Berechnung, die eine Auswertung des Random Oracle beinhaltet, nötig ist. Wir wollen diese Interaktion auf ein Minimum reduzieren. Um obiges Unmöglichkeitsresultat zu umgehen, muss die Auswertung des Random Oracle auf einer frischen Eingabe Interaktion der auswertenden Partei mit einer anderen Partei beinhalten. Dies ist jedoch nicht der einzige Verwendungszweck von Random Oracles, der häufig in kryptographischen Protokollen auftritt. Bei einem weiteren solchen Zweck wertet zunächst eine Partei A das Orakel auf einer Eingabe aus und erhält einen Hashwert. Im Anschluss sendet A Eingabe und Ausgabe (im Kontext eines Protokolls) an eine zweite Partei B und möchte B davon überzeugen, dass das Random Oracle korrekt ausgewertet wurde. Eine einfache Möglichkeit dies zu prüfen besteht darin, dass B selbst eine Auswertung des Random Oracle auf der erhaltenen Eingabe tätigt und die beiden Ausgaben vergleicht. In unserem Kontext benötigt dies jedoch erneut Interaktion. Der Wunsch diesen zweiten Verwendungszweck nicht-interaktiv zu machen führt uns zum Begriff eines Verifiable Random Oracle (VRO) als Erweiterung eines Random Oracle. Abstrakt besteht ein VRO aus zwei Orakeln. Das erste Orakel verhält sich wie ein Random Oracle dessen Ausgabe um einen Korrektheitsbeweis erweitert wurde. Mit Hilfe dieses Beweises kann das zweite Orakel dazu verwendet werden öffentlich die korrekte Auswertung des Random Oracle zu verifizieren. Obwohl diese Orakel-basierte Formulierung nicht notwendigerweise nicht-interaktive Verifikation besitzt, so erlaubt jedoch die Einführung expliziter Korrektheitsbeweise dies. In dieser Masterarbeit formalisieren wir zunächst den Begriff eines VRO im Universal Composability Framework von Canetti (FOCS ’01). Danach wenden wir VROs auf zwei kryptographische Anwendungen an, die in ihrer ursprünglichen Formulierung das Random Oracle Modell verwenden, und zeigen, das deren Sicherheitseigenschaften erhalten bleiben. Um zu zeigen, dass unsere Definition realisierbar ist, konstruieren wir mehrere Protokolle, die die ideale VRO Funktionalität realisieren. Diese reichen von Protokollen für eine einzelne vertrauenswürdige Partei bis hin zu verteilten Protokollen, die eine gewisse Menge an böswilliger Korruption erlauben. Wir vergleichen weiterhin VROs mit ähnlichen existierenden Primitiven

Modeling Advanced Security Aspects of Key Exchange and Secure Channel Protocols

Secure communication has become an essential ingredient of our daily life. Mostly unnoticed, cryptography is protecting our interactions today when we read emails or do banking over the Internet, withdraw cash at an ATM, or chat with friends on our smartphone. Security in such communication is enabled through two components. First, two parties that wish to communicate securely engage in a key exchange protocol in order to establish a shared secret key known only to them. The established key is then used in a follow-up secure channel protocol in order to protect the actual data communicated against eavesdropping or malicious modification on the way. In modern cryptography, security is formalized through abstract mathematical security models which describe the considered class of attacks a cryptographic system is supposed to withstand. Such models enable formal reasoning that no attacker can, in reasonable time, break the security of a system assuming the security of its underlying building blocks or that certain mathematical problems are hard to solve. Given that the assumptions made are valid, security proofs in that sense hence rule out a certain class of attackers with well-defined capabilities. In order for such results to be meaningful for the actually deployed cryptographic systems, it is of utmost importance that security models capture the system's behavior and threats faced in that 'real world' as accurately as possible, yet not be overly demanding in order to still allow for efficient constructions. If a security model fails to capture a realistic attack in practice, such an attack remains viable on a cryptographic system despite a proof of security in that model, at worst voiding the system's overall practical security. In this thesis, we reconsider the established security models for key exchange and secure channel protocols. To this end, we study novel and advanced security aspects that have been introduced in recent designs of some of the most important security protocols deployed, or that escaped a formal treatment so far. We introduce enhanced security models in order to capture these advanced aspects and apply them to analyze the security of major practical key exchange and secure channel protocols, either directly or through comparatively close generic protocol designs. Key exchange protocols have so far always been understood as establishing a single secret key, and then terminating their operation. This changed in recent practical designs, specifically of Google's QUIC ("Quick UDP Internet Connections") protocol and the upcoming version 1.3 of the Transport Layer Security (TLS) protocol, the latter being the de-facto standard for security protocols. Both protocols derive multiple keys in what we formalize in this thesis as a multi-stage key exchange (MSKE) protocol, with the derived keys potentially depending on each other and differing in cryptographic strength. Our MSKE security model allows us to capture such dependencies and differences between all keys established in a single framework. In this thesis, we apply our model to assess the security of both the QUIC and the TLS 1.3 key exchange design. For QUIC, we are able to confirm the intended overall security but at the same time highlight an undesirable dependency between the two keys QUIC derives. For TLS 1.3, we begin by analyzing the main key exchange mode as well as a reduced resumption mode. Our analysis attests that TLS 1.3 achieves strong security for all keys derived without undesired dependencies, in particular confirming several of this new TLS version's design goals. We then also compare the QUIC and TLS 1.3 designs with respect to a novel 'zero round-trip time' key exchange mode establishing an initial key with minimal latency, studying how differences in these designs affect the achievable key exchange security. As this thesis' last contribution in the realm of key exchange, we formalize the notion of key confirmation which ensures one party in a key exchange execution that the other party indeed holds the same key. Despite being frequently mentioned in practical protocol specifications, key confirmation was never comprehensively treated so far. In particular, our formalization exposes an inherent, slight difference in the confirmation guarantees both communication partners can obtain and enables us to analyze the key confirmation properties of TLS 1.3. Secure channels have so far been modeled as protecting a sequence of distinct messages using a single secret key. Our first contribution in the realm of channels originates from the observation that, in practice, secure channel protocols like TLS actually do not allow an application to transmit distinct, or atomic, messages. Instead, they provide applications with a streaming interface to transmit a stream of bits without any inherent demarcation of individual messages. Necessarily, the security guarantees of such an interface differ significantly from those considered in cryptographic models so far. In particular, messages may be fragmented in transport, and the recipient may obtain the sent stream in a different fragmentation, which has in the past led to confusion and practical attacks on major application protocol implementations. In this thesis, we formalize such stream-based channels and introduce corresponding security notions of confidentiality and integrity capturing the inherently increased complexity. We then present a generic construction of a stream-based channel based on authenticated encryption with associated data (AEAD) that achieves the strongest security notions in our model and serves as validation of the similar TLS channel design. We also study the security of such applications whose messages are inherently atomic and which need to safely transport these messages over a streaming, i.e., possibly fragmenting, channel. Formalizing the desired security properties in terms of confidentiality and integrity in such a setting, we investigate and confirm the security of the widely adopted approach to encode the application's messages into the continuous data stream. Finally, we study a novel paradigm employed in the TLS 1.3 channel design, namely to update the keys used to secure a channel during that channel's lifetime in order to strengthen its security. We propose and formalize the notion of multi-key channels deploying such sequences of keys and capture their advanced security properties in a hierarchical framework of confidentiality and integrity notions. We show that our hierarchy of notions naturally connects to the established notions for single-key channels and instantiate its strongest security notions with a generic AEAD-based construction. Being comparatively close to the TLS 1.3 channel protocol, our construction furthermore enables a comparative design discussion

Pseudorandom Signatures

Abstract. We develop a three-level hierarchy of privacy notions for (unforgeable) digital signatures, starting with existing notions of anonymity and confidentiality, whose independence we prove formally. The ultimate privacy goal in our hierarchy is pseudorandomness: signatures with this property hide the entire information about the signing process and they cannot be recognized as signatures when transmitted over a public network. This implies very strong unlinkability guarantees across different signers and even different signing algorithms and gives rise to new forms of private public-key authentication. We prove that one way towards pseudorandom signatures leads over the mid-level notion, called indistinguishability: these signatures can be simulated using only the public parameters of the scheme. Indistinguishable signatures exist in different cryptographic settings (e.g. based on RSA, discrete logarithms, pairings) and can be efficiently lifted to the highest privacy level using general transformations based on appropriate encoding techniques. We also show a more direct way for obtaining pseudorandomness from any unforgeable signature scheme. Our transformations work in the standard model. We keep public verifiability of signatures in the setting of system-wide known public keys and we allow full disclosure of signatures, and even of secret signing keys, while working with messages of high entropy.