Randomness Recoverable Secret Sharing Schemes

It is well-known that randomness is essential for secure cryptography. The randomness used in cryptographic primitives is not necessarily recoverable even by the party who can, e.g., decrypt or recover the underlying secret/message. Several cryptographic primitives that support randomness recovery have turned out useful in various applications. In this paper, we study randomness recoverable secret sharing schemes (RR-SSS), in both information-theoretic and computational settings and provide two results. First, we show that while every access structure admits a perfect RR-SSS, there are very simple access structures (e.g., in monotone AC?) that do not admit efficient perfect (or even statistical) RR-SSS. Second, we show that the existence of efficient computational RR-SSS for certain access structures in monotone AC? implies the existence of one-way functions. This stands in sharp contrast to (non-RR) SSS schemes for which no such results are known. RR-SSS plays a key role in making advanced attributed-based encryption schemes randomness recoverable, which in turn have applications in the context of designated-verifier non-interactive zero knowledge

Group Diffie-Hellman Key Exchange Secure against Dictionary Attacks

Group Diffie-Hellman schemes for password-based key exchange are designed to provide a pool of players communicating over a public network, and sharing just a human-memorable password, with a session key (e.g, the key is used for multicast data integrity and confidentiality) . The fundamental security goal to achieve in this scenario is security against dictionary attacks. While solutions have been proposed to solve this problem no formal treatment has ever been suggested. In this paper, we define a security model and then present a protocol with its security proof in both the random oracle model and the ideal-cipher model

Post-Quantum Verification of Fujisaki-Okamoto

We present a computer-verified formalization of the post-quantum security proof of the Fujisaki-Okamoto transform (as analyzed by Hövelmanns, Kiltz, Schäge, and Unruh, PKC 2020). The formalization is done in quantum relational Hoare logic and checked in the qrhl-tool (Unruh, POPL 2019)

Omniring: Scaling Up Private Payments Without Trusted Setup - Formal Foundations and Constructions of Ring Confidential Transactions with Log-size Proofs

Monero is the largest cryptocurrency with built-in cryptographic privacy features. The transactions are authenticated using spend proofs, which provide a certain level of anonymity by hiding the source accounts from which the funds are sent among a set (known as a ring) of other accounts. Due to its similarities to ring signatures, this core cryptographic component is called Ring Confidential Transactions (RingCT). Because of its practical relevance, several works attempt to analyze the security of RingCT. However, due to the complexity of RingCT they are either informal, miss fundamental functionalities, or introduce undesirable trusted setup assumptions. Regarding efficiency, Monero currently deploys a scheme in which the size of the spend proof is linear in the ring size. This limits the ring size to only a few accounts, which in turn limits the acquired anonymity significantly and facilitates de-anonymization attacks. As a solution to these problems, we present the first complete rigorous formalization of RingCT as a cryptographic primitive. We then propose a generic construction of RingCT and prove it secure in our formal security model. By instantiating our generic construction with new efficient zero-knowledge proofs we obtain Omniring, a fully-fledged RingCT scheme in the discrete logarithm setting that provides the highest concrete and asymptotic efficiency as of today. Omniring is the first RingCT scheme which 1) does not require a trusted setup or pairing-friendly elliptic curves, 2) has a proof size logarithmic in the size of the ring, and 3) allows to share the same ring between all source accounts in a transaction, thereby enabling significantly improved privacy level without sacrificing performance. Our zero-knowledge proofs rely on novel enhancements to the Bulletproofs framework (S&P 2018), which we believe are of independent interest

Secure group key agreement

As a result of the increased popularity of group-oriented applications and protocols, group communication occurs in many different settings: from network multicasting to application layer tele- and video-conferencing. Regardless of the application environment, security services are necessary to provide communication privacy and integrity. This thesis considers the problem of key management in a special class of groups, namely dynamic peer groups. Key management, especially in a group setting, is the corner stone for all other security services. Dynamic peer groups require not only initial key agreement but also auxiliary key agreement operations such as member addition, member exclusion and group fusion. We discuss all group key agreement operations and present a concrete protocol suite, CLIQUES, which offers all of these operations. By providing the first formal model for group key establishment and investigating carefully the underlying cryptographic assumptions as well as their relations, we formally prove the security of a subset of the protocols based on the security of the Decisional Diffie-Hellman assumption; achieving as a side-effect the first provably secure group key agreement protocolMit der Verbreitung offener Netze, insbesondere des Internets, fand auch die Gruppenkommunikation eine rasante Verbreitung. Eine Vielzahl heutiger Protokolle sind gruppen-orientiert: angefangen bei Multicast-Diensten in der Netzwerkschicht bis hin zu Videokonferenzsystemen auf der Anwendungsschicht. Alle diese Dienste haben Sicherheitsanforderungen wie Vertraulichkeit und Integrität zu erfüllen, die den Einsatz kryptographischer Techniken und die Verfügbarkeit gemeinsamer kryptographischen Schlüssel oft unumgänglich machen. In der folgenden Doktorarbeit betrachte ich dieses grundlegendste Problem der Gruppenkommunikation, nämlich das Schlüsselmanagement, für dynamische Gruppen, die sogenannten "Dynamic Peer-Groups\u27;. Die Dynamik dieser Gruppen erfordert nicht nur initialen Schlüsselaustausch innerhalb einer Gruppe sondern auch sichere und effiziente Verfahren für die Aufnahme neuer und den Ausschluß alter Gruppenmitglieder. Ich diskutiere alle dafür notwendigen Dienste und präsentiere CLIQUES, eine Familie von Protokollen, die diese Dienste implementiert. Ich gebe erstmalig eine formale Definition fü sicheres Gruppen-Schlüsselmanagement und beweise die Sicherheit der genannten Protokolle basierend auf einer kryptographischen Standardannahme, der "Decisional Diffie-Hellman\u27; Annahme. Diese Sicherheitsbetrachtung wird durch eine detaillierte Untersuchung dieser Annahme und ihrer Relation zu verwandten Annahmen abgeschlossen

Secure group key agreement

As a result of the increased popularity of group-oriented applications and protocols, group communication occurs in many different settings: from network multicasting to application layer tele- and video-conferencing. Regardless of the application environment, security services are necessary to provide communication privacy and integrity. This thesis considers the problem of key management in a special class of groups, namely dynamic peer groups. Key management, especially in a group setting, is the corner stone for all other security services. Dynamic peer groups require not only initial key agreement but also auxiliary key agreement operations such as member addition, member exclusion and group fusion. We discuss all group key agreement operations and present a concrete protocol suite, CLIQUES, which offers all of these operations. By providing the first formal model for group key establishment and investigating carefully the underlying cryptographic assumptions as well as their relations, we formally prove the security of a subset of the protocols based on the security of the Decisional Diffie-Hellman assumption; achieving as a side-effect the first provably secure group key agreement protocolMit der Verbreitung offener Netze, insbesondere des Internets, fand auch die Gruppenkommunikation eine rasante Verbreitung. Eine Vielzahl heutiger Protokolle sind gruppen-orientiert: angefangen bei Multicast-Diensten in der Netzwerkschicht bis hin zu Videokonferenzsystemen auf der Anwendungsschicht. Alle diese Dienste haben Sicherheitsanforderungen wie Vertraulichkeit und Integrität zu erfüllen, die den Einsatz kryptographischer Techniken und die Verfügbarkeit gemeinsamer kryptographischen Schlüssel oft unumgänglich machen. In der folgenden Doktorarbeit betrachte ich dieses grundlegendste Problem der Gruppenkommunikation, nämlich das Schlüsselmanagement, für dynamische Gruppen, die sogenannten "Dynamic Peer-Groups';. Die Dynamik dieser Gruppen erfordert nicht nur initialen Schlüsselaustausch innerhalb einer Gruppe sondern auch sichere und effiziente Verfahren für die Aufnahme neuer und den Ausschluß alter Gruppenmitglieder. Ich diskutiere alle dafür notwendigen Dienste und präsentiere CLIQUES, eine Familie von Protokollen, die diese Dienste implementiert. Ich gebe erstmalig eine formale Definition fü sicheres Gruppen-Schlüsselmanagement und beweise die Sicherheit der genannten Protokolle basierend auf einer kryptographischen Standardannahme, der "Decisional Diffie-Hellman'; Annahme. Diese Sicherheitsbetrachtung wird durch eine detaillierte Untersuchung dieser Annahme und ihrer Relation zu verwandten Annahmen abgeschlossen

Flexible Digital Authentication Techniques

Abstract This dissertation investigates authentication techniques in some emerging areas. Specifically, authentication schemes have been proposed that are well-suited for embedded systems, and privacy-respecting pay Web sites. With embedded systems, a person could own several devices which are capable of communication and interaction, but these devices use embedded processors whose computational capabilities are limited as compared to desktop computers. Examples of this scenario include entertainment devices or appliances owned by a consumer, multiple control and sensor systems in an automobile or airplane, and environmental controls in a building. An efficient public key cryptosystem has been devised, which provides a complete solution to an embedded system, including protocols for authentication, authenticated key exchange, encryption, and revocation. The new construction is especially suitable for the devices with constrained computing capabilities and resources. Compared with other available authentication schemes, such as X.509, identity-based encryption, etc, the new construction provides unique features such as simplicity, efficiency, forward secrecy, and an efficient re-keying mechanism. In the application scenario for a pay Web site, users may be sensitive about their privacy, and do not wish their behaviors to be tracked by Web sites. Thus, an anonymous authentication scheme is desirable in this case. That is, a user can prove his/her authenticity without revealing his/her identity. On the other hand, the Web site owner would like to prevent a bunch of users from sharing a single subscription while hiding behind user anonymity. The Web site should be able to detect these possible malicious behaviors, and exclude corrupted users from future service. This dissertation extensively discusses anonymous authentication techniques, such as group signature, direct anonymous attestation, and traceable signature. Three anonymous authentication schemes have been proposed, which include a group signature scheme with signature claiming and variable linkability, a scheme for direct anonymous attestation in trusted computing platforms with sign and verify protocols nearly seven times more efficient than the current solution, and a state-of-the-art traceable signature scheme with support for variable anonymity. These three schemes greatly advance research in the area of anonymous authentication. The authentication techniques presented in this dissertation are based on common mathematical and cryptographical foundations, sharing similar security assumptions. We call them flexible digital authentication schemes

On the foundations of proof-of-work based blockchain protocols

Proof-of-work (PoW) based blockchain protocols, are protocols that organize data into blocks, connected through the use of a hash function to form chains, and which make use of PoW to reach agreement, i.e., proofs that require spending some amount of computational power to be generated. This type of protocols rose into prominence with the advent of Bitcoin, the first protocol that provably implements a distributed transaction ledger against an adversary that controls less than half of the total computational power in the network, in a setting where protocol participants join and leave dynamically without the need for a registration service. Protocols in this class were also the first to be shown sufficient to solve consensus under similar conditions, a problem of fundamental importance in distributed computing. In this thesis, we explore foundational issues of PoW-based blockchain protocols that mainly have to do with the assumptions required to ensure their safe operation. We start by examining whether a common random string that is shared at the start of the protocol execution among the protocol participants is required to efficiently run such protocols. Bitcoin's security is based on the existence of such a string, called the genesis block. On the other hand, protocols found in previous works that do not assume such a setup are inefficient, in the sense that their round complexity strongly depends on the number of protocol participants. Our first contribution is the construction of efficient PoW-based blockchain protocols that provably implement a distributed ledger and consensus without such setup. Next, we turn our attention to the PoW primitive. All previous analyses model PoW using a random oracle. While satisfactory as a sanity check, the random oracle methodology has received significant criticism and shown not to be sound. We make progress by introducing a non-idealized security model and appropriate computational assumptions that are sufficient to implement a distributed ledger or consensus when combined with the right PoW-based protocol. Finally, we analyze GHOST, a recently proposed blockchain protocol, and prove its security against a byzantine adversary under similar assumptions as Bitcoin. Previous works only considered specific attacks