Tightly Secure Hierarchical Identity-Based Encryption

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

On Improving Communication Complexity in Cryptography

Cryptography grew to be much more than "the study of secret writing". Modern cryptography is concerned with establishing properties such as privacy, integrity and authenticity in protocols for secure communication and computation. This comes at a price: Cryptographic tools usually introduce an overhead, both in terms of communication complexity (that is, number and size of messages transmitted) and computational efficiency (that is, time and memory required). As in many settings communication between the parties involved is the bottleneck, this thesis is concerned with improving communication complexity in cryptographic protocols. One direction towards this goal is scalable cryptography: In many cryptographic schemes currently deployed, the security degrades linearly with the number of instances (e.g. encrypted messages) in the system. As this number can be huge in contexts like cloud computing, the parameters of the scheme have to be chosen considerably larger - and in particular depending on the expected number of instances in the system - to maintain security guarantees. We advance the state-of-the-art regarding scalable cryptography by constructing schemes where the security guarantees are independent of the number of instances. This allows to choose smaller parameters, even when the expected number of instances is immense. - We construct the first scalable encryption scheme with security against active adversaries which has both compact public keys and ciphertexts. In particular, we significantly reduce the size of the public key to only about 3% of the key-size of the previously most efficient scalable encryption scheme. (Gay,Hofheinz, and Kohl, CRYPTO, 2017) - We present a scalable structure-preserving signature scheme which improves both in terms of public-key and signature size compared to the previously best construction to about 40% and 56% of the sizes, respectively. (Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018) Another important area of cryptography is secure multi-party computation, where the goal is to jointly evaluate some function while keeping each party’s input private. In traditional approaches towards secure multi-party computation either the communication complexity scales linearly in the size of the function, or the computational efficiency is poor. To overcome this issue, Boyle, Gilboa, and Ishai (CRYPTO, 2016) introduced the notion of homomorphic secret sharing. Here, inputs are shared between parties such that each party does not learn anything about the input, and such that the parties can locally evaluate functions on the shares. Homomorphic secret sharing implies secure computation where the communication complexity only depends on the size of the inputs, which is typically much smaller than the size of the function. A different approach towards efficient secure computation is to split the protocol into an input-independent preprocessing phase, where long correlated strings are generated, and a very efficient online phase. One example for a useful correlation are authenticated Beaver triples, which allow to perform efficient multiplications in the online phase such that privacy of the inputs is preserved and parties deviating the protocol can be detected. The currently most efficient protocols implementing the preprocessing phase require communication linear in the number of triples to be generated. This results typically in high communication costs, as the online phase requires at least one authenticated Beaver triple per multiplication. We advance the state-of-the art regarding efficient protocols for secure computation with low communication complexity as follows. - We construct the first homomorphic secret sharing scheme for computing arbitrary functions in NC 1 (that is, functions that are computably by circuits with logarithmic depth) which supports message spaces of arbitrary size, has only negligible correctness error, and does not require expensive multiplication on ciphertexts. (Boyle, Kohl, and Scholl, EUROCRYPT, 2019) - We introduce the notion of a pseudorandom correlation generator for general correlations. Pseudorandom correlation generators allow to locally extend short correlated seeds into long pseudorandom correlated strings. We show that pseudorandom correlation generators can replace the preprocessing phase in many protocols, leading to a preprocessing phase with sublinear communication complexity. We show connections to homomorphic secret sharing schemes and give the first instantiation of pseudorandom correlation generators for authenticated Beaver triples at reasonable computational efficiency. (Boyle, Couteau, Gilboa, Ishai, Kohl, and Scholl, CRYPTO, 2019

Tightly-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model

Key-encapsulation mechanisms secure against chosen ciphertext attacks (IND-CCA-secure KEMs) in the quantum random oracle model have been proposed by Boneh, Dagdelen, Fischlin, Lehmann, Schafner, and Zhandry (CRYPTO 2012), Targhi and Unruh (TCC 2016-B), and Hofheinz, Hövelmanns, and Kiltz (TCC 2017). However, all are non-tight and, in particular, security levels of the schemes obtained by these constructions are less than half of original security levels of their building blocks. In this paper, we give a conversion that tightly converts a weakly secure public-key encryption scheme into an IND-CCA-secure KEM in the quantum random oracle model. More precisely, we define a new security notion for deterministic public key encryption (DPKE) called the disjoint simulatability, and we propose a way to convert a disjoint simulatable DPKE scheme into an IND-CCA-secure key-encapsulation mechanism scheme without incurring a significant security degradation. In addition, we give DPKE schemes whose disjoint simulatability is tightly reduced to post-quantum assumptions. As a result, we obtain IND-CCA-secure KEMs tightly reduced to various post-quantum assumptions in the quantum random oracle model

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

On Tightly Secure Primitives in the Multi-Instance Setting

We initiate the study of general tight reductions in cryptography. There already exist a variety of works that offer tight reductions for a number of cryptographic tasks, ranging from encryption and signature schemes to proof systems. However, our work is the first to provide a universal definition of a tight reduction (for arbitrary primitives), along with several observations and results concerning primitives for which tight reductions have not been known. Technically, we start from the general notion of reductions due to Reingold, Trevisan, and Vadhan (TCC 2004), and equip it with a quantification of the respective reduction loss, and a canonical multi-instance extension to primitives. We then revisit several standard reductions whose tight security has not yet been considered. For instance, we revisit a generic construction of signature schemes from one-way functions, and show how to tighten the corresponding reduction by assuming collision-resistance from the used one-way function. We also obtain tightly secure pseudorandom generators (by using suitable rerandomisable hard-core predicates), and tightly secure lossy trapdoor functions

Anonymity of NIST PQC Round 3 KEMs

This paper investigates __anonymity__ of all NIST PQC Round 3 KEMs: Classic McEliece, Kyber, NTRU, Saber, BIKE, FrodoKEM, HQC, NTRU Prime (Streamlined NTRU Prime and NTRU LPRime), and SIKE. We show the following results: * NTRU is anonymous in the quantum random oracle model (QROM) if the underlying deterministic PKE is strongly disjoint-simulatable. NTRU is collision-free in the QROM. A hybrid PKE scheme constructed from NTRU as KEM and appropriate DEM is anonymous and robust. (Similar results for BIKE, FrodoKEM, HQC, NTRU LPRime, and SIKE hold except for two of three parameter sets of HQC.) * Classic McEliece is anonymous in the QROM if the underlying PKE is strongly disjoint-simulatable and a hybrid PKE scheme constructed from it as KEM and appropriate DEM is anonymous. * Grubbs, Maram, and Paterson pointed out that Kyber and Saber have a gap in the current IND-CCA security proof in the QROM (EUROCRYPT 2022). We found that Streamlined NTRU Prime has another technical obstacle for the IND-CCA security proof in the QROM. Those answer the open problem to investigate the anonymity and robustness of NIST PQC Round~3 KEMs posed by Grubbs, Maram, and Paterson (EUROCRYPT 2022). We use strong disjoint-simulatability of the underlying PKE of KEM and strong pseudorandomness and smoothness/sparseness of KEM as the main tools, which will be of independent interest

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

Unique-Path Identity Based Encryption With Applications to Strongly Secure Messaging

Hierarchical Identity Based Encryption (HIBE) is a well studied, versatile tool used in many cryptographic protocols. Yet, since the performance of all known HIBE constructions is broadly considered prohibitive, some real-world applications avoid relying on HIBE at the expense of security. A prominent example for this is secure messaging: Strongly secure messaging protocols are provably equivalent to Key-Updatable Key Encapsulation Mechanisms (KU-KEMs; Balli et al., Asiacrypt 2020); so far, all KU-KEM constructions rely on adaptive unbounded-depth HIBE (Poettering and Rösler, Jaeger and Stepanovs, both CRYPTO 2018). By weakening security requirements for better efficiency, many messaging protocols dispense with using HIBE. In this work, we aim to gain better efficiency without sacrificing security. For this, we observe that applications like messaging only need a restricted variant of HIBE for strong security. This variant, that we call Unique-Path Identity Based Encryption (UPIBE), restricts HIBE by requiring that each secret key can delegate at most one subordinate secret key. However, in contrast to fixed secret key delegation in Forward-Secure Public Key Encryption, the delegation in UPIBE, as in HIBE, is uniquely determined by variable identity strings from an exponentially large space. We investigate this mild but surprisingly effective restriction and show that it offers substantial complexity and performance advantages. More concretely, we generically build bounded-depth UPIBE from only bounded-collusion IBE in the standard model; and we generically build adaptive unbounded-depth UPIBE from only selective bounded-depth HIBE in the random oracle model. These results significantly extend the range of underlying assumptions and efficient instantiations. We conclude with a rigorous performance evaluation of our UPIBE design. Beyond solving challenging open problems by reducing complexity and improving efficiency of KU-KEM and strongly secure messaging protocols, we offer a new definitional perspective on the bounded-collusion setting