In this paper, we introduce a novel approach to Multi-Key Fully Homomorphic Encryption (MK-FHE) that enhances both efficiency and security beyond the capabilities of traditional MK-FHE and MultiParty Computation (MPC) systems. Our method generates a unified key structure, enabling constant ciphertext size and constant execution time for encrypted computations, regardless of the number of participants involved. This approach addresses critical limitations such as ciphertext size expansion,...

We consider the multi-user security under the adaptive corruptions and key leakages ($\rm{MU^{c\&l}}$ security) for lattice-based signatures. Although there exists an $\rm{MU^{c\&l}}$ secure signature based on a number-theoretic assumption, or a leakage-resilient lattice-based signature in the single-user setting, $\rm{MU^{c\&l}}$ secure lattice-based signature is not known. We examine the existing lattice-based signature schemes from the viewpoint of $\rm{MU^{c\&l}}$ security, and find...

This paper is a report on how we tackled constructing a digital signature scheme whose multi-user security with corruption can be tightly reduced to search assumptions. We fail to (dis)prove the statement but obtain the following new results: - We reveal two new properties of signature schemes whose security cannot be tightly reduced to standard assumptions. - We construct a new signature scheme. Its multi-user security with corruption is reduced to the CDH assumption (in the ROM), and...

In the multi-user with corruptions (muc) setting there are $n\geq 1$ users, and the goal is to prove that, even in the face of an adversary that adaptively corrupts users to expose their keys, un-corrupted users retain security. This can be considered for many primitives including signatures and encryption. Proofs of muc security, while possible, generally suffer a factor n loss in tightness, which can be large. This paper gives new proofs where this factor is reduced to the number c of...

We consider constructions that combine outputs of a single permutation $\pi:\{0,1\}^n \rightarrow \{0,1\}^n$ using a public function. These are popular constructions for achieving security beyond the birthday bound when implementing a pseudorandom function using a block cipher (i.e., a pseudorandom permutation). One of the best-known constructions (denoted SXoP$[2,n]$) XORs the outputs of 2 domain-separated calls to $\pi$. Modeling $\pi$ as a uniformly chosen permutation, several previous...

Asymmetric Password-Authenticated Key Exchange (aPAKE) protocols, particularly Strong aPAKE (saPAKE) have enjoyed significant attention, both from academia and industry, with the well-known OPAQUE protocol currently undergoing standardization. In (s)aPAKE, a client and a server collaboratively establish a high-entropy key, relying on a previously exchanged password for authentication. A main feature is its resilience against offline and precomputation (for saPAKE) attacks. OPAQUE, as well as...

Recent years have witnessed a significant development for functional encryption (FE) in the multi-user setting, particularly with multi-client functional encryption (MCFE). The challenge becomes more important when combined with access control, such as attribute-based encryption (ABE), which was actually not covered by the FE and MCFE frameworks. On the other hand, as for complex primitives, many works have studied the admissibility of adversaries to ensure that the security model...

We show that the adaptive compromise security definitions of Jaeger and Tyagi (Crypto '20) cannot be applied in several natural use-cases. These include proving multi-user security from single-user security, the security of the cascade PRF, and the security of schemes sharing the same ideal primitive. We provide new variants of the definitions and show that they resolve these issues with composition. Extending these definitions to the asymmetric settings, we establish the security of the...

In FSE'16, Luykx et al. have proposed $\textsf{LightMAC}$ that provably achieves a query length independent PRF security bound. To be precise, the construction achieves security roughly in the order of $O(q^2/2^n)$, when instantiated with two independently keyed $n$-bit block ciphers and $q$ is the total number of queries made by the adversary. Subsequently, in ASIACRYPT'17, Naito proposed a beyond-birthday-bound variant of the $\textsf{LightMAC}$ construction, dubbed as...

In this paper, we study the problem of lower bounding any given cost function depending on the false positive and false negative probabilities of adversaries against indistinguishability security notions in symmetric-key cryptography. We take the cost model as an input, so that this becomes a purely information-theoretical question. We propose power bounds as an easy-to-use alternative for advantage bounds in the context of indistinguishability with asymmetric cost functions. We show that...

The Ascon cipher suite has recently become the preferred standard in the NIST Lightweight Cryptography standardization process. Despite its prominence, the initial dedicated security analysis for the Ascon mode was conducted quite recently. This analysis demonstrated that the Ascon AEAD mode offers superior security compared to the generic Duplex mode, but it was limited to a specific scenario: single-user nonce-respecting, with a capacity strictly larger than the key size. In this paper, we...

Hash chain based password systems are a useful way to guarantee authentication with one-time passwords. The core idea is specified in RFC 1760 as S/Key. At CCS 2017, Kogan et al. introduced T/Key, an improved password system where one-time passwords are only valid for a limited time period. They proved security of their construction in the random oracle model under a basic modeling of the adversary. In this work, we make various advances in the analysis and instantiation of hash chain based...

The XOR of two independent permutations (XoP) is a well-known construction for achieving security beyond the birthday bound when implementing a pseudorandom function using a block cipher (i.e., a pseudorandom permutation). The idealized construction (where the permutations are uniformly chosen and independent) and its variants have been extensively analyzed over nearly 25 years. The best-known asymptotic information-theoretic indistinguishability bound for the XoP construction is...

Multi-user (mu) security considers large-scale attackers that, given access to a number of cryptosystem instances, attempt to compromise at least one of them. We initiate the study of mu security of the so-called GGMtree that stems from the PRG-to-PRF transformation of Goldreich, Goldwasser, and Micali, with a goal to provide references for its recently popularized use in applied cryptography. We propose a generalized model for GGM trees and analyze its mu prefix-constrained PRF security in...

We continue the study of blockcipher-based (tweakable) correlation robust hash functions, which are central building blocks of circuit garbling and oblivious-transfer extension schemes. Motivated by Roy (CRYPTO 2022), we first enhance the multi-user tweakable correlation robust notion of Guo et al. (CRYPTO 2020) with a {\it key leaking oracle} that tells the adversary whether a certain user key satisfies the adversarially-chosen predicate. We then investigate the state-of-the-art hash...

Security proofs of symmetric-key primitives typically consider an idealized world with access to a (uniformly) random function. The starting point of our work is the observation that such an ideal world can lead to underestimating the actual security of certain primitives. As a demonstrating example, $\mathsf{XoP2}$, which relies on two independent random permutations, has been proven to exhibit superior concrete security compared to $\mathsf{XoP}$, which employs a single permutation with...

We present a construction, called Kirby, for building a variable-input-length pseudorandom function (VIL-PRF) from a $b$-bit permutation. For this construction we prove a tight bound of $b/2$ bits of security on the PRF distinguishing advantage in the random permutation model and in the multi-user setting. Similar to full-state keyed sponge/duplex, it supports full-state absorbing and additionally supports full-state squeezing, while the sponge/duplex can squeeze at most $b-c$ bits per...

At CRYPTO'18, Datta et al. proposed nPolyMAC and proved the security up to 2^{2n/3} authentication queries and 2^{n} verification queries. At EUROCRYPT'19, Dutta et al. proposed CWC+ and showed the security up to 2^{2n/3} queries. At FSE'19, Datta et al. proposed PolyMAC and its key-reduced variant 2k-PolyMAC, and showed the security up to 2^{2n/3} queries. This security bound was then improved by Kim et al. (EUROCRYPT'20) and Datta et al (FSE'23) respectively to 2^{3n/4} and in the...

Non-interactive key exchange (NIKE) schemes like the Diffie-Hellman key exchange are a widespread building block in several cryptographic protocols. Since the Diffie-Hellman key exchange is not post-quantum secure, it is important to investigate post-quantum alternatives. We analyze the security of the LWE-based NIKE by Ding et al. (ePrint 2012) and Peikert (PQCrypt 2014) in a multi-user setting where the same public key is used to generate shared keys with multiple other users. The...

We give a tighter security proof for authenticated key exchange (AKE) protocols that are generically constructed from key encapsulation mechanisms (KEMs) in the quantum random oracle model (QROM). Previous works (Hövelmanns et al., PKC 2020) gave reductions for such a KEM-based AKE protocol in the QROM to the underlying primitives with square-root loss and a security loss in the number of users and total sessions. Our proof is much tighter and does not have square-root loss. Namely, it only...

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs), to allow instantiations with post-quantums KEM like KYBER. The ACNS23 paper left as an open problem to argue security against quantum attackers, with its security proof being in the universal composability (UC) framework. This is common for PAKE, however, at the time of this submission’s writing, it was not known how to prove (computational)...

When modelling how public key encryption can enable secure communication, we should acknowledge that secret information, such as private keys or the randomness used for encryption, could become compromised. Intuitively, one would expect unrelated communication to remain secure, yet formalizing this intuition has proven challenging. Several security notions have appeared that aim to capture said scenario, ranging from the multi-user setting with corruptions, via selective opening attacks...

Proxy re-encryption (PRE) allows a proxy with a re-encryption key to translate a ciphertext intended for Alice (delegator) to another ciphertext intended for Bob (delegatee) without revealing the underlying message. However, with PRE, Bob can obtain the whole message from the re-encrypted ciphertext, and Alice cannot take flexible control of the extent of the message transmitted to Bob. In this paper, we propose a new variant of PRE, called Fine-Grained PRE (FPRE), to support...

In this work, we construct the first digital signature (SIG) and public-key encryption (PKE) schemes with almost tight multi-user security under adaptive corruptions based on the learning-with-errors (LWE) assumption in the standard model. Our PKE scheme achieves almost tight IND-CCA security and our SIG scheme achieves almost tight strong EUF-CMA security, both in the multi-user setting with adaptive corruptions. The security loss is quadratic in the security parameter, and independent of...

Commodity encrypted storage platforms (e.g., IceDrive, pCloud) permit data store and sharing across multiple users while preserving data confidentiality. However, end-to-end encryption may not be sufficient since it only offers confidentiality when the data is at rest or in transit. Meanwhile, sensitive information can be leaked from metadata representing activities during data operations (e.g., query, processing). Recent encrypted search platforms such as DORY (OSDI’20) or DURASIFT...

Proving security bounds in contexts with a large number of users is one of the central problems in symmetric-key cryptography today. This paper introduces a new method for information-theoretic multi-user security proofs, called ``the Squared-Ratio Method''. At its core, the method requires the expectation of the square of the ratio of observing the so-called good transcripts (from Patarin's H-coefficient technique) in the real and the ideal world. Central to the method is the...

In Internet security protocols including TLS 1.3, KEMTLS, MLS and Noise, HMAC is being assumed to be a dual-PRF, meaning a PRF not only when keyed conventionally (through its first input), but also when "swapped" and keyed (unconventionally) through its second (message) input. We give the first in-depth analysis of the dual-PRF assumption on HMAC. For the swap case, we note that security does not hold in general, but completely characterize when it does; we show that HMAC is swap-PRF...

The Ascon authenticated encryption scheme has recently been selected as winner of the NIST Lightweight Cryptography competition. Despite its fame, however, there is no known overall generic security treatment of its mode: most importantly, all earlier related generic security results only use the key to initialize the state and do not take into account key blinding internally and at the end. In this work we present a thorough security analysis of the Ascon mode: we consider multi-user and...

Searchable encrypted systems enable privacy-preserving keyword search on encrypted data. Symmetric systems achieve high efficiency (e.g., sublinear search), but they mostly support single-user search. Although systems based on public-key or hybrid models support multi-user search, they incur inherent security weaknesses (e.g., keyword-guessing vulnerabilities) and scalability limitations due to costly public-key operations (e.g., pairing). More importantly, most encrypted search designs leak...

Consider a state-level adversary who observes and stores large amounts of encrypted data from all users on the Internet, but does not have the capacity to store it all. Later, it may target certain "persons of interest" in order to obtain their decryption keys. We would like to guarantee that, if the adversary's storage capacity is only (say) $1\%$ of the total encrypted data size, then even if it can later obtain the decryption keys of arbitrary users, it can only learn something about the...

We give the first examples of public-key encryption schemes which can be proven to achieve multi-challenge, multi-user CCA security via reductions that are tight in time, advantage, and memory. Our constructions are obtained by applying the KEM-DEM paradigm to variants of Hashed ElGamal and the Fujisaki-Okamoto transformation that are augmented by adding uniformly random strings to their ciphertexts and/or keys. The reductions carefully combine recent proof techniques introduced by...

Encrypting too much data using the same key is a bad practice from a security perspective. Hence, it is customary to perform re-keying after a given amount of data is transmitted. While in many cases, the re-keying is done using a fresh execution of some key exchange protocol (e.g., in IKE or TLS), there are scenarios where internal re-keying, i.e., without exchange of information, is performed, mostly due to performance reasons. Originally suggested by Abdalla and Bellare, there are...

In this paper, we consider tight multi-user security under adaptive corruptions, where the adversary can adaptively corrupt some users and obtain their secret keys. We propose generic constructions for a bunch of primitives, and the instantiations from the matrix decision Diffie-Hellman (MDDH) assumptions yield the following schemes: (1) the first digital signature (SIG) scheme achieving almost tight strong EUF-CMA security in the multi-user setting with adaptive corruptions in the...

Re-randomizable Replayable CCA-secure public key encryption (Rand-RCCA PKE) schemes guarantee security against chosen-ciphertext attacks while ensuring the useful property of re-randomizable ciphertexts. We introduce the notion of multi-user and multi-ciphertext Rand-RCCA PKE and we give the first construction of such a PKE scheme with an almost tight security reduction to a standard assumption. Our construction is structure preserving and can be instantiated over Type-1 pairing groups....

We introduce CorrGapCDH, the Gap Computational Diffie-Hellman problem in the multi-user setting with Corruptions. In the random oracle model, our assumption tightly implies the security of the authenticated key exchange protocols NAXOS in the eCK model and (a simplified version of) X3DH without ephemeral key reveal. We prove hardness of CorrGapCDH in the generic group model, with optimal bounds matching the one of the discrete logarithm problem. We also introduce CorrCRGapCDH, a stronger...

The ChaCha20-Poly1305 AEAD scheme is being increasingly widely deployed in practice. Practitioners need proven security bounds in order to set data limits and rekeying intervals for the scheme. But the formal security analysis of ChaCha20-Poly1305 currently lags behind that of AES-GCM. The only extant analysis (Procter, 2014) contains a flaw and is only for the single-user setting. We rectify this situation. We prove a multi-user security bound on the AEAD security of ChaCha20-Poly1305 and...

Cloud storage and computing offers significant convenience and management efficiency in the information era. Privacy protection is a major challenge in cloud computing. Public key encryption with keyword search (PEKS) is an ingenious tool for ensuring privacy and functionality in certain scenario, such as ensuring privacy for data retrieval appearing in the cloud computing. Despite many attentions received, PEKS schemes still face several challenges in practical applications, such as low...

We define the security notion of (strong) collision resistance for chameleon hash functions in the multi-user setting ((S-)MU-CR security). We also present three constructions, CHF_dl, CHF_rsa and CHF_fac, and prove their tight S-MU-CR security based on the discrete logarithm, RSA and factoring assumptions, respectively. In applications, our tightly S-MU-CR secure chameleon hash functions help us to lift a signature scheme from (weak) unforgeability to strong unforgeability in the multi-user...

Constructions based on two public permutation calls are very common in today’s cryptographic community. However, each time a new construction is introduced, a dedicated proof must be carried out to study the security of the construction. In this work, we propose a new tool to analyze the security of these constructions in a modular way. This tool is built on the idea of the classical mirror theory for block cipher based constructions, such that it can be used for security proofs in the ideal...

For several decades, constructing pseudorandom functions from pseudorandom permutations, so-called Luby-Rackoff backward construction, has been a popular cryptographic problem. Two methods are well-known and comprehensively studied for this problem: summing two random permutations and truncating partial bits of the output from a random permutation. In this paper, by combining both summation and truncation, we propose new Luby-Rackoff backward constructions, dubbed SaT1 and SaT2,...

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their...

Both multi-user PRFs and sponge-based constructions have generated a lot of research interest lately. Dedicated analyses for multi-user security have improved the bounds a long distance from the early generic bounds obtained through hybrid arguments, yet the bounds generally don't allow the number of users to be more than birthday-bound in key-size. Similarly, known sponge constructions suffer from being only birthday-bound secure in terms of their capacity. We present in this paper...

We study the problem of multi-user dynamic searchable symmetric encryption (DMUSSE) where a data owner stores its encrypted documents on an untrusted remote server and wishes to selectively allow multiple users to access them by issuing keyword search queries. Specifically, we consider the case where some of the users may be corrupted and colluding with the server to extract additional information about the dataset (beyond what they have access to). We provide the first formal security...

The notion of public key encryption with keyword search (PEKS) was introduced to efficiently search over encrypted data. In this paper, we propose a PEKS scheme in which both the encrypted keyword and the trapdoor are randomized, so that the cloud server is not able to recognize identical queries. Our scheme is CI-secure in the single-user setting and TI-secure in the multi-user setting with multi-trapdoor.

A secure $n$-bit tweakable block cipher~(TBC) using $t$-bit tweaks can be modeled as a tweakable uniform random permutation, where each tweak defines an independent random $n$-bit permutation. When an input to this tweakable permutation is fixed, it can be viewed as a perfectly secure $t$-bit random function. On the other hand, when a tweak is fixed, it can be viewed as a perfectly secure $n$-bit random permutation, and it is well known that the sum of two random permutations is...

Public key encryption schemes are increasingly being studied concretely, with an emphasis on tight bounds even in a multi-user setting. Here, two types of formalization have emerged, one with a single challenge bit and one with multiple challenge bits. Another modelling choice is whether to allow key corruptions or not. How tightly the various notions relate to each other has hitherto not been studied in detail. We show that in the absence of corruptions, single-bit left-or-right...

We analyze the multi-user (mu) security of a family of nonce-based authentication encryption (nAE) schemes based on a tweakable block cipher (TBC). The starting point of our work is an analysis of the mu security of the SCT-2 mode which underlies the nAE scheme Deoxys-II, winner of the CAESAR competition for the defense-in-depth category. We extend this analysis in two directions, as we detail now. First, we investigate the mu security of several TBC-based variants of the counter...

In CRYPTO'21, Shen et al. have proved in the ideal cipher model that $\textsf{Two-Keyed-DbHtS}$ construction is secure up to $2^{2n/3}$ queries in the multi-user setting independent of the number of users, where the underlying double-block hash function $\textsf{H}$ of the \textsf{Two-Keyed-DbHtS} construction is realized as the concatenation of two independent $n$-bit keyed hash functions $(\textsf{H}_{K_h,1}, \textsf{H}_{K_h, 2})$ such that each of the $n$-bit keyed hash function is...

3kf9 is a three-key CBC-type MAC that enhances the standardized integrity algorithm f9 (3GPP-MAC). It has beyond-birthday-bound security and is expected to be a possible candidate in constrained environments when instantiated with lightweight blockciphers. Two variants 2kf9 and 1kf9 were proposed to reduce key size for efficiency, but recently, Leurent et al. (CRYPTO'18) and Shen et al. (CRYPTO'21) pointed out critical flaws on these two variants and invalidated their security proofs with...

Selective opening (SO) security is one of the most important security notions of public key encryption (PKE) in a multi-user setting. Even though messages and random coins used in some ciphertexts are leaked, SO security guarantees the confidentiality of the other ciphertexts. Actually, it is shown that there exist PKE schemes which meet the standard security such as indistinguishability against chosen ciphertext attacks (IND-CCA security) but do not meet SO security against chosen...

We propose an efficient oblivious transfer in the random oracle model based on public key encryption with pseudorandom public keys. The construction is as efficient as the state of art though it has a significant advantage. It has a tight security reduction to the multi-user security of the underlying public key encryption. In previous constructions, the security reduction has a multiplicative loss that amounts in at least the amount of adversarial random oracle queries. When considering...

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs achieve beyond-birthday-bound (BBB) security, including SUM-ECBC, PMAC_Plus, 3kf9 and LightMAC_Plus etc. Recently, Shen et al. (Crypto 2021) proposed a security framework for two-key DbHtS MACs in the multi-user setting, stating that when the underlying blockcipher is ideal and the universal hash function is regular and almost universal, the two-key DbHtS MACs achieve 2n/3-bit security. Unfortunately, the regular and universal...

At CRYPTO 2019, Chen et al. have shown a beyond the birthday bound secure $n$-bit to $n$-bit PRF based on public random permutations. Followed by the work, Dutta and Nandi have proposed a beyond the birthday bound secure nonce based MAC $\textsf{nEHtM}_p$ based on public random permutation. In particular, the authors have shown that $\textsf{nEHtM}_p$ achieves tight $2n/3$-bit security ({\em with respect to the state size of the permutation}) in the single-user setting, and their proven...

Distributed secret sharing techniques, where a specific secret is encoded into its shares which are conveyed to the IoT device or its user via storage nodes, are considered. A verifiably distributed secret sharing (VDSS) provides a way for a legitimate user to verify the secret he reconstructs through the downloaded shares while the secrecy condition is satisfied in a weak or a perfect sense. This article examines the impact of minimizing verification information in a VDSS on the...

Multi-Client Functional Encryption ($\mathsf{MCFE}$) and Multi-Input Functional Encryption ($\mathsf{MIFE}$) are very interesting extensions of Functional Encryption for practical purpose. They allow to compute joint function over data from multiple parties. Both primitives are aimed at applications in multi-user settings where decryption can be correctly output for users with appropriate functional decryption keys only. While the definitions for a single user or multiple users were quite...

We construct the first tightly secure signature schemes in the multi-user setting with adaptive corruptions from lattices. In stark contrast to the previous tight constructions whose security is solely based on number-theoretic assumptions, our schemes are based on the Learning with Errors (LWE) assumption which is supposed to be post-quantum secure. The security of our scheme is independent of the numbers of users and signing queries, and it is in the non-programmable random oracle model....

Constructing an efficient CCA-secure KEM is generally done by first constructing a passively-secure PKE scheme, and then applying the Fujisaki-Okamoto (FO) transformation. The original FO transformation was designed to offer security in a single user setting. A stronger notion, known as multi-user security, considers the attacker's advantage in breaking one of many user's ciphertexts. Bellare et al.~(EUROCRYPT 2020) showed that standard single user security implies multi-user security with...

Selective opening attacks (SOA) (for public-key encryption, PKE) concern such a multi-user scenario, where an adversary adaptively corrupts some fraction of the users to break into a subset of honestly created ciphertexts, and tries to learn the information on the messages of some unopened (but potentially related) ciphertexts. Until now, the notion of selective opening attacks is only considered in two settings: sender selective opening (SSO), where part of senders are corrupted and...

Secure computing methods such as fully homomorphic encryption and hardware solutions such as Intel Software Guard Extension (SGX) have been applied to provide security for user input in privacy-oriented computation outsourcing. Fully homomorphic encryption is amenable to parallelization and hardware acceleration to improve its scalability and latency, but is limited in the complexity of functions it can efficiently evaluate. SGX is capable of arbitrarily complex calculations, but due to...

For Key Encapsulation Mechanism (KEM) deployed in a multi-user setting, an adversary may corrupt some users to learn their secret keys, and obtain some encapsulated keys due to careless key managements of users. To resist such attacks, we formalize Enhanced security against Chosen Plaintext/Ciphertext Attack (ECPA/ECCA), which ask the pseudorandomness of unrevealed encapsulated keys under uncorrupted users. This enhanced security for KEM serves well for the security of a class of...

We construct a short and adaptively secure identity-based signature scheme tightly based on the well-known Short Integer Solution (SIS) assumption. Although identity-based signature schemes can be tightly constructed from either standard signature schemes against adaptive corruptions in the multi-user setting or a two-level hierarchical identity-based encryption scheme, neither of them is known with short signature size and tight security based on the SIS assumption. Here ``short'' means the...

We construct the first authenticated key exchange protocols that achieve tight security in the standard model. Previous works either relied on techniques that seem to inherently require a random oracle, or achieved only “Multi-Bit-Guess” security, which is not known to compose tightly, for instance, to build a secure channel. Our constructions are generic, based on digital signatures and key encapsulation mechanisms (KEMs). The main technical challenges we resolve is to determine suitable...

We propose the first tight security proof for the ordinary two-message signed Diffie-Hellman key exchange protocol in the random oracle model. Our proof is based on the strong computational Diffie-Hellman assumption and the multi-user security of a digital signature scheme. With our security proof, the signed DH protocol can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate any security loss. We abstract our approach with a...

As a solution to mitigate the key exposure problems in the digital signature, forward security has been proposed. The forward security guarantees the integrity of the messages generated in the past despite leaks of a current time period secret key by evolving a secret key on each time period. However, there is no forward secure signature scheme whose all metrics have constant complexities. Furthermore, existing works do not support multi-user aggregation of signatures. In this paper, we...

In modern times, data collected from multi-user distributed applications must be analyzed on a massive scale to support critical business objectives. While analytics often requires the use of personal data, it may compromise user privacy expectations if this analysis is conducted over plaintext data. Private Stream Aggregation (PSA) allows for the aggregation of time-series data, while still providing strong privacy guarantees, and is significantly more efficient over a network than related...

We extend a basic key agreement model with a hidden identifier source to a multi-user model with joint secrecy and privacy constraints over all entities that do not trust each other. Different entities that use different measurements of the same remote source through broadcast channels (BCs) to agree on mutually-independent local secret keys are considered. This model is the proper multi-user extension of the basic model since the encoder and decoder pairs are not assumed to trust other...

We construct two tightly secure signature schemes based on the computational Diffie-Hellman (CDH) and factoring assumptions in the random oracle model. Our schemes are proven secure in the multi-user setting, and their security loss is constant and does not depend on the number of users or signing queries. They are the first schemes that achieve this based on standard search assumptions, as all existing schemes we are aware of are either based on stronger decisional assumptions, or proven...

Group key exchange (GKE) protocols let a group of users jointly establish fresh and secure key material. Many flavors of GKE have been proposed, differentiated by, among others, whether group membership is static or dynamic, whether a single key or a continuous stream of keys is established, and whether security is provided in the presence of state corruptions (forward and post-compromise security). In all cases, an indispensable ingredient to the rigorous analysis of a candidate solution is...

We construct the currently most efficient signature schemes with tight multi-user security against adaptive corruptions. It is the first generic construction of such schemes, based on lossy identification schemes (Abdalla etal; JoC 2016), and the first to achieve strong existential unforgeability. It also has significantly more compact signatures than the previously most efficient construction by Gjosteen and Jager (CRYPTO 2018). When instantiated based on the decisional Diffie-Hellman...

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs that aim for achieving beyond-birthday-bound security, including SUM-ECBC, PMAC\_Plus, 3kf9 and LightMAC_Plus. Recently Datta et al. (FSE'19), and then Kim et al. (Eurocrypt'20) prove that DbHtS constructions are secure beyond the birthday bound in the single-user setting. However, by a generic reduction, their results degrade to (or even worse than) the birthday bound in the multi-user setting. In this work, we revisit the...

This work studies signcryption of classical data in the quantum setting. Essentially, we investigate the quantum security of generic constructions of signcryption schemes based on three paradigms, viz., encrypt-then-sign (EtS), sign-then-encrypt (StE) and commit-then-encrypt-and-sign (CtE&S). For doing that we define the confidentiality and authenticity of signcryption for classical data both in insider and outsider models against quantum adversaries. In the insider model, we show that the...

We consider the security of two of the most commonly used cryptographic primitives—message authentication codes (MACs) and pseudorandom functions (PRFs)—in a multi-user setting with adaptive corruption. Whereas is it well known that any secure MAC or PRF is also multi-user secure under adaptive corruption, the trivial reduction induces a security loss that is linear in the number of users. Our main result shows that black-box reductions from “standard” assumptions cannot be used to provide a...

We analyze the multi-user security of the streaming encryption in Google's Tink library via an extended version of the framework of nonce-based online authenticated encryption of Hoang et al. (CRYPTO'15) to support random-access decryption. We show that Tink's design choice of using random nonces and a nonce-based key-derivation function indeed improves the concrete security bound. We then give two better alternatives that are more robust against randomness failure. In addition, we show how...

We provide a new definitional framework capturing the multi-user security of encryption schemes and pseudorandom functions in the face of adversaries that can adaptively compromise users' keys. We provide a sequence of results establishing the security of practical symmetric encryption schemes under adaptive compromise in the random oracle or ideal cipher model. The bulk of analysis complexity for adaptive compromise security is relegated to the analysis of lower-level primitives such as...

We consider the theoretically-sound selection of cryptographic parameters, such as the size of algebraic groups or RSA keys, for TLS 1.3 in practice. While prior works gave security proofs for TLS 1.3, their security loss is quadratic in the total number of sessions across all users, which due to the pervasive use of TLS is huge. Therefore, in order to deploy TLS 1.3 in a theoretically-sound way, it would be necessary to compensate this loss with unreasonably large parameters that would be...

File-sharing systems like Dropbox offer insufficient privacy because a compromised server can see the file contents in the clear. Although encryption can hide such contents from the servers, metadata leakage remains significant. The goal of our work is to develop a file-sharing system that hides metadata---including user identities and file access patterns. Metal is the first file-sharing system that hides such metadata from malicious users and that has a latency of only a few seconds. The...

The Schnorr signature scheme is an efficient digital signature scheme with short signature lengths, i.e., $4k$-bit signatures for $k$ bits of security. A Schnorr signature $\sigma$ over a group of size $p\approx 2^{2k}$ consists of a tuple $(s,e)$, where $e \in \{0,1\}^{2k}$ is a hash output and $s\in \mathbb{Z}_p$ must be computed using the secret key. While the hash output $e$ requires $2k$ bits to encode, Schnorr proposed that it might be possible to truncate the hash value without...

Password-Authenticated Key Exchange (PAKE) is a method to establish cryptographic keys between two users sharing a low-entropy password. In its asymmetric version, one of the users acts as a server and only stores some function of the password, e.g., a hash. Upon server compromise, the adversary learns H(pw). Depending on the strength of the password, the attacker now has to invest more or less work to reconstruct pw from H(pw). Intuitively, asymmetric PAKE seems more challenging than...

We present a searchable encryption scheme for dynamic document collections in a multi-user scenario. Our scheme features fine-grained access control to search results, as well as access control to operations such as adding documents to the document collection, or changing individual documents. The scheme features verifiability of search results. Our scheme also satisfies the forward privacy notion crucial for the security of dynamic searchable encryption schemes.

We show that chosen plaintext attacks (CPA) security is equivalent to chosen ciphertext attacks (CCA) security for key-dependent message (KDM) security. Concretely, we show how to construct a public-key encryption (PKE) scheme that is KDM-CCA secure with respect to all functions computable by circuits of a-priori bounded size, based only on a PKE scheme that is KDM-CPA secure with respect to projection functions. Our construction works for KDM security in the single user setting. Our main...

The ongoing NIST lightweight standardization process explicitly puts forward a requirement of side-channel security, which has renewed the interest for Authenticated Encryption schemes (AEs) with light(er)-weight side-channel secure implementations. To address this challenge, we investigate the leakage-resilience of a generic duplex-based stream cipher, and prove the classical bound, i.e., $\approx2^{c/2}$, under an assumption of non-invertible leakage. Based on this, we propose a new 1-pass...

We propose TEDT, a new Authenticated Encryption with Associated Data (AEAD) mode leveraging Tweakable Block Ciphers (TBCs). TEDT provides the following features: (i) It offers asymptotically optimal security in the multi-user setting. (ii) It offers nonce misuse-resilience, that is, the repetition of nonces does not impact the security of ciphertexts produced with fresh nonces. (iii) It offers KDM security in the multi-user setting, that is, its security is maintained even if key-dependent...

Tightly secure cryptographic schemes have been extensively studied in the fields of chosen-ciphertext secure public-key encryption (CCA-secure PKE), identity-based encryption (IBE), signatures and more. We extend tightly secure cryptography to inner product functional encryption (IPFE) and present the first tightly secure schemes related to IPFE. We first construct a new IPFE scheme that is tightly secure in the multi-user and multi-challenge setting. In other words, the security of our...

We present qTESLA, a family of post-quantum digital signature schemes that exhibits several attractive features such as simplicity and strong security guarantees against quantum adversaries, and built-in protection against certain side-channel and fault attacks. qTESLA---selected for round 2 of NIST's post-quantum cryptography standardization project---consolidates a series of recent schemes originating in works by Lyubashevsky, and Bai and Galbraith. We provide full-fledged, constant-time...

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argued informally that these strange features should imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we perform the first rigorous study of the problem of signing quantum states. We first show that the intuition of Barnum et al. was correct, by proving an impossibility result which rules out even very weak...

Multi-user (mu) security considers large-scale attackers (e.g., state actors) that given access to a number of sessions, attempt to compromise {\em at least} one of them. Mu security of authenticated encryption (AE) was explicitly considered in the development of TLS 1.3. This paper revisits the mu security of GCM, which remains to date the most widely used dedicated AE mode. We provide new concrete security bounds which improve upon previous work by adopting a refined parameterization of...

We construct the first (almost) tightly-secure unbounded-simulation-sound quasi-adaptive non-interactive zero-knowledge arguments (USS-QA-NIZK) for linear-subspace languages with compact (number of group elements independent of the security parameter) common reference string (CRS) and compact proofs under standard assumptions in bilinear-pairings groups. Specifically, our construction has $ O(\log Q) $ reduction to the SXDH, DLIN and matrix-DDH assumptions, where $ Q $ is the number of...

We propose a framework for achieving a public-key encryption (PKE) scheme that satisfies key dependent message security against chosen ciphertext attacks (KDM-CCA security) based on projective hash function. Our framework can be instantiated under the decisional diffie-hellman (DDH), quadratic residuosity (QR), and decisional composite residuosity (DCR) assumptions. The constructed schemes are KDM-CCA secure with respect to affine functions and compatible with the amplification method shown...

Key-Alternating Feistel (KAF) ciphers, a.k.a. Feistel-2 models, refer to Feistel networks with round functions of the form $F_i(k_i\oplus x_i)$, where $k_i$ is the (secret) round-key and $F_i$ is a public random function. This model roughly captures the structures of many famous Feistel ciphers, and the most prominent instance is DES. Existing provable security results on KAF assumed independent round-keys and round functions (ASIACRYPT 2004 & FSE 2014). In this paper, we investigate how to...

Security against selective opening attack (SOA) for receivers requires that in a multi-user setting, even if an adversary has access to all ciphertexts, and adaptively corrupts some fraction of the users to obtain the decryption keys corresponding to some of the ciphertexts, the remaining (potentially related) ciphertexts retain their privacy. In this paper, we study simulation-based selective opening security for receivers of public key encryption (PKE) schemes under chosen-ciphertext...

Tight security is increasingly gaining importance in real-world cryptography, as it allows to choose cryptographic parameters in a way that is supported by a security proof, without the need to sacrifice efficiency by compensating the security loss of a reduction with larger parameters. However, for many important cryptographic primitives, including digital signatures and authenticated key exchange (AKE), we are still lacking constructions that are suitable for real-world deployment. We...

Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a $wn$-bit (tweakable) block cipher from $n$-bit public permutations. Many widely deployed block ciphers are part of this family and rely on very small public permutations. Surprisingly, this structure has seen little theoretical interest when compared with Feistel networks, another high-level structure for block ciphers. This paper extends the work initiated by Dodis et al. in three directions; first,...

A proxy re-encryption (PRE) scheme is a public-key encryption scheme that allows the holder of a key pk to derive a re-encryption key for any other key pk'. This re-encryption key lets anyone transform ciphertexts under pk into ciphertexts under pk' without knowing the underlying message, while transformations from pk' to pk should not be possible (unidirectional). Security is defined in a multi-user setting against an adversary that gets the users’ public keys and can ask for re-encryption...

In Crypto 2017, Auerbach et al. initiated the study on memory-tight reductions and proved two negative results on the memory-tightness of restricted black-box reductions from multi-challenge security to single-challenge security for signatures and an artificial hash function. In this paper, we revisit the results by Auerbach et al. and show that for a large class of reductions treating multi-challenge security, it is impossible to avoid loss of memory-tightness unless we sacrifice the...

This paper revisits the multi-user (mu) security of symmetric encryption, from the perspective of delivering an analysis of the AES-GCM-SIV AEAD scheme. Our end result shows that its mu security is comparable to that achieved in the single-user setting. In particular, even when instantiated with short keys (e.g., 128 bits), the security of AES-GCM-SIV is not impacted by the collisions of two user keys, as long as each individual nonce is not re-used by too many users. Our bounds also improve...

By allowing a large number of users to behave as readers or writers, Multi-User Searchable Encryption (MUSE) raises new security and performance challenges beyond the typical requirements of Symmetric Searchable Encryption (SSE). In this paper we identify two core mandatory requirements of MUSE protocols being privacy in face of users colluding with the CSP and low complexity for the users, pointing that no existing MUSE protocol satisfies these two requirements at the same time. We then...

Selective opening security (SO security) is desirable for public key encryption (PKE) in a multi-user setting. {In a selective opening attack, an adversary receives a number of ciphertexts for possibly correlated messages, then it opens a subset of them and gets the corresponding messages together with the randomnesses used in the encryptions. SO security aims at providing security for the unopened ciphertexts.} Among the existing simulation-based, selective opening, chosen ciphertext secure...

We consider a setting where users store their encrypted documents on a remote server and can selectively share documents with each other. A user should be able to perform keyword searches over all the documents she has access to, including the ones that others shared with her. The contents of the documents, and the search queries, should remain private from the server. This setting was considered by Popa et al. (NSDI '14) who developed a new cryptographic primitive called Multi-Key...

An identity-based encryption scheme enables the efficient distribution of keys in a multi-user system. Such schemes are particularly attractive in resource constrained environments where critical resources such as processing power, memory and bandwidth are severely limited. This research examines the first pragmatic lattice-based IBE scheme pre- sented by Ducas, Lyubashevsky and Prest in 2014 and brings it into the realm of practicality for use on small devices. This is the first standalone...

We consider Symmetric Searchable Encryption with Sharing and Unsharing (SSEwSU), a notion that models Symmetric Searchable Encryption (SSE) in a multi-user setting in which documents can be dynamically shared and unshared among users. Previous works on SSE involving multiple users have assumed that all users have access to the same set of documents and/or their security models assume that all users in the system are trusted. As in SSE, every construction of a SSEwSU will be a trade-off...