International Association
for Cryptologic Research

End-to-End (E2E) encrypted messaging, which prevents even the service provider from learning communication contents, is gaining popularity. Since users care about maintaining access to their data even if their devices are lost or broken or just replaced, these systems are often paired with cloud backup solutions: typically, the user will encrypt its messages with a fixed key, and upload the ciphertexts to the server. Unfortunately, this naive solution has many drawbacks. First, it often undermines the fancy security guarantees of the core application, such as forward-secrecy (FS) and post-compromise security (PCS), in case the single backup key is compromised. Second, they are wasteful for backing up conversations in large groups, where many users are interested in backing up the same sequence of messages. Instead, we formalize a new primitive called Compact Key Storage (CKS) as the "right" solution to this problem. Such CKS scheme allows a mutable set of parties to delegate to a server storage of an increasing set of keys, while each client maintains only a small state. Clients update their state as they learn new keys (maintaining PCS), or whenever they want to forget keys (achieving FS), often without the need to interact with the server. Moreover, access to the keys (or some subset of them) can be efficiently delegated to new group members, who all efficiently share the same server's storage. We carefully define syntax, correctness, privacy, and integrity of CKS schemes, and build two efficient schemes provably satisfying these notions. Our line scheme covers the most basic "all-or-nothing" flavor of CKS, where one wishes to compactly store and delegate the entire history of past secrets. Thus, new users enjoy the efficiency and compactness properties of the CKS only after being granted access to the entire history of keys. In contrast, our interval scheme is only slightly less efficient but allows for finer-grained access, delegation, and deletion of past keys.

Forward-Secure Key-Encapsulation Mechanism (FS-KEM; Canetti et al. Eurocrypt 2003) allows Alice to encapsulate a key k to Bob for some time t such that Bob can decapsulate it at any time t'=<t. Crucially, a corruption of Bob's secret key after time t does not reveal k. In this work, we generalize and extend this idea by also taking Post-Compromise Security (PCS) into account and call it Interval Key-Encapsulation Mechanism (IKEM). Thus, we do not only protect confidentiality of previous keys against future corruptions but also confidentiality of future keys against past corruptions. For this, Bob can regularly renew his secret key and inform others about the corresponding public key. IKEM enables Bob to decapsulate keys sent to him over an interval of time extending into the past, in case senders have not obtained his latest public key; forward security only needs to hold with respect to keys encapsulated before this interval. This basic IKEM variant can be instantiated based on standard KEM, which we prove to be optimal in terms of assumptions as well as ciphertext and key sizes. We also extend this notion of IKEM for settings in which Bob decapsulates (much) later than Alice encapsulates (e.g., in high-latency or segmented networks): if a third user Charlie forwards Alice's ciphertext to Bob and, additionally, knows a recently renewed public key of Bob's, Charlie could re-encrypt the ciphertext for better PCS. We call this extended notion IKEMR. Our first IKEMR construction based on trapdoor permutations has (almost) constant sized ciphertexts in the number of re-encryptions; and our second IKEMR construction based on FS-PKE has constant sized public keys in the interval size. Finally, to bypass our lower bound on the IKEM(R) secret key size, which must be linear in the interval size, we develop a new Interval RAM primitive with which Bob only stores a constant sized part of his secret key locally, while outsourcing the rest to a (possibly adversarial) server. For all our constructions, we achieve security against active adversaries. For this, we obtain new insights on Replayable CCA security for KEM-type primitives, which might be of independent interest.

In recent work [Crypto'24], Dodis, Jost, and Marcedone introduced Compact Key Storage (CKS) as a modern approach to backup for end-to-end (E2E) secure applications. As most E2E-secure applications rely on a sequence of secrets (s_1,...,s_n) from which, together with the ciphertexts sent over the network, all content can be restored, Dodis et al.\ introduced CKS as a primitive for backing up (s_1,...,s_n). The authors provided definitions as well as two practically efficient schemes (with different functionality-efficiency trade-offs). Both, their security definitions and schemes relied however on the random oracle model (ROM). In this paper, we first show that this reliance is inherent. More concretely, we argue that in the standard model, one cannot have a general CKS instantiation that is applicable to all "CKS-compatible games", as defined by Dodis et al., and realized by their ROM construction. Therefore, one must restrict the notion of CKS-compatible games to allow for standard model CKS instantiations. We then introduce an alternative standard-model CKS definition that makes concessions in terms of functionality (thereby circumventing the impossibility). More precisely, we specify CKS which does not recover the original secret s_i but a derived key k_i, and then observe that this still suffices for many real-world applications. We instantiate this new notion based on minimal assumptions. For passive security, we provide an instantiation based on one-way functions only. For stronger notions, we additionally need collision-resistant hash functions and dual-PRFs, which we argue to be minimal. Finally, we provide a modularization of the CKS protocols of Dodis et al. In particular, we present a unified protocol (and proof) for standard-model equivalents for both protocols introduced in the original work.

The goal of the bounded storage model (BSM) is to construct unconditionally secure cryptographic protocols, by only restricting the storage capacity of the adversary, but otherwise giving it unbounded computational power. Here, we consider a streaming variant of the BSM, where honest parties can stream huge amounts of data to each other so as to overwhelm the adversary's storage, even while their own storage capacity is significantly smaller than that of the adversary. Prior works showed several impressive results in this model, including key agreement and oblivious transfer, but only as long as adversary's storage $m = O(n^2)$ is at most quadratically larger than the honest user storage $n$. Moreover, the work of Dziembowski and Maurer (DM) also gave a seemingly matching lower bound, showing that key agreement in the BSM is impossible when $m > n^2$. In this work, we observe that the DM lower bound only applies to a significantly more restricted version of the BSM, and does not apply to the streaming variant. Surprisingly, we show that it is possible to construct key agreement and oblivious transfer protocols in the streaming BSM, where the adversary's storage can be significantly larger, and even exponential $m = 2^{O(n)}$. The only price of accommodating larger values of $m$ is that the round and communication complexities of our protocols grow accordingly, and we provide lower bounds to show that an increase in rounds and communication is necessary. As an added benefit of our work, we also show that our oblivious transfer (OT) protocol in the BSM satisfies a simulation-based notion of security. In contrast, even for the restricted case of $m = O(n^2)$, prior solutions only satisfied a weaker indistinguishability based definition. As an application of our OT protocol, we get general multiparty computation (MPC) in the BSM that allows for up to exponentially large gaps between $m$ and $n$, while also achieving simulation-based security.

In May 2020, Zoom Video Communications, Inc. (Zoom) announced a multi-step plan to comprehensively support end-to-end encrypted (E2EE) group video calls and subsequently rolled out basic E2EE support to customers in October 2020. In this work we provide the first formal security analysis of Zoom's E2EE protocol, and also lay foundation to the general problem of E2EE group video communication. We observe that the vast security literature analyzing asynchronous messaging does not translate well to synchronous video calls. Namely, while strong forms of forward secrecy and post compromise security are less important for (typically short-lived) video calls, various liveness properties become crucial. For example, mandating that participants quickly learn of updates to the meeting roster and key, media streams being displayed are recent, and banned participants promptly lose any access to the meeting. Our main results are as follows: 1. Propose a new notion of leader-based continuous group key agreement with liveness, which accurately captures the E2EE properties specific to the synchronous communication scenario. 2. Prove security of the core of Zoom's E2EE meetings protocol in the above well-defined model. 3. Propose ways to strengthen Zoom's liveness properties by simple modifications to the original protocol, which have since been deployed in production.

Suppose we have two hash functions h1 and h2, but we trust the security of only one of them. To mitigate this worry, we wish to build a hash combiner C^{h1,h2} which is secure so long as one of the underlying hash functions is. This question has been well-studied in the regime of collision resistance. In this case, concatenating the two hash function outputs clearly works. Unfortunately for practice, a long series of works (Boneh and Boyen, CRYPTO’06; Pietrzak, Eurocrypt’07; Pietrzak, Crypto’08) showed no (noticeably) better combiner for collision resistance is possible. In this work, we revisit this pessimistic state of affairs, motivated the observation that collision-resistance is insufficient for many interesting applications of cryptographic hash functions anyway. Thus, we believe (and argue) the right formulation of the “hash combiner” is to build what we call random oracle (RO) combiners, utilizing stronger assumptions for stronger constructions. Indeed, we circumvent the previous lower bounds for collision resistance by constructing a simple length-preserving RO combiner C^{h1,h2}_{Z1,Z2} (M ) = h1(M, Z1) ⊕ h2(M, Z2), where Z1, Z2 are random salts of appropriate length. We show that this extra randomness is necessary for RO combiners, and indeed our construction is somewhat tight with this lower bound. On the negative side, we show that one cannot generically apply the composition theorem to further replace “monolithic” hash functions h1 and h2 by some simpler indifferentiable (such as the Merkle-Damgard transformation) from smaller components, such as fixed-length compression functions. Finally, despite this issue, we directly prove collision resistance of the Merkle-Damgard variant of our combiner, where h1 and h2 are replaced by iterative Merkle-Damgard hashes applied to a fixed-length compression function. Thus, we can still subvert the concatenation barrier for collision-resistance combiners while utilizing practically small fixed-length components underneath.

A backdoored Pseudorandom Generator (PRG) is a PRG which looks pseudorandom to the outside world, but a saboteur can break PRG security by planting a backdoor into a seemingly honest choice of public parameters, pk, for the system. Backdoored PRGs became increas- ingly important due to revelations about NIST’s backdoored Dual EC PRG, and later results about its practical exploitability. Motivated by this, at Eurocrypt’15 Dodis et al. [20] initiated the ques- tion of immunizing backdoored PRGs. A k-immunization scheme repeat- edly applies a post-processing function to the output of k backdoored PRGs, to render any (unknown) backdoors provably useless. For k = 1, [20] showed that no deterministic immunization is possible, but then constructed “seeded” 1-immunizer either in the random oracle model, or under strong non-falsifiable assumptions. As our first result, we show that no seeded 1-immunization scheme can be black-box reduced to any efficiently falsifiable assumption. This motivates studying k-immunizers for k ≥ 2, which have an ad- ditional advantage of being deterministic (i.e., “seedless”). Indeed, prior work at CCS’17 [35] and CRYPTO’18 [7] gave supporting evidence that simple k-immunizers might exist, albeit in slightly different settings. Un- fortunately, we show that simple standard model proposals of [35,7] (including the XOR function [7]) provably do not work in our setting. On a positive, we confirm the intuition of [35] that a (seedless) random oracle is a provably secure 2-immunizer. On a negative, no (seedless) 2-immunization scheme can be black-box reduced to any efficiently falsi- fiable assumption, at least for a large class of natural 2-immunizers which includes all “cryptographic hash functions.” In summary, our results show that k-immunizers occupy a peculiar place in the cryptographic world. While they likely exist, and can be made practical and efficient, it is unlikely one can reduce their security to a “clean” standard-model assumption.

The notion of functional re-encryption security (funcCPA) for public-key encryption schemes was recently introduced by Akavia et al. (TCC'22), in the context of homomorphic encryption. This notion lies in between CPA security and CCA security: we give the attacker a *functional re-encryption oracle* instead of the decryption oracle of CCA security. This oracle takes a ciphertext ct and a function f, and returns fresh encryption of f applied to the decryption of ct; in symbols, ct'=Enc(f(Dec(ct))). In this work we observe that funcCPA security may have applications beyond homomorphic encryption, and set out to study its properties. As our main contribution, we prove that funcCPA is "closer to CPA than to CCA"; that is, funcCPA secure encryption can be constructed in a black-box manner from CPA-secure encryption. We stress that, prior to our work, this was not known even for regular re-encryption queries corresponding to identity function f. At the core of our result is a new technique, showing how to handle *adaptive* functional re-encryption queries using tools previously developed in the context of non-malleable encryption, which roughly corresponds to a single *non-adaptive* parallel decryption query.

We build the first *sub-linear* (in fact, potentially constant-time) *public-key* searchable encryption system: - server can publish a public key $PK$. - anybody can build an encrypted index for document $D$ under $PK$. - client holding the index can obtain a token $z_w$ from the server to check if a keyword $w$ belongs to $D$. - search using $z_w$ is almost as fast (e.g., sub-linear) as the non-private search. - server granting the token does not learn anything about the document $D$, beyond the keyword $w$. - yet, the token $z_w$ is specific to the pair $(D,w)$: the client does not learn if other keywords $w'\neq w$ belong to $D$, or if $w$ belongs to other, freshly indexed documents $D'$. - server cannot fool the client by giving a wrong token $z_w$. We call such a primitive *encapsulated search index* (ESI). Our ESI scheme can be made $(t,n)$-distributed among $n$ servers in the best possible way: *non-interactive*, verifiable, and resilient to any coalition of up to $(t-1)$ malicious servers. We also introduce the notion of *delegatable* ESI and show how to extend our construction to this setting. Our solution --- including public indexing, sub-linear search, delegation, and distributed token generation --- is deployed as a commercial application by a real-world company.

We consider the streaming variant of the Bounded Storage Model (BSM), where the honest parties can stream large amounts of data to each other, while only maintaining a small memory of size $n$. The adversary also operates as a streaming algorithm, but has a much larger memory size $m \gg n$. The goal is to construct unconditionally secure cryptographic schemes in the BSM, and prior works did so for symmetric-key encryption, key agreement, oblivious transfer and multiparty computation. In this work, we construct message authentication and signatures in the BSM. First, we consider the symmetric-key setting, where Alice and Bob share a small secret key. Alice can authenticate arbitrarily many messages to Bob by streaming long authentication tags of size $k \gg m$, while ensuring that the tags can be generated and verified using only $n$ bits of memory. We show a solution using local extractors (Vadhan; JoC '04), which allows for up to exponentially large adversarial memory $m = 2^{O(n)}$, and has tags of size $k= O(m)$. Second, we consider the same setting as above, but now additionally require each individual tag to be small, of size $k \leq n$. We show a solution is still possible when the adversary's memory is $m = O(n^2)$, which is optimal. Our solution relies on a space lower bound for leaning parities (Raz; FOCS '16). Third, we consider the public-key signature setting. A signer Alice initially streams a long verification key over an authentic channel, while only keeping a short signing key in her memory. A verifier Bob receives the streamed verification key and generates some short verification digest that he keeps in his memory. Later, Alice can sign arbitrarily many messages using her signing key by streaming the signatures to Bob, who can verify them using his verification digest. We show a solution for $m= O(n^2)$, which we show to be optimal. Our solution relies on a novel entropy lemma, of independent interest. We show that, if a sequence of blocks has sufficiently high min-entropy, then a large fraction of individual blocks must have high min-entropy. Naive versions of this lemma are false, but we show how to patch it to make it hold.

Continuous Group Key Agreement (CGKA) is the basis of modern Secure Group Messaging (SGM) protocols. At a high level, a CGKA protocol enables a group of users to continuously compute a shared (evolving) secret while members of the group add new members, remove other existing members, and perform state updates. The state updates allow CGKA to offer desirable security features such as forward secrecy and post-compromise security. CGKA is regarded as a practical primitive in the real-world. Indeed, there is an IETF Messaging Layer Security (MLS) working group devoted to developing a standard for SGM protocols, including the CGKA protocol at their core. Though known CGKA protocols seem to perform relatively well when considering natural sequences of performed group operations, there are no formal guarantees on their efficiency, other than the O(n) bound which can be achieved by trivial protocols, where n is the number of group numbers. In this context, we ask the following questions and provide negative answers. 1. Can we have CGKA protocols that are efficient in the worst case? We start by answering this basic question in the negative. First, we show that a natural primitive that we call Compact Key Exchange (CKE) is at the core of CGKA, and thus tightly captures CGKA’s worst-case communication cost. Intuitively, CKE requires that: first, n users non-interactively generate key pairs and broadcast their public keys, then, some other special user securely communicates to these n users a shared key. Next, we show that CKE with communication cost o(n) by the special user cannot be realized in a black-box manner from public-key encryption and one-way functions, thus implying the same for CGKA, where n is the corresponding number of group members. 2. Can we realize one CGKA protocol that works as well as possible in all cases? Here again, we present negative evidence showing that no such protocol based on black-box use of public-key encryption and one-way functions exists. Specifically, we show two distributions over sequences of group operations such that no CGKA protocol obtains optimal communication costs on both sequences.

Forward-secure encryption (FSE) allows communicating parties to refresh their keys across epochs, in a way that compromising the current secret key leaves all prior encrypted communication secure. We investigate a novel dimension in the design of FSE schemes: fast-forwarding (FF). This refers to the ability of a stale communication party, that is "stuck" in an old epoch, to efficiently "catch up" to the newest state, and frequently arises in practice. While this dimension was not explicitly considered in prior work, we observe that one can augment prior FSEs -- both in symmetric- and public-key settings -- to support fast-forwarding which is sublinear in the number of epochs. However, the resulting schemes have disadvantages: the symmetric-key scheme is a security parameter slower than any conventional stream cipher, while the public-key scheme inherits the inefficiencies of the HIBE-based forward-secure PKE. To address these inefficiencies, we look at the common real-life situation which we call the bulletin board model, where communicating parties rely on some infrastructure -- such as an application provider -- to help them store and deliver ciphertexts to each other. We then define and construct FF-FSE in the bulletin board model, which addresses the above-mentioned disadvantages. In particular, * Our FF-stream-cipher in the bulletin-board model has: (a) constant state size; (b) constant normal (no fast-forward) operation; and (c) logarithmic fast-forward property. This essentially matches the efficiency of non-fast-forwardable stream ciphers, at the cost of constant communication complexity with the bulletin board per update. * Our public-key FF-FSE avoids HIBE-based techniques by instead using so-called updatable public-key encryption (UPKE), introduced in several recent works (and more efficient than public-key FSEs). Our UPKE-based scheme uses a novel type of "update graph" that we construct in this work. Our graph has constant in-degree, logarithmic diameter, and logarithmic "cut property" which is essential for the efficiency of our schemes. Combined with recent UPKE schemes, we get two FF-FSEs in the bulletin board model, under DDH and LWE.

Recently, the area of Key Transparency (KT) has received a lot of attention, as it allows the service provider to provide auditable and verifiable proofs regarding authenticity of public keys used by various participants. Moreover, it is highly preferable to do it in a privacy-preserving ways, so that users and auditors do not learn anything beyond what is necessary to keep the service provider accountable. Abstractly, the problem of building such systems reduces to constructing so called append-only Zero-Knowledge Sets (aZKS). Unfortunately, none of the previous aZKS constructions adequately addressed the problem of key rotation, which would provide Post-Compromise Security (PCS) in case the server in compromised. In this work we address this concern, and refine an extension of aZKS called Rotatable ZKS (RZKS). In addition to addressing the PCS concern, our notion of RZKS has several other attractive features, such as stronger soundness notion (called extractability), and the ability for a stale communication party to quickly catch up with the current epoch, while ensuring the the server did not erase any of the past data. Of independent interest, we also introduce and build a new primitive called Rotatable Verifiable Random Function (VRF), and show how to build RZKS in a modular fashion from rotatable VRF, ordered accumulators and append-only vector commitment schemes.

Real-world random number generators (RNGs) cannot afford to use (slow) cryptographic hashing every time they refresh their state R with a new entropic input X. Instead, they use ``super-efficient'' simple entropy-accumulation procedures, such as R <- rot_{alpha, n}(R) XOR X where rot_{alpha,n} rotates an n-bit state R by some fixed number alpha. For example, Microsoft's RNG uses alpha=5 for n=32 and alpha=19 for n=64. Where do these numbers come from? Are they good choices? Should rotation be replaced by a better permutation pi of the input bits? In this work we initiate a rigorous study of these pragmatic questions, by modeling the sequence of successive entropic inputs X_1,X_2, ... as independent (but otherwise adversarial) samples from some natural distribution family D. We show a simple but surprisingly powerful connection between entropy accumulation and understanding the Fourier spectrum of distributions in D. Our contribution is as follows. - We define 2-monotone distributions as a rich family D that includes relevant real-world distributions (Gaussian, exponential, etc.), but avoids trivial impossibility results. - For any alpha with gcd(alpha,n)=1, we show that rotation accumulates Omega(n) bits of entropy from n independent samples X_1,...,X_n from any (unknown) 2-monotone distribution with entropy k > 1. - However, we also show some choices of alpha perform much better than others for a given n. E.g., we show alpha=19 is one of the best choices for n=64; in contrast, alpha=5 is good, but generally worse than alpha=7, for n=32. - More generally, given a permutation pi and k > 1, we define a simple parameter, the covering number C_{pi,k}, and show that it characterizes the number of steps before the rule (R_1,...,R_n) <- (R_{pi(1)},..., R_{pi(n)}) XOR X accumulates nearly n bits of entropy from independent, 2-monotone samples of min-entropy k each. - We build a simple permutation pi^*, which achieves nearly optimal C_{pi^*,k} \approx n/k for all values of k simultaneously, and experimentally validate that it compares favorably with all rotations rot_{alpha,n}.

In this paper, we study forward secret encrypted RAMs (FS eRAMs) which enable clients to outsource the storage of an n-entry array to a server. In the case of a catastrophic attack where both client and server storage are compromised, FS eRAMs guarantee that the adversary may not recover any array entries that were deleted or overwritten prior to the attack. A simple folklore FS eRAM construction with O(logn) overhead has been known for at least two decades. Unfortunately, no progress has been made since then. We show the lack of progress is fundamental by presenting an \Omega(log n) lower bound for FS eRAMs proving that the folklore solution is optimal. To do this, we introduce the symbolic model for proving cryptographic data structures lower bounds that may be of independent interest. Given this limitation, we investigate applications where forward secrecy may be obtained without the additional O(log n) overhead. We show this is possible for oblivious RAMs, memory checkers, and multicast encryption by incorporating the ideas of the folklore FS eRAM solution into carefully chosen constructions of the corresponding primitives.

Forward security (FS) ensures that corrupting the current secret key in the system preserves the privacy or integrity of the prior usages of the system. Achieving forward security is especially hard in the setting of public-key encryption (PKE), where time is divided into periods, and in each period the receiver derives the next-period secret key from their current secret key, while the public key stays constant. Indeed, all current constructions of FS-PKE are built from hierarchical identity-based encryption (HIBE) and are rather complicated. Motivated by applications to secure messaging, recent works of Jost et al. (Eurocrypt’19) and Alwen et al. (CRYPTO’20) consider a natural relaxation of FS-PKE, which they term *updatable* PKE (UPKE). In this setting, the transition to the next period can be initiated by any sender, who can compute a special update ciphertext. This ciphertext directly produces the next-period public key and can be processed by the receiver to compute the next-period secret key. If done honestly, future (regular) ciphertexts produced with the new public key can be decrypted with the new secret key, but past such ciphertexts cannot be decrypted with the new secret key. Moreover, this is true even if all other previous-period updates were initiated by untrusted senders. Both papers also constructed a very simple UPKE scheme based on the CDH assumption in the random oracle model. However, they left open the question of building such schemes in the standard model, or based on other (e.g., post-quantum) assumptions, without using the heavy HIBE techniques. In this work, we construct two efficient UPKE schemes in the standard model, based on the DDH and LWE assumptions, respectively. Somewhat interestingly, our constructions gain their efficiency (compared to prior FS-PKE schemes from the same assumptions) by using tools from the area of circular-secure and leakage resilient public-key encryption schemes (rather than HIBE).

We revisit the well-studied problem of extracting nearly uniform randomness from an arbitrary source of sufficient min-entropy. Strong seeded extractors solve this problem by relying on a public random seed, which is unknown to the source. Here, we consider a setting where the seed is reused over time and the source may depend on prior calls to the extractor with the same seed. Can we still extract nearly uniform randomness? In more detail, we assume the seed is chosen randomly, but the source can make arbitrary oracle queries to the extractor with the given seed before outputting a sample. We require that the sample has entropy and differs from any of the previously queried values. The extracted output should look uniform even to a distinguisher that gets the seed. We consider two variants of the problem, depending on whether the source only outputs the sample, or whether it can also output some correlated public auxiliary information that preserves the sample's entropy. Our results are: * Without Auxiliary Information: We show that every pseudo-random function (PRF) with a sufficiently high security level is a good extractor in this setting, even if the distinguisher is computationally unbounded. We further show that the source necessarily needs to be computationally bounded and that such extractors imply one-way functions. * With Auxiliary Information: We construct secure extractors in this setting, as long as both the source and the distinguisher are computationally bounded. We give several constructions based on different intermediate primitives, yielding instantiations based on the DDH, DLIN, LWE or DCR assumptions. On the negative side, we show that one cannot prove security against computationally unbounded distinguishers in this setting under any standard assumption via a black-box reduction. Furthermore, even when restricting to computationally bounded distinguishers, we show that there exist PRFs that are insecure as extractors in this setting and that a large class of constructions cannot be proven secure via a black-box reduction from standard assumptions.

Secure messaging (SM) protocols allow users to communicate securely over untrusted infrastructure. In contrast to most other secure communication protocols (such as TLS, SSH, or Wireguard), SM sessions may be long-lived (e.g., years) and highly asynchronous. In order to deal with likely state compromises of users during the lifetime of a session, SM protocols do not only protect authenticity and privacy, but they also guarantee forward secrecy (FS) and post-compromise security (PCS). The former ensures that messages sent and received before a state compromise remain secure, while the latter ensures that users can recover from state compromise as a consequence of normal protocol usage. SM has received considerable attention in the two-party case, where prior work has studied the well-known double-ratchet paradigm, in particular, and SM as a cryptographic primitive, in general. Unfortunately, this paradigm does not scale well to the problem of secure group messaging (SGM). In order to address the lack of satisfactory SGM protocols, the IETF has launched the message-layer security (MLS) working group, which aims to standardize an eponymous SGM protocol. In this work we analyze the TreeKEM protocol, which is at the core of the SGM protocol proposed by the MLS working group. On a positive note, we show that TreeKEM achieves PCS in isolation (and slightly more). However, we observe that the current version of TreeKEM does not provide an adequate form of FS. More precisely, our work proceeds by formally capturing the exact security of TreeKEM as a so-called continuous group key agreement (CGKA) protocol, which we believe to be a primitive of independent interest. To address the insecurity of TreeKEM, we propose a simple modification to TreeKEM inspired by recent work of Jost et al. (EUROCRYPT '19) and an idea due to Kohbrok (MLS Mailing List). We then show that the modified version of TreeKEM comes with almost no efficiency degradation but achieves optimal (according to MLS specification) CGKA security, including FS and PCS. Our work also lays out how a CGKA protocol can be used to design a full SGM protocol.

In the backdoored random-oracle (BRO) model, besides access to a random function $\hash$, adversaries are provided with a backdoor oracle that can compute arbitrary leakage functions $f$ of the function table of $\hash$. Thus, an adversary would be able to invert points, find collisions, test for membership in certain sets, and more. This model was introduced in the work of Bauer, Farshim, and Mazaheri (Crypto 2018) and extends the auxiliary-input idealized models of Unruh (Crypto 2007), Dodis, Guo, and Katz (Eurocrypt 2017), Coretti et al. (Eurocrypt 2018), and Coretti, Dodis, and Guo (Crypto~2018). It was shown that certain security properties, such as one-wayness, pseudorandomness, and collision resistance can be re-established by combining two independent BROs, even if the adversary has access to both backdoor oracles. In this work we further develop the technique of combining two or more independent BROs to render their backdoors useless in a more general sense. More precisely, we study the question of building an \emph{indifferentiable} and backdoor-free random function by combining multiple BROs. Achieving full indifferentiability in this model seems very challenging at the moment. We however make progress by showing that the xor combiner goes well beyond security against preprocessing attacks and offers indifferentiability as long as the adaptivity of queries to different backdoor oracles remains logarithmic in the input size of the BROs. We even show that an extractor-based combiner of three BROs can achieve indifferentiability with respect to a linear adaptivity of backdoor queries. Furthermore, a natural restriction of our definition gives rise to a notion of \emph{indifferentiability with auxiliary input}, for which we give two positive feasibility results. To prove these results we build on and refine techniques by Göös et al. (STOC 2015) and Kothari et al. (STOC 2017) for decomposing distributions with high entropy into distributions with more structure and show how they can be applied in the more involved adaptive settings.

Post-Compromise Security, or PCS, refers to the ability of a given protocol to recover—by means of normal protocol operations—from the exposure of local states of its (otherwise honest) participants. While PCS in the two-party setting has attracted a lot of attention recently, the problem of achieving PCS in the group setting—called group ratcheting here—is much less understood. On the one hand, one can achieve excellent security by simply executing, in parallel, a two-party ratcheting protocol (e.g., Signal) for each pair of members in a group. However, this incurs O(n) communication overhead for every message sent, where n is the group size. On the other hand, several related protocols were recently developed in the context of the IETF Messaging Layer Security (MLS) effort that improve the communication overhead per message to O(log n). However, this reduction of communication overhead involves a great restriction: group members are not allowed to send and recover from exposures concurrently such that reaching PCS is delayed up to n communication time slots (potentially even more). In this work we formally study the trade-off between PCS, concurrency, and communication overhead in the context of group ratcheting. Since our main result is a lower bound, we define the cleanest and most restrictive setting where the tension already occurs: static groups equipped with a synchronous (and authenticated) broadcast channel, where up to t arbitrary parties can concurrently send messages in any given round. Already in this setting, we show in a symbolic execution model that PCS requires Omega(t) communication overhead per message. Our symbolic model permits as building blocks black-box use of (even "dual") PRFs, (even key-updatable) PKE (which in our symbolic definition is at least as strong as HIBE), and broadcast encryption, covering all tools used in previous constructions, but prohibiting the use of exotic primitives. To complement our result, we also prove an almost matching upper bound of O(t(1+log(n/t))), which smoothly increases from O(log n) with no concurrency, to O(n) with unbounded concurrency, matching the previously known protocols.

One approach toward basing public-key encryption (PKE) schemes on weak and credible assumptions is to build “stronger” or more general schemes generically from “weaker” or more restricted ones. One particular line of work in this context was initiated by Myers and Shelat (FOCS ’09) and continued by Hohenberger, Lewko, and Waters (Eurocrypt ’12), who provide constructions of multi-bit CCA-secure PKE from single-bit CCA-secure PKE. It is well known that encrypting each bit of a plaintext string independently is not CCA-secure—the resulting scheme is malleable . We therefore investigate whether this malleability can be dealt with using the conceptually simple approach of applying a suitable non-malleable code (Dziembowski et al., ICS ’10) to the plaintext and subsequently encrypting the resulting codeword bit by bit. We find that an attacker’s ability to ask multiple decryption queries requires that the underlying code be continuously non-malleable (Faust et al., TCC ’14). Since, as we show, this flavor of non-malleability can only be achieved if the code is allowed to “self-destruct,” the resulting scheme inherits this property and therefore only achieves a weaker variant of CCA security. We formalize this new notion of so-called indistinguishability under self-destruct attacks (IND-SDA) as CCA security with the restriction that the decryption oracle stops working once the attacker submits an invalid ciphertext. We first show that the above approach based on non-malleable codes yields a solution to the problem of domain extension for IND-SDA-secure PKE, provided that the underlying code is continuously non-malleable against (a reduced form of) bit-wise tampering. Then, we prove that the code of Dziembowski et al. is actually already continuously non-malleable against bit-wise tampering. We further investigate the notion of security under self-destruct attacks and combine IND-SDA security with non-malleability under chosen-ciphertext attacks (NM-CPA) to obtain the strictly stronger notion of non-malleability under self-destruct attacks (NM-SDA) . We show that NM-SDA security can be obtained from basic IND-CPA security by means of a black-box construction based on the seminal work by Choi et al. (TCC ’08). Finally, we provide a domain extension technique for building a multi-bit NM-SDA scheme from a single-bit NM-SDA scheme. To achieve this goal, we define and construct a novel type of continuous non-malleable code, called secret-state NMC , since, as we show, standard continuous NMCs are insufficient for the natural “encode-then-encrypt-bit-by-bit” approach to work.

Signal is a famous secure messaging protocol used by billions of people, by virtue of many secure text messaging applications including Signal itself, WhatsApp, Facebook Messenger, Skype, and Google Allo. At its core it uses the concept of “double ratcheting,” where every message is encrypted and authenticated using a fresh symmetric key; it has many attractive properties, such as forward security, post-compromise security, and “immediate (no-delay) decryption,” which had never been achieved in combination by prior messaging protocols.While the formal analysis of the Signal protocol, and ratcheting in general, has attracted a lot of recent attention, we argue that none of the existing analyses is fully satisfactory. To address this problem, we give a clean and general definition of secure messaging, which clearly indicates the types of security we expect, including forward security, post-compromise security, and immediate decryption. We are the first to explicitly formalize and model the immediate decryption property, which implies (among other things) that parties seamlessly recover if a given message is permanently lost—a property not achieved by any of the recent “provable alternatives to Signal.”We build a modular “generalized Signal protocol” from the following components: (a) continuous key agreement (CKA), a clean primitive we introduce and which can be easily and generically built from public-key encryption (not just Diffie-Hellman as is done in the current Signal protocol) and roughly models “public-key ratchets;” (b) forward-secure authenticated encryption with associated data (FS-AEAD), which roughly captures “symmetric-key ratchets;” and (c) a two-input hash function that is a pseudorandom function (resp. generator with input) in its first (resp. second) input, which we term PRF-PRNG. As a result, in addition to instantiating our framework in a way resulting in the existing, widely-used Diffie-Hellman based Signal protocol, we can easily get post-quantum security and not rely on random oracles in the analysis.

The need for high-quality randomness in cryptography makes random-number generation one of its most fundamental tasks.A recent important line of work (initiated by Dodis et al., CCS ’13) focuses on the notion of robustness for pseudorandom number generators (PRNGs) with inputs. These are primitives that use various sources to accumulate sufficient entropy into a state, from which pseudorandom bits are extracted. Robustness ensures that PRNGs remain secure even under state compromise and adversarial control of entropy sources. However, the achievability of robustness inherently depends on a seed, or, alternatively, on an ideal primitive (e.g., a random oracle), independent of the source of entropy. Both assumptions are problematic: seed generation requires randomness to start with, and it is arguable whether the seed or the ideal primitive can be kept independent of the source. This paper resolves this dilemma by putting forward new notions of robustness which enable both (1) seedless PRNGs and (2) primitive-dependent adversarial sources of entropy. To bypass obvious impossibility results, we make a realistic compromise by requiring that the source produce sufficient entropy even given its evaluations of the underlying primitive. We also provide natural, practical, and provably secure constructions based on hash-function designs from compression functions, block ciphers, and permutations. Our constructions can be instantiated with minimal changes to industry-standard hash functions SHA-2 and SHA-3, or key derivation function HKDF, and can be downgraded to (online) seedless randomness extractors, which are of independent interest.On the way we consider both a computational variant of robustness, where attackers only make a bounded number of queries to the ideal primitive, as well as a new information-theoretic variant, which dispenses with this assumption to a certain extent, at the price of requiring a high rate of injected weak randomness (as it is, e.g., plausible on Intel’s on-chip RNG). The latter notion enables applications such as everlasting security. Finally, we show that the CBC extractor, used by Intel’s on-chip RNG, is provably insecure in our model.

We consider the problem of Non-Interactive Two-Party Secure Computation (NISC), where Rachel wishes to publish an encryption of her input x, in such a way that any other party, who holds an input y, can send her a single message which conveys to her the value f(x, y), and nothing more. We demand security against malicious parties. While such protocols are easy to construct using garbled circuits and general non-interactive zero-knowledge proofs, this approach inherently makes a non-black-box use of the underlying cryptographic primitives and is infeasible in practice.Ishai et al. (Eurocrypt 2011) showed how to construct NISC protocols that only use parallel calls to an ideal oblivious transfer (OT) oracle, and additionally make only a black-box use of any pseudorandom generator. Combined with the efficient 2-message OT protocol of Peikert et al. (Crypto 2008), this leads to a practical approach to NISC that has been implemented in subsequent works. However, a major limitation of all known OT-based NISC protocols is that they are subject to selective failure attacks that allows a malicious sender to entirely compromise the security of the protocol when the receiver’s first message is reused.Motivated by the failure of the OT-based approach, we consider the problem of basing reusable NISC on parallel invocations of a standard arithmetic generalization of OT known as oblivious linear-function evaluation (OLE). We obtain the following results:We construct an information-theoretically secure reusable NISC protocol for arithmetic branching programs and general zero-knowledge functionalities in the OLE-hybrid model. Our zero-knowledge protocol only makes an absolute constant number of OLE calls per gate in an arithmetic circuit whose satisfiability is being proved. We also get reusable NISC in the OLE-hybrid model for general Boolean circuits using any one-way function.We complement this by a negative result, showing that reusable NISC is impossible to achieve in the OT-hybrid model. This provides a formal justification for the need to replace OT by OLE.We build a universally composable 2-message reusable OLE protocol in the CRS model that can be based on the security of Paillier encryption and requires only a constant number of modular exponentiations. This provides the first arithmetic analogue of the 2-message OT protocols of Peikert et al. (Crypto 2008).By combining our NISC protocol in the OLE-hybrid model and the 2-message OLE protocol, we get protocols with new attractive asymptotic and concrete efficiency features. In particular, we get the first (designated-verifier) NIZK protocols for NP where following a statement-independent preprocessing, both proving and verifying are entirely “non-cryptographic” and involve only a constant computational overhead. Furthermore, we get the first statistical designated-verifier NIZK argument for NP under an assumption related to factoring.

The random-permutation model (RPM) and the ideal-cipher model (ICM) are idealized models that offer a simple and intuitive way to assess the conjectured standard-model security of many important symmetric-key and hash-function constructions. Similarly, the generic-group model (GGM) captures generic algorithms against assumptions in cyclic groups by modeling encodings of group elements as random injections and allows to derive simple bounds on the advantage of such algorithms.Unfortunately, both well-known attacks, e.g., based on rainbow tables (Hellman, IEEE Transactions on Information Theory ’80), and more recent ones, e.g., against the discrete-logarithm problem (Corrigan-Gibbs and Kogan, EUROCRYPT ’18), suggest that the concrete security bounds one obtains from such idealized proofs are often completely inaccurate if one considers non-uniform or preprocessing attacks in the standard model. To remedy this situation, this workdefines the auxiliary-input (AI) RPM/ICM/GGM, which capture both non-uniform and preprocessing attacks by allowing an attacker to leak an arbitrary (bounded-output) function of the oracle’s function table;derives the first non-uniform bounds for a number of important practical applications in the AI-RPM/ICM, including constructions based on the Merkle-Damgård and sponge paradigms, which underly the SHA hashing standards, and for AI-RPM/ICM applications with computational security; andusing simpler proofs, recovers the AI-GGM security bounds obtained by Corrigan-Gibbs and Kogan against preprocessing attackers, for a number of assumptions related to cyclic groups, such as discrete logarithms and Diffie-Hellman problems, and provides new bounds for two assumptions. An important step in obtaining these results is to port the tools used in recent work by Coretti et al. (EUROCRYPT ’18) from the ROM to the RPM/ICM/GGM, resulting in very powerful and easy-to-use tools for proving security bounds against non-uniform and preprocessing attacks.

Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a wn-bit block cipher from n-bit public permutations (often called S-boxes), which alternate keyless and “local” substitution steps utilizing such S-boxes, with keyed and “global” permutation steps which are non-cryptographic. Many widely deployed block ciphers are constructed based on the SPNs, but there are essentially no provable-security results about SPNs.In this work, we initiate a comprehensive study of the provable security of SPNs as (possibly tweakable) wn-bit block ciphers, when the underlying n-bit permutation is modeled as a public random permutation. When the permutation step is linear (which is the case for most existing designs), we show that 3 SPN rounds are necessary and sufficient for security. On the other hand, even 1-round SPNs can be secure when non-linearity is allowed. Moreover, 2-round non-linear SPNs can achieve “beyond-birthday” (up to $$2^{2n/3}$$ 22n/3 adversarial queries) security, and, as the number of non-linear rounds increases, our bounds are meaningful for the number of queries approaching $$2^n$$ 2n. Finally, our non-linear SPNs can be made tweakable by incorporating the tweak into the permutation layer, and provide good multi-user security.As an application, our construction can turn two public n-bit permutations (or fixed-key block ciphers) into a tweakable block cipher working on wn-bit inputs, 6n-bit key and an n-bit tweak (for any $$w\ge 2$$ w≥2); the tweakable block cipher provides security up to $$2^{2n/3}$$ 22n/3 adversarial queries in the random permutation model, while only requiring w calls to each permutation, and 3w field multiplications for each wn-bit input.

Message franking enables cryptographically verifiable reporting of abusive messages in end-to-end encrypted messaging. Grubbs, Lu, and Ristenpart recently formalized the needed underlying primitive, what they call compactly committing authenticated encryption (AE), and analyze security of a number of approaches. But all known secure schemes are still slow compared to the fastest standard AE schemes. For this reason Facebook Messenger uses AES-GCM for franking of attachments such as images or videos.We show how to break Facebook’s attachment franking scheme: a malicious user can send an objectionable image to a recipient but that recipient cannot report it as abuse. The core problem stems from use of fast but non-committing AE, and so we build the fastest compactly committing AE schemes to date. To do so we introduce a new primitive, called encryptment, which captures the essential properties needed. We prove that, unfortunately, schemes with performance profile similar to AES-GCM won’t work. Instead, we show how to efficiently transform Merkle-Damgärd-style hash functions into secure encryptments, and how to efficiently build compactly committing AE from encryptment. Ultimately our main construction allows franking using just a single computation of SHA-256 or SHA-3. Encryptment proves useful for a variety of other applications, such as remotely keyed AE and concealments, and our results imply the first single-pass schemes in these settings as well.