International Association
for Cryptologic Research

As cloud computing continues to gain widespread adoption, safeguarding the confidentiality of data entrusted to third-party cloud service providers becomes a critical concern. While traditional encryption methods offer protection for data at rest and in transit, they fall short when it comes to where it matters the most, i.e., during data processing. To address this limitation, we present HELM, a framework for privacy-preserving data processing using homomorphic encryption. HELM automatically transforms arbitrary programs expressed in a Hardware Description Language (HDL), such as Verilog, into equivalent homomorphic circuits, which can then be efficiently evaluated using encrypted inputs. HELM features two modes of encrypted evaluation: a) a gate mode that consists of standard Boolean gates, and b) a lookup table mode which significantly reduces the size of the circuit by combining multiple gates into lookup tables. Finally, HELM introduces a scheduler that enables embarrassingly parallel processing in the encrypted domain. We evaluate HELM with the ISCAS'85 and ISCAS'89 benchmark suites as well as real-world applications such as AES and image filtering. Our results outperform prior works by up to $65\times$.

We investigate the conditions under which straight-line extractable NIZKs in the random oracle model (i.e. without a CRS) permit multiparty realizations that are black-box in the same random oracle. We show that even in the semi-honest setting, any MPC protocol to compute such a NIZK cannot make black-box use of the random oracle or a hash function instantiating it if security against all-but-one corruptions is desired, unless the size of the NIZK grows with the number of parties. This presents a fundamental barrier to constructing efficient protocols to securely distribute the computation of NIZKs (and signatures) based on MPC-in-the-head, PCPs/IOPs, and sigma protocols compiled with transformations due to Fischlin, Pass, or Unruh.

When the adversary is restricted to corrupt only a constant fraction of parties, we give a positive result by means of a tailored construction, which demonstrates that our impossibility does not extend to weaker corruptions models in general.

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 loses a factor depending on the number of users, not on the number of sessions.

Our main enabler is a new variant of lossy encryption which we call parameter lossy encryption. In this variant, there are not only lossy public keys but also lossy system parameters. This allows us to embed a computational assumption into the system parameters, and the lossy public keys are statistically close to the normal public keys. Combining with the Fujisaki-Okamoto transformation, we obtain the first tightly IND-CCA secure KEM in the QROM in a multi-user (without corruption), multi-challenge setting.

Finally, we show that a multi-user, multi-challenge KEM implies a square-root-tight and session-tight AKE protocol in the QROM. By implementing the parameter lossy encryption tightly from lattices, we obtain the first square-root-tight and session-tight AKE from lattices in the QROM.

The National Cyber Security Centre (NCSC) is the government organisation responsible for mitigating cyber security risks to the UK. Our work securing UK public- and private-sector networks involves (amongst many other security measures) research into cryptographic design, primarily to protect data requiring long-term security or data for which we have a particularly low tolerance of risk to its transmission and storage. Our algorithms prioritise robustness over other important considerations, such as performance, more highly than other designs.

We present GLEVIAN and VIGORNIAN: two AEAD modes with proofs of beyond-birthday security, security against nonce misuse, and against the release of unverified plaintext – both of the latter in strong notions of these security properties. We discuss our hierarchy of requirements for AEAD modes, and the rationale for the design choices made.

GLEVIAN and VIGORNIAN demonstrate we can achieve significantly improved robustness over GCM for use cases where some performance degradation is acceptable. We are not aware of other designs offering exactly the security properties of GLEVIAN and VIGORNIAN, and are publishing our designs to support the research that will inform the recently announced effort by NIST to standardise new modes of operation. We believe our work could be of interest to those with use cases similar to ours, and we offer suggestions for future research that might build on the work in this paper.

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and fully-decomposable randomized encoding (or garbling schemes). In fact, for all these primitives we do not even have super-linear lower bounds. Furthermore, it is unknown how to relate these questions to each other or to other complexity-theoretic questions.

In this note, we relate all these questions to the classical topic of query/space trade-offs, lifted to the setting of interactive proof systems. Specifically, we consider the following Advisor-Verifier-Prover (AVP) game: First, a function $f$ is given to the advisor who computes an advice $a$. Next, an input $x$ is given to the verifier and to the prover who claims that $f(x)=1$. The verifier should check this claim via a single round of interaction based on the private advice $a$ and without having any additional information on $f$. We focus on the case where the prover is laconic and communicates only a constant number of bits, and, mostly restrict the attention to the simplest, purely information-theoretic setting, where all parties are allowed to be computationally unbounded. The goal is to minimize the total communication complexity which is dominated by the length of the advice plus the length of the verifier's query.

As our main result, we show that a super-polynomial lower bound for AVPs implies a super-polynomial lower bound for a wide range of information-theoretic cryptographic tasks. In particular, we present a communication-efficient transformation from any of the above primitives into an AVP protocol. Interestingly, each primitive induces some additional property over the resulting protocol. Thus AVP games form a new common yardstick that highlights the differences between all the above primitives.

Equipped with this view, we revisit the existing (somewhat weak) lower bounds for the above primitives, and show that many of these lower bounds can be unified by proving a single counting-based lower bound on the communication of AVPs, whereas some techniques are inherently limited to specific domains. The latter is shown by proving the first polynomial separations between the complexity of secret-sharing schemes and conditional disclosure of secrets and between the complexity of randomized encodings and conditional disclosure of secrets.

TLS oracles guard the transition of web data from an authenticated session between a client and a server to a data representation that any third party can verify. Current TLS oracles resolve weak security assumptions with cryptographic algorithms that provide strong security guarantees (e.g., maliciously secure two-party computation). However, we notice that the conditions and characteristics of TLS 1.3 allow for reconsidering security assumptions. Our work shows that the deployment of semi-honest two-party computation is feasible with a single exception, while retaining equivalent security properties. Further, we introduce a new parity checksum construction to decouple the integrity verification over AEAD stream ciphers into dedicated proof systems and improve end-to-end performance benchmarks. We achieve a selective and privacy-preserving data opening on 16 kB of TLS 1.3 data in 2.11 seconds and open 10x more data compared to related approaches. Thus, our work sets new boundaries for privacy-preserving TLS 1.3 data proofs.

Homomorphic encryption is a central object in modern cryptography, with far-reaching applications. Constructions supporting homomorphic evaluation of arbitrary Boolean circuits have been known for over a decade, based on standard lattice assumptions. However, these constructions are leveled, meaning that they only support circuits up to some a-priori bounded depth. These leveled constructions can be bootstrapped into fully homomorphic ones, but this requires additional circular security assumptions, which are construction-dependent, and where reductions to standard lattice assumptions are no longer known. Alternative constructions are known based on indistinguishability obfuscation, which has been recently constructed under standard assumptions. However, this alternative requires subexponential hardness of the underlying primitives.

We prove a new bootstrapping theorem relying on functional encryption, which is known based on standard polynomial hardness assumptions. As a result we obtain the first fully homomorphic encryption scheme that avoids both circular security assumptions and super-polynomial hardness assumptions. The construction is secure against uniform adversaries, and can be made non-uniformly secure, under a widely-believed worst-case complexity assumption (essentially that non-uniformity does not allow arbitrary polynomial speedup).

At the heart of the construction is a new proof technique based on cryptographic puzzles. Unlike most cryptographic reductions, our security reduction does not fully treat the adversary as a black box, but rather makes explicit use of its running time (or circuit size).

DeepCover is a secure authenticator circuit family developed by Analog Devices. It was designed to provide cryptographic functions, true random number generation, and EEPROM secure storage. DS28C36 is one of the DeepCover family, which is widely used in secure boot and secure download for IoT. It has been recently deployed in the Coldcard Mk4 hardware wallet as a second secure element to enhance its security. In this paper, we present for the first time, a detailed evaluation for the DS28C36 secure EEPROM against Laser Fault Injection (LFI). In the context of a black box approach, we prove by experimental results that the chip resists single fault attacks. In order to overcome this, we present the use of leakage detection such as Welch’s T-test to facilitate finding the correct moments for injecting successful faults, which is not common in Fault Injection (FI) as this method has been used only for Side-Channel Attacks (SCAs). By using this knowledge, we found two moments for injecting laser pulses to extract the protected EEPROM user pages with 99% success rate. The attack can be reproduced within a day. The presented attack negatively impacts the users of DS28C36 (including Coldcard Mk4).

Latin squares are a classical and well-studied topic of discrete mathematics, and recently Takeuti and Adachi (IACR ePrint, 2023) proposed (2,n)-threshold secret sharing based on mutually orthogonal Latin squares (MOLS). Hence efficient constructions of as large sets of MOLS as possible are also important from practical viewpoints. In this letter, we determine the maximum number of MOLS among a known class of Latin squares defined by weighted sums. We also mention some known property of Latin squares interpreted via the relation to secret sharing and a connection of Takeuti-Adachi's scheme to Shamir's secret sharing scheme.

In the context of circuits leaking the internal state, there are various models to analyze what the adversary can see, like the $p$-random probing model in which the adversary can see the value of each wire with probability $p$. In this model, for a fixed $p$, it's possible to reach an arbitrary security by 'expanding' a stateless circuit via iterated compilation, reaching a security of $2^{-\kappa}$ with a polynomial size in $\kappa$.

The existing proofs of the expansion work by first compiling the gadgets multiple times, and then by compiling the circuit with the resulting gadgets while assuming the worst from the original circuit. Instead, we reframe the expansion as a security reduction from the compiled circuit to the original one. Additionally, we extend it to support a broader range of encodings, and arbitrary probabilistic gates with an arbitrary number of inputs and outputs.

This allows us to obtain two concrete results: (i) At the cost of an additional size factor $\mathcal{O}(\log(d)^3)$, any $d$-probing secure compiler can be used to produce stateless circuits with security $2^{-d}$ against any adversary that sees all wires with a constant SD-noise of $2^{-7.41}/p$, where $p$ is the characteristic of the circuit's field. (ii) Any $n$-shares compiler with $(t,f)$-RPE gadgets needs $t+1$ (which in practice is $\lceil\frac{n}{2}\rceil$) randoms in the random gadget instead of $n$.

This article evaluates the innovation landscape facing the challenge of generating fresh shared randomness for cryptographic key exchange and various cyber security protocols. It discusses the main innovation thrust today, focused on quantum entanglement and on efficient engineering solutions to BB84, and its related alternatives. This innovation outlook highlights non-quantum solutions, and describes NEPSAR – a mechanical complexity based solution, which is applicable to any number of key sharing parties. Short-lived secret keys are also mentioned, as well as far-fetched innovation routes.

In Crypto 2019, Zhandry showed how to define compressed oracles, which record quantum superposition queries to the quantum random oracle. In this paper, we extend Zhandry's compressed oracle technique to non-uniformly distributed functions with independently sampled outputs. We define two quantum oracles $\mathsf{CStO}_D$ and $\mathsf{CPhsO}_D$, which are indistinguishable to the non-uniform quantum random oracle where quantum access is given to a random function $H$ whose images $H(x)$ are sampled from a probability distribution $D$ independently for each $x$. We show that these compressed oracles record the adversarial quantum superposition queries. Also, we re-prove the optimality of Grover search and the collision resistance of non-uniform random functions, using our extended compressed oracle technique.

The presumed hardness of the Shortest Vector Problem for ideal lattices (Ideal-SVP) has been a fruitful assumption to understand other assumptions on algebraic lattices and as a security foundation of cryptosystems. Gentry [CRYPTO'10] proved that Ideal-SVP enjoys a worst-case to average-case reduction, where the average-case distribution is the uniform distribution over the set of inverses of prime ideals of small algebraic norm (below $d^{O(d)}$ for cyclotomic fields, here $d$ refers to the field degree). De Boer et al. [CRYPTO'20] obtained another random self-reducibility result for an average-case distribution involving integral ideals of norm $2^{O(d^2)}$.

In this work, we show that Ideal-SVP for the uniform distribution over inverses of small-norm prime ideals reduces to Ideal-SVP for the uniform distribution over small-norm prime ideals. Combined with Gentry's reduction, this leads to a worst-case to average-case reduction for the uniform distribution over the set of \emph{small-norm prime ideals}. Using the reduction from Pellet-Mary and Stehl\'e [ASIACRYPT'21], this notably leads to the first distribution over NTRU instances with a polynomial modulus whose hardness is supported by a worst-case lattice problem.

Beerliová-Trubíniová and Hirt introduced hyper-invertible matrix technique to construct the first perfectly secure MPC protocol in the presence of maximal malicious corruptions $\lfloor \frac{n-1}{3} \rfloor$ with linear communication complexity per multiplication gate [5]. This matrix allows MPC protocol to generate correct shares of uniformly random secrets in the presence of malicious adversary. Moreover, the amortized communication complexity of generating each sharing is linear. Due to this prominent feature, the hyper-invertible matrix plays an important role in the construction of MPC protocol and zero-knowledge proof protocol where the randomness needs to be jointly generated. However, the downside of this matrix is that the size of its base field is linear in the size of its matrix. This means if we construct an $n$-party MPC protocol over $\mathbb{F}_q$ via hyper-invertible matrix, $q$ is at least $2n$.

In this paper, we propose the ramp hyper-invertible matrix which can be seen as the generalization of hyper-invertible matrix. Our ramp hyper-invertible matrix can be defined over constant-size field regardless of the size of this matrix. Similar to the arithmetic secret sharing scheme, to apply our ramp hyper-invertible matrix to perfectly secure MPC protocol, the maximum number of corruptions has to be compromised to $\frac{(1-\epsilon)n}{3}$. As a consequence, we present the first perfectly secure MPC protocol in the presence of $\frac{(1-\epsilon)n}{3}$ malicious corruptions with constant communication complexity. Besides presenting the variant of hyper-invertible matrix, we overcome several obstacles in the construction of this MPC protocol. Our arithmetic secret sharing scheme over constant-size field is compatible with the player elimination technique, i.e., it supports the dynamic changes of party number and corrupted party number. Moreover, we rewrite the public reconstruction protocol to support the sharings over constant-size field. Putting these together leads to the constant-size field variant of celebrated MPC protocol in [5].

We note that although it was widely acknowledged that there exists an MPC protocol with constant communication complexity by replacing Shamir secret sharing scheme with arithmetic secret sharing scheme, there is no reference seriously describing such protocol in detail. Our work fills the missing detail by providing MPC primitive for any applications relying on MPC protocol of constant communication complexity. As an application of our perfectly secure MPC protocol which implies perfect robustness in the MPC-in-the-Head framework, we present the constant-rate zero-knowledge proof with $3$ communication rounds. The previous work achieves constant-rate with $5$ communication rounds [32] due to the statistical robustness of their MPC protocol. Another application of our ramp hyper-invertible matrix is the information-theoretic multi-verifier zero-knowledge for circuit satisfiability[43]. We manage to remove the dependence of the size of circuit and security parameter from the share size.

We revisit OCAKE (ACNS 23), a generic recipe that constructs password-based authenticated key exchange (PAKE) from key encapsulation mechanisms (KEMs) in a black-box way. This allows to potentially achieve post-quantum security by instantiating the KEM with a post-quantum KEM like KYBER. It was left as an open problem to further adapt the proof such that it also holds against quantum attackers. The security proof is given in the universal composability (UC) framework, which is commonly used to model and prove security of PAKE. So far, however, it is not known how to model or prove computational UC security against quantum adversaries. Even more so, if the proof makes use of idealized primitives like random oracles or ideal ciphers.

To pave the way towards reasoning post-quantum security, we therefore resort to a (still classical) game-based security proof in the BPR model (EUROCRYPT 2000). We consider this a crucial stepping stone towards a full proof of post-quantum security. We prove security of (a minor variation of) OCAKE generically, assuming the underlying KEM satisfies common notions of ciphertext indistinguishability, anonymity, and (computational) public key uniformity. To achieve tight security bounds, we relate security of OCAKE to multi-user variants of the aforementioned properties.

We provide a full detailed proof, something often omitted in publications concerned with game-based security of PAKE. As a side-contribution, we demonstrate how to handle password guesses in a game-based proof in detail. Something we were unable to find in the existing literature.

Single Input Functionality (SIF) is a special case of MPC, where only one distinguished party called dealer holds the secret input. SIF allows the dealer to complete a computation task and send to other parties their respective outputs without revealing any additional information about its secret input. SIF has many applications, including multiple-verifier zero-knowledge and verifiable relation sharing, etc. Recently, several works devote to round-efficient realization of SIF, and achieve 2-round communication in the honest majority setting (Applebaum et al., Crypto 2022; Baum et al., CCS 2022; Yang and Wang, Asiacrypt 2022).

In this work, we propose the first practical 2-round protocol for SIF against \emph{a dishonest majority} in the preprocessing model; moreover, the online phase is highly efficient as it requires no cryptographic operations and achieves information theoretical security. For SIF among 5 parties, our construction takes 152.34ms (total) to evaluate an AES-128 circuit with 7.36ms online time. Compared to the state-of-the-art (honest majority) solution (Baum et al., CCS 2022), our construction is roughly 2$\times$ faster in the online phase, although more preprocessing time is needed. Compared to the state-of-the-art generic MPC against a dishonest majority (Wang et al., CCS 2017; Cramer et al., Crypto 2018), our construction outperforms them w.r.t. both total running time and online running time.

Count-Min Sketch (CMS) and HeavyKeeper (HK) are two realizations of a compact frequency estimator (CFE). These are a class of probabilistic data structures that maintain a compact summary of (typically) high-volume streaming data, and provides approximately correct estimates of the number of times any particular element has appeared. CFEs are often the base structure in systems looking for the highest-frequency elements (i.e., top-$K$ elements, heavy hitters, elephant flows). Traditionally, probabilistic guarantees on the accuracy of frequency estimates are proved under the implicit assumption that stream elements do not depend upon the internal randomness of the structure. Said another way, they are proved in the presence of data streams that are created by non-adaptive adversaries. Yet in many practical use-cases, this assumption is not well-matched with reality; especially, in applications where malicious actors are incentivized to manipulate the data stream. We show that the CMS and HK structures can be forced to make significant estimation errors, by concrete attacks that exploit adaptivity. We analyze these attacks analytically and experimentally, with tight agreement between the two. Sadly, these negative results seem unavoidable for (at least) sketch-based CFEs with parameters that are reasonable in practice. On the positive side, we give a new CFE (Count-Keeper) that can be seen as a composition of the CMS and HK structures. Count-Keeper estimates are typically more accurate (by at least a factor of two) than CMS for ``honest" streams; our attacks against CMS and HK are less effective (and more resource intensive) when used against Count-Keeper; and Count-Keeper has a native ability to flag estimates that are suspicious, which neither CMS or HK (or any other CFE, to our knowledge) admits.

Correlation intractability is an emerging cryptographic paradigm that enabled several recent breakthroughs in establishing soundness of the Fiat-Shamir transform and, consequently, basing non-interactive zero-knowledge proofs and succinct arguments on standard cryptographic assumptions. In a nutshell, a hash family is said to be \emph{correlation intractable} for a class of relations $\mathcal{R}$ if, for any relation $R\in\mathcal{R}$, it is hard given a random hash function $h\gets H$ to find an input $z$ s.t. $(z,h(z))\in R$, namely a correlation.

Despite substantial progress in constructing correlation intractable hash functions, all constructions known to date are based on highly-structured hardness assumptions and, further, are of complexity scaling with the circuit complexity of the target relation class.

In this work, we initiate the study of the barriers for building correlation intractability. Our main result is a lower bound on the complexity of any black-box construction of CIH from collision resistant hash (CRH), or one-way permutations (OWP), for any sufficiently expressive relation class. In particular, any such construction for a class of relations with circuit complexity $t$ must make at least $\Omega(t)$ invocations of the underlying building block.

We see this as a first step in developing a methodology towards broader lower bounds.

Convex Consensus (CC) allows a set of parties to agree on a value $v$ inside the convex hull of their inputs with respect to a predefined convexity notion, even in the presence of byzantine parties. In this work, we focus on achieving CC in the best-of-both-worlds paradigm, i.e., simultaneously tolerating at most $t_s$ corruptions if communication is synchronous, and at most $t_a \leq t_s$ corruptions if it is asynchronous. Our protocol is randomized, which is a requirement under asynchrony, and we prove that it achieves optimal resilience. In the process, we introduce communication primitives tailored to the best-of-both-worlds model, which we believe to be of independent interest. These are a deterministic primitive, which allows honest parties to obtain intersecting views, and a randomized primitive, leading to identical views (which is impossible to achieve deterministically).

Afterwards, we consider achieving consensus using deterministic protocols, for which the agreement condition must be appropriately relaxed depending on the convexity space. For the relevant case of graph convexity spaces, we find that a previous asynchronous approximate agreement protocol for chordal graphs is incorrect, and hereby give a new protocol for the problem designed for the best-of-both-worlds model and achieving tight point-wise resilience bounds. Finally, we show that asynchronous graph approximate agreement remains unsolvable by deterministic protocols even when corruptions are restricted to at most two crashing nodes and the distance agreement threshold is linear in the size of the graph.

Reversed multiplication friendly embedding (RMFE) amortization has been playing an active role in the state-of-the-art constructions of MPC protocols over rings (in particular, the ring $\mathbb{Z}_{2^k}$). As far as we know, this powerful technique has NOT been able to find applications in the crown jewel of two-party computation, the non-interactive secure computation (NISC), where the requirement of the protocol being non-interactive constitutes a formidable technical bottle-neck. We initiate such a study focusing on statistical NISC protocols in the VOLE-hybrid model. Our study begins with making the {\em decomposable affine randomized encoding (DARE)} based semi-honest NISC protocol compatible with RMFE techniques, which together with known techniques for forcing a malicious sender Sam to honestly follow DARE already yield a secure amortized protocol, assuming both parties follow RMFE encoding. Achieving statistical security in the full malicious setting is much more challenging, as applying known techniques for enforcing compliance with RMFE incurs interaction. To solve this problem, we put forward a new notion dubbed non-malleable RMFE (NM-RMFE), which is a randomized RMFE such that, once one party deviates from the encoding specification, the randomness injected by the other party will randomize the output, preventing information from being leaked. NM-RMFE simultaneously forces both parties to follow RMFE encoding, offering a desired {\em non-interactive} solution to amortizing NISC. We believe that NM-RMFE is on its own an important primitive that has applications in secure computation and beyond, interactive and non-interactive alike. With an asymptotically good instantiation of our NM-RMFE, we obtain the first {\em statistical} reusable NISC protocols in the VOLE-hybrid model with {\em constant communication overhead} for arithmetic branching programs over $\mathbb{Z}_{2^k}$. As side contributions, we consider computational security and present two concretely efficient NISC constructions in the random oracle model from conventional RMFEs.