International Association
for Cryptologic Research

We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to some desired probability distribution. However, in the quantum case, this is possible if one has access to a prover who can supply a purification of the mixed state.

In this work, we introduce the concept of mixed-state certification, and we show that a natural sampling protocol offers secure certification in the presence of a possibly dishonest prover: if the verifier accepts then he can be almost certain that the state in question has been correctly prepared, up to a small number of errors.

We then apply this result to two-party quantum coin-tossing. Given that strong coin tossing is impossible, it is natural to ask ``how close can we get". This question has been well studied and is nowadays well understood from the perspective of the bias of individual coin tosses. We approach and answer this question from a different---and somewhat orthogonal---perspective, where we do not look at individual coin tosses but at the global entropy instead. We show how two distrusting parties can produce a common high-entropy source, where the entropy is an arbitrarily small fraction below the maximum.

We continue the study of protocols for secure multiparty computation (MPC) that require only two rounds of interaction. The recent works of Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) essentially settle the question by showing that such protocols are implied by the minimal assumption that a two-round oblivious transfer (OT) protocol exists. However, these protocols inherently make a non-black-box use of the underlying OT protocol, which results in poor concrete efficiency. Moreover, no analogous result was known in the information-theoretic setting, or alternatively based on one-way functions, given an OT correlations setup or an honest majority.

Motivated by these limitations, we study the possibility of obtaining information-theoretic and ``black-box'' implementations of two-round MPC protocols. We obtain the following results:

- Two-round MPC from OT correlations. Given an OT correlations setup, we get protocols that make a black-box use of a pseudorandom generator (PRG) and are secure against a malicious adversary corrupting an arbitrary number of parties. For a semi-honest adversary, we get similar information-theoretic protocols for branching programs.

- New NIOT constructions. Towards realizing OT correlations, we extend the DDH-based non-interactive OT (NIOT) protocol of Bellare and Micali (Crypto '89) to the malicious security model, and present new NIOT constructions from the Quadratic Residuosity Assumption (QRA) and the Learning With Errors (LWE) assumption.

- Two-round black-box MPC with strong PKI setup. Combining the two previous results, we get two-round MPC protocols that make a black-box use of any DDH-hard or QRA-hard group. The protocols can offer security against a malicious adversary, and require a PKI setup that depends on the number of parties and the size of computation, but not on the inputs or the identities of the participating parties.

- Two-round honest-majority MPC from secure channels. Given secure point-to-point channels, we get protocols that make a black-box use of a pseudorandom generator (PRG), as well as information-theoretic protocols for branching programs. These protocols can tolerate a semi-honest adversary corrupting a strict minority of the parties, where in the information-theoretic case the complexity is quasi-polynomial in the number of parties.

We construct Indistinguishability Obfuscation (iO) and Functional Encryption (FE) schemes in the Turing machine model from the minimal assumption of compact FE for circuits (CktFE). Our constructions overcome the barrier of sub-exponential loss incurred by all prior work. Our contributions are:

1. We construct iO in the Turing machine model from the same assumptions as required in the circuit model, namely, sub-exponentially secure FE for circuits. The previous best constructions [41, 6] require sub-exponentially secure iO for circuits, which in turn requires sub-exponentially secure FE for circuits [5, 15].

2. We provide a new construction of single input FE for Turing machines with unbounded length inputs and optimal parameters from polynomially secure, compact FE for circuits. The previously best known construction by Ananth and Sahai [7] relies on iO for circuits, or equivalently, sub-exponentially secure FE for circuits.

3. We provide a new construction of multi-input FE for Turing machines. Our construction supports a fixed number of encryptors (say k), who may each encrypt a string xi of unbounded length. We rely on sub-exponentially secure FE for circuits, while the only previous construction [10] relies on a strong knowledge type assumption, namely, public coin differing inputs obfuscation.

Our techniques are new and from first principles, and avoid usage of sophisticated iO specific machinery such as positional accumulators and splittable signatures that were used by all relevant prior work [41, 7, 6].

This paper introduces Spice, a system for building verifiable state machines (VSMs). A VSM is a request-processing service that produces proofs establishing that requests were executed correctly according to a specification. Such proofs are succinct (a verifier can check them efficiently without reexecution) and zero- knowledge (a verifier learns nothing about the content of the requests, responses, or the internal state of the service). Recent systems for proving the correct execution of state- ful computations—Pantry [24], Geppetto [34], CTV [30], Hawk [49], vSQL [87]—implicitly implement VSMs, but they incur prohibitive costs. Spice reduces these costs by over two orders of magnitude with a new storage primitive. More notably, Spice’s storage primitive supports multiple writers, making Spice the first system that can succinctly prove the correct execution of concurrent services. We nd that Spice running on a cluster of 16 servers achieves 488–1048 transactions/second for a variety of applications including inter-bank transactions [27], cloud- hosted ledgers [28], and dark pools [65]. This represents a 16,000—620,000× higher throughput than prior work.

A software watermarking scheme can embed some information called a mark into a program while preserving its functionality. No adversary can remove the mark without damaging the functionality of the program. Cohen et al. (STOC '16) gave the first positive results for watermarking, showing how to watermark certain pseudorandom function (PRF) families using indistinguishability obfuscation (iO). Their scheme has a secret marking procedure to embed marks in programs and a public extraction procedure to extract the marks from programs; security holds even against an attacker that has access to a marking oracle. Kim and Wu (CRYPTO '17) later constructed a PRF watermarking scheme under only the LWE assumption. In their scheme, both the marking and extraction procedures are secret, but security only holds against an attacker with access to a marking oracle but not an extraction oracle. In fact, it is possible to completely break the security of the latter scheme using extraction queries, which is a significant limitation in any foreseeable application.

In this work, we construct a new PRF watermarking scheme with the following properties.

* The marking procedure is public and therefore anyone can embed marks in PRFs from the family. Previously we had no such construction even using obfuscation.

* The extraction key is secret, but marks remain unremovable even if the attacker has access to an extraction oracle. Previously we had no such construction under standard assumptions.

* Our scheme is simple, uses generic components and can be instantiated under many different assumptions such as DDH, Factoring or LWE.

The above benefits come with one caveat compared to prior work: the PRF family that we can watermark depends on the public parameters of the watermarking scheme and the watermarking authority has a secret key which can break the security of all of the PRFs in the family. Since the watermarking authority is usually assumed to be trusted, this caveat appears to be acceptable.

We consider the question of whether the security of unique digital signature schemes can be based on game-based cryptographic assumptions using linear-preserving black-box security reductions—that is, black-box reductions for which the security loss (i.e., the ratio between "work" of the adversary and the "work" of the reduction) is some a priori bounded polynomial. A seminal result by Coron (Eurocrypt'02) shows limitations of such reductions; however, his impossibility result and its subsequent extensions all suffer from two notable restrictions: (1) they only rule out so-called "simple" reductions, where the reduction is restricted to only sequentially invoke "straight-line" instances of the adversary; and (2) they only rule out reductions to non-interactive (two-round) assumptions.

In this work, we present the first full impossibility result: our main result shows that the existence of any linear-preserving black-box reduction for basing the security of unique signatures on some bounded-round assumption implies that the assumption can be broken in polynomial time.

We present an improved version of the one-way to hiding (O2H) lemma by Unruh, J ACM 2015. Our new O2H lemma gives higher flexibility (arbitrary joint distributions of oracles and inputs, multiple reprogrammed points) as well as tighter bounds (removing square-root factors, taking parallelism into account).

Concerns about the impact of quantum computers on currently deployed public key cryptography have instigated research into not only quantum-resistant cryptographic primitives but also how to transition applications from classical to quantum-resistant solutions. One approach to mitigate the risk of quantum attacks and to preserve common security guarantees are hybrid schemes, which combine classically secure and quantum-resistant schemes. Various academic and industry experiments and draft standards related to the Transport Layer Security (TLS) protocol already use some form of hybrid key exchange; however sound theoretical approaches to substantiate the design and security of such hybrid key exchange protocols are missing so far.

We initiate the modeling of hybrid authenticated key exchange protocols. We consider security against adversaries with varying levels of quantum power over time, such as adversaries who may become quantum in the future or are quantum in the present. We reach our goal using a three-step approach: First, we introduce security notions for key encapsulation mechanisms (KEMs) that enable a fine-grained distinction between different quantum scenarios. Second, we propose several combiners for constructing hybrid KEMs that correspond closely to recently proposed Internet-Drafts for hybrid key exchange in TLS 1.3. Finally, we present a provably sound design for hybrid key exchange using KEMs as building blocks.

Intel's Software Guard Extensions (SGX) enables isolated execution environments, called enclaves, on untrusted operating systems (OS), and thus it can improve the security for various applications and online services. However, SGX has also well-known limitations. First, its remote attestation mechanism is vulnerable to relay attacks that allow the attacker to redirect attestation and the following provisioning of secrets to an unintended platform. Second, attestation keys have been shown to leak thus enabling attackers to fake the secure attested environment by emulating it. Third, there exists no secure way to let enclaves communicate with the I/O devices and as a consequence the user.

To address these shortcomings, we propose a hardened variant of SGX attestation using proximity verification. We design and implement a system called ProximiTEE, where a simple embedded device with a low TCB is attached to the target platform. The embedded device verifies the proximity of the attested enclave by using distance bounding and secure boot-time initialization, thus allowing secure attestation regardless of a compromised OS or leaked attestation keys. Our boot-time initialization can be seen as a novel variant of ``trust on first use'' (TOFU) that makes deployment of secure attestation easier, reduces the system's attack surface and enables secure revocation. We further leverage the embedded device to build a trusted I/O path between peripherals (e.g., keyboards, displays) and enclaves, by letting it securely mediate every I/O communication between them. Our prototype implementation shows that such proximity verification is reliable in practice.

A two-party coin-flipping protocol is $\epsilon$-fair if no efficient adversary can bias the output of the honest party (who always outputs a bit, even if the other party aborts) by more than $\epsilon$. Cleve [STOC '86] showed that $r$-round $o(1/r)$-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript '85] constructed a $\Theta(1/\sqrt{r})$-fair coin-flipping protocol, assuming the existence of one-way functions. Moran et al. [Journal of Cryptology '16] constructed an $r$-round coin-flipping protocol that is $\Theta(1/r)$-fair (thus matching the aforementioned lower bound of Cleve [STOC '86]), assuming the existence of oblivious transfer.

The above gives rise to the intriguing question of whether oblivious transfer, or more generally ``public-key primitives'', is required for an $o(1/\sqrt r)$-fair coin flipping. This question was partially answered by Dachman-Soled et al. [TCC '11] and Dachman-Soled et al. [TCC '14], who showed that restricted types of fully black-box reductions cannot establish $o(1/\sqrt r)$-fair coin-flipping protocols from one-way functions. In particular, for constant-round coin-flipping protocols, Dachman-Soled et al. showed that black-box techniques from one-way functions can only guarantee fairness of order $1/\sqrt{r}$.

We make progress towards answering the above question by showing that, for any constant $r\in \mathbb N$, the existence of an $1/(c\cdot \sqrt{r})$-fair, $r$-round coin-flipping protocol implies the existence of an infinitely-often key-agreement protocol, where $c$ denotes some universal constant (independent of $r$). Our reduction is non black-box and makes a novel use of the recent dichotomy for two-party protocols of Haitner et al. [FOCS '18] to facilitate a two-party variant of the recent attack of Beimel et al. [FOCS '18] on multi-party coin-flipping protocols.

Trapdoor permutations (TDP) are a fundamental primitive in cryptography. Over the years, several variants of this notion have emerged as a result of various applications. However, it is not clear whether these variants may be based on the standard notion of TDPs.

We study the question of whether enhanced trapdoor permutations can be based on classical trapdoor permutations. The main motivation of our work is in the context of existing TDP-based constructions of oblivious transfer and non-interactive zero-knowledge protocols, which require enhancements to the classical TDP notion. We prove that these enhancements are non-trivial, in the sense that there does not exist fully blackbox constructions of enhanced TDPs from classical TDPs.

At a technical level, we show that the enhanced TDP security of any construction in the random TDP oracle world can be broken via a polynomial number of queries to the TDP oracle as well as a weakening oracle, which provides inversion with respect to randomness. We also show that the standard one-wayness of a random TDP oracle stays intact in the presence of this weakening oracle.

We propose a new algorithm inspired by Nested to find differential path in ARX ciphers. To enhance the decision process of our algorithm and to reduce the search space of our heuristic nested tool, we used the concept of partial difference distribution table (pDDT) along with the algorithm. The algorithm is applied on reduced round variants of SPECK block cipher family. In our previous paper we applied naive algorithm with a large search space of values and presented the result only for one block size variant of SPECK. Our new approach in this paper provide the results within a simpler framework and within a very short period of time (few minutes) for all bigger block size variants of SPECK. More specifically, we report the differential path for up to 8, 9, 11, 10 and 11 rounds of SPECK32, SPECK48, SPECK64, SPECK96 and SPECK128, respectively. To construct a differential characteristics for large number of rounds, we divide long characteristics into short ones, say constructing a large characteristics from two short characteristics. Instead of starting from first round we start from the middle and run experiment in forward as well as reverse direction. Using this method we improved our results and report the differential path for up to 9, 10, 12, 13 and 15 rounds of SPECK32, SPECK48, SPECK64, SPECK96 and SPECK128, respectively.

In this paper we focus on differential cryptanalysis dedicated to a particular class of cryptographic algorithms, namely ARX ciphers. We propose a new algorithm inspired by the Nested Monte-Carlo Search algorithm to find a differential path in ARX ciphers. We apply our algorithm to a round reduced variant of the block cipher LEA. We use the concept of a partial difference distribution table (pDDT) in our algorithm to reduce the search space. This methodology reduced the search space of the algorithm by using only those differentials whose probabilities are greater than or equal to pre-defined threshold. Using this concept we removed many differentials which are not valid or whose probabilities are very low. By doing this we decreased the time of finding a differential path by our nested algorithm due to a smaller search space. This partial difference distribution table also made our nested algorithm suitable for bigger block size ARX ciphers. Finding long differential characteristics is one of the hardest problems where we have seen other algorithms take many hours or days to find differential characteristics in ARX ciphers. Our algorithm finds the differential characteristics in just a few minutes with a very simple framework. We report the differential path for up to 9 rounds in LEA. To construct differential characteristics for a large number of rounds, we divide long characteristics into short ones, by constructing a large characteristic from two short characteristics. Instead of starting from the first round, we start from the middle and run experiments in forward as well as in the reverse direction. Using this method we improved our results and report the differential path for up to 13 rounds. Overall, the best property of our algorithm is that it has potential to provide state-of-the-art results but within a simpler framework as well as less time. Our algorithm is also very interesting for future aspect of research, as it could be applied to other ARX ciphers with a very easy going framework.

A traitor tracing scheme is a public key encryption scheme for which there are many secret decryption keys. Any of these keys can decrypt a ciphertext; moreover, even if a coalition of users collude, put together their decryption keys and attempt to create a new decryption key, there is an efficient algorithm to trace the new key to at least one the colluders.

Recently, Goyal, Koppula and Waters (GKW, STOC 18) provided the first traitor tracing scheme from LWE with ciphertext and secret key sizes that grow polynomially in $\log n$, where $n$ is the number of users. The main technical building block in their construction is a strengthening of (bounded collusion secure) secret-key functional encryption which they refer to as mixed functional encryption (FE).

In this work, we improve upon and extend the GKW traitor tracing scheme: - We provide simpler constructions of mixed FE schemes based on the LWE assumption. Our constructions improve upon the GKW construction in terms of expressiveness, modularity, and security. - We provide a construction of attribute-based traitor tracing for all circuits based on the LWE assumption.

Event date: 17 June to 21 June 2019

We consider the following paradoxical question: Can one prove lack of knowledge? We define the notion of Proofs of Ignorance, construct such proofs, and use these proofs to construct a 2-message witness hiding protocol for all of NP.

More specifically, we define a proof of ignorance (PoI) with respect to any language L in NP and distribution D over instances in L. Loosely speaking, such a proof system allows a prover to generate an instance x according to D along with a proof that she does not know a witness corresponding to x. We construct construct a PoI protocol for any random self-reducible NP language L that is hard on average. Our PoI protocol is non-interactive assuming the existence of a common reference string.

We use such a PoI protocol to construct a 2-message witness hiding protocol for NP with adaptive soundness. Constructing a 2-message WH protocol for all of NP has been a long standing open problem. We construct our witness hiding protocol using the following ingredients (where T is any super-polynomial function in the security parameter):

1. T-secure PoI protocol,

2. T-secure non-interactive witness indistinguishable (NIWI) proofs,

3. T-secure rerandomizable encryption with strong KDM security,

where the first two ingredients can be constructed based on the T-security of DLIN.

At the heart of our witness-hiding proof is a new non-black-box technique. As opposed to previous works, we do not apply an efficiently computable function to the code of the cheating verifier, rather we resort to a form of case analysis and show that the prover's message can be simulated in both cases, without knowing in which case we reside.

The round complexity of zero-knowledge protocols is a long-standing open question, yet to be settled under standard assumptions. So far, the question has appeared equally challenging for relaxations such as weak zero-knowledge and witness hiding. Protocols satisfying these relaxed notions, under standard assumptions, have at least four messages, just like full-fledged zero knowledge. The difficulty in improving round complexity stems from a fundamental barrier: non of these notions can be achieved in three messages via reductions (or simulators) that treat the verifier as a black box.

We introduce a new non-black-box technique and use it to obtain the first protocols that cross this barrier under standard assumptions. Our main results are: - Weak zero-knowledge for NP in three messages, assuming fully-homomorphic encryption, and other standard primitives (known for example under the Learning with Errors assumption). - Weak zero-knowledge for NP intersect coNP in two messages, assuming in addition non-interactive witness-indistinguishable proofs.

We also give witness-hiding protocol for NP in two-message, assuming in addition witness encryption. This protocol is also publicly verifiable.

Our technique is based on a new homomorphic trapdoor paradigm, which can be seen as a non-black-box analog of the classical Feige-Lapidot-Shamir trapdoor paradigm.

We show that any multi-party functionality can be evaluated using a two-round protocol with perfect correctness and perfect semi-honest security, provided that the majority of parties are honest. This settles the round complexity of information-theoretic semi-honest MPC, resolving a longstanding open question (cf. Ishai and Kushilevitz, FOCS 2000). The protocol is efficient for $NC^1$ functionalities. Furthermore, given black-box access to a one-way function, the protocol can be made efficient for any polynomial functionality, at the cost of only guaranteeing computational security.

Technically, we extend and relax the notion of randomized encoding to specifically address multi-party functionalities. The property of a multi-party randomized encoding (MPRE) is that if the functionality $g$ is an encoding of the functionality $f$, then for any (permitted) coalition of players, their respective outputs and inputs in $g$ allow them to simulate their respective inputs and outputs in $f$, without learning anything else, including the other outputs of $f$.

One approach for blockchain based applications to provide a proof-of-work is the computation of hash-values. In our opinion these computations are a waste of energy. It would be highly desirable to find an alternative method that generates useful output. We show how to substitute hashing by performing multiplications on Elliptic Curves in order to find distinguished points that can then be used to solve the discrete logarithm problem on a chosen curve. Today's digital infrastructures rely on only a few curves. We argue that the advent of blockchain based technologies makes the use of only few standardised curves questionable.

In principle all cryptanalytic algorithms that use Rabin's idea of distinguished points can be used in blockchain based attacks. Similar ideas can be used for the number field sieve.

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC '87 and J. ACM '96) is a technique for provably obfuscating programs' access patterns, such that the access patterns leak no information about the programs' secret inputs. To compile a general program to an oblivious counterpart, it is well-known that $\Omega(\log N)$ amortized blowup is necessary, where $N$ is the size of the logical memory. This was shown in Goldreich and Ostrovksy's original ORAM work for statistical security and in a somewhat restricted model (the so called balls-and-bins model), and recently by Larsen and Nielsen (CRYPTO '18) for computational security.

A long standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this paper, we resolve this problem and present the first secure ORAM with $O(\log N)$ amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS '18) who gave a construction with $O(\log N\cdot {\sf poly}(\log\log N))$ amortized blowup, assuming one-way functions.