Structure-preserving signatures on equivalence classes, or equivalence-class signatures for short (EQS), are signature schemes defined over bilinear groups whose messages are vectors of group elements. Signatures are perfectly randomizable and given a signature on a vector, anyone can derive a signature on any multiple of the vector; EQS thus sign projective equivalence classes. Applications of EQS include the first constant-size anonymous attribute-based credentials, efficient round-optimal blind signatures without random oracles and efficient access-control encryption.
To date, the only existing instantiation of EQS is proven secure in the generic-group model. In this work we show that by relaxing the definition of unforgeability, which makes it efficiently verifiable, we can construct EQS from standard assumptions, namely the Matrix-Diffie-Hellman assumptions. We then show that our unforgeability notion is sufficient for most applications.

We present a new approach to extending oblivious transfer with communication complexity that is logarithmic in the security parameter. Our method only makes black-box use of the underlying cryptographic primitives, and can achieve security against an active adversary with almost no overhead on top of passive security. This results in the first oblivious transfer protocol with sublinear communication and active security, which does not require any non-black-box use of cryptographic primitives.
Our main technique is a novel twist on the classic OT extension of Ishai et al. (Crypto 2003), using an additively key-homomorphic PRF to reduce interaction. We first use this to construct a protocol for a large batch of 1-out-of-$n$ OTs on random inputs, with amortized $o(1)$ communication. Converting these to 1-out-of-2 OTs on chosen strings requires logarithmic communication. The key-homomorphic PRF used in the protocol can be instantiated under the learning with errors assumption with exponential modulus-to-noise ratio.

We propose a concrete procedure of a $\Sigma$-protocol proving knowledge that a set of witnesses satisfies a monotone predicate in the witness-indistinguishable manner. Inspired by the high-level work proposed by Cramer, Damg\r{a}rd and Schoenmakers at CRYPTO '94, we provide a concrete procedure by extending the so-called OR-proof.

qDSA is a high-speed, high-security signature scheme that facilitates implementations with a very small memory footprint, a crucial requirement for embedded systems and IoT devices, and that uses the same public keys as modern Diffie--Hellman schemes based on Montgomery curves (such as Curve25519) or Kummer surfaces. qDSA resembles an adaptation of EdDSA to the world of Kummer varieties, which are quotients of algebraic groups by \(\pm1\). Interestingly, qDSA does not require any full group operations or point recovery: all computations, including signature verification, occur on the quotient where there is no group law. We include details on four implementations of qDSA, using Montgomery and fast Kummer surface arithmetic on the 8-bit AVR {ATmega} and 32-bit ARM Cortex~M0 platforms. We find that qDSA significantly outperforms state-of-the-art signature implementations in terms of stack usage and code size. We also include an efficient compression algorithm for points on fast Kummer surfaces, reducing them to the same size as compressed elliptic curve points for the same security level.

In delegated computing, prominent in the context of cloud computing, guaranteeing both the correctness and authenticity of computations is of critical importance. Homomorphic signatures can be used as cryptographic solutions to this problem.
In this paper we solve the open problem of constructing a linearly homomorphic signature scheme that is secure against an active adversary under standard assumptions. We provide a construction based on the DL and CDH assumption. Furthermore we show how our scheme can be combined with homomorphic encryption under the framework of Linearly Homomorphic Authenticated Encryption with Public Verifiability. This way we can provide the first such scheme that is context hiding. Furthermore our solution even allows verification in constant time (in an amortized sense).

Lattice-based group signature is an active research topic in
recent years. Since the pioneering work by Gordon, Katz and Vaikuntanathan
(Asiacrypt 2010), ten other schemes have been proposed,
providing various improvements in terms of security, efficiency and functionality.
However, in all known constructions, one has to fix the number $N$ of group users in the setup stage, and as a consequence, the signature sizes are dependent on $N$.
In this work, we introduce the first constant-size group signature from lattices, which means that the size of signatures produced by the scheme is independent of $N$ and only depends on the security parameter $\lambda$. More precisely, in our scheme, the sizes of signatures, public key and users' secret keys are all of order $\widetilde{\mathcal{O}}(\lambda)$. The scheme supports dynamic enrollment of users and is proven secure in the random oracle model under the Ring Short Integer Solution (RSIS) and Ring Learning With Errors (RLWE) assumptions. At the heart of our design is a zero-knowledge argument of knowledge of a valid message-signature pair for the Ducas-Micciancio signature scheme (Crypto 2014), that may be of independent interest.

Selective opening security (SO security) is desirable for public key encryption (PKE) in a multi-user setting. {In a selective opening attack, an adversary receives a number of ciphertexts for possibly correlated messages, then it opens a subset of them and gets the corresponding messages together with the randomnesses used in the encryptions. SO security aims at providing security for the unopened ciphertexts.} Among the existing simulation-based, selective opening, chosen ciphertext secure (SIM-SO-CCA secure) PKEs, only one (Libert et al. Crypto'17) enjoys tight security, which is reduced to the Non-Uniform LWE assumption. However, their public key and ciphertext are not compact.
In this work, we focus on constructing PKE with tight SIM-SO-CCA security based on standard assumptions. We formalize security notions needed for key encapsulation mechanism (KEM) and show how to transform these securities into SIM-SO-CCA security of PKE through a tight security reduction, while the construction of PKE from KEM follows the general framework proposed by Liu and Paterson (PKC'15). We present two KEM constructions with tight securities based on the Matrix Decision Diffie-Hellman assumption. These KEMs in turn lead to two tightly SIM-SO-CCA secure PKE schemes. One of them enjoys not only tight security but also compact public key.

Abstract—We introduce a simple and practical Proof of Space (PoS) with applicability to ledger-based payment schemes. It has a dramatically simpler structure than previous proposals, and with that, becomes very easy to analyze. A proof can be as short as a few hundred bits, and can be publicly verified using only two hash function computations.

More than ten years ago, a devastating data substitution attack was shown to successfully compromise all previously proposed remote attestation techniques. In fact, the authors went further than simply attacking previously proposed methods: they called into question whether it is theoretically possible for remote attestation methods to exist in face of their attack. Subsequently, it has been shown that it is possible, by relying on self-modifying code.
We show that it is possible to create remote attestation that is secure against all data substitution attacks, without relying on self-modifying code. Our proposed method relies on a construction of the checksum process that forces frequent L2 cache overflows if any data substitution attack takes place.

We consider reputation systems in the Universal Composability Framework where users can anonymously rate each others products that they purchased previously. To obtain trustworthy, reliable, and honest ratings, users are allowed to rate products only once. Everybody is
able to detect users that rate products multiple times. In this paper we present an ideal functionality for such reputation systems and give an efficient realization that is usable in practical applications.

Authentication and integrity are fundamental security services that are critical for any viable system. However, some of the emerging systems (e.g., smart grids, aerial drones) are delay-sensitive, and therefore their safe and reliable operation requires delay-aware authentication mechanisms. Unfortunately, the current state-of-the-art authentication mechanisms either incur heavy computations or lack scalability for such large and distributed systems. Hence, there is a crucial need for digital signature schemes that can satisfy the requirements of delay-aware applications.
In this paper, we propose a new digital signature scheme that we refer to as Compact Energy and Delay-aware Authentication (CEDA). In CEDA, signature generation and verification only require a small-constant number of multiplications and Pseudo Random Function (PRF) calls. Therefore, it achieves the lowest end-to-end delay among its counterparts. Our implementation results on an ARM processor and commodity hardware show that CEDA has the most efficient signature generation on both platforms, while offering a fast signature verification. Among its delay-aware counterparts, CEDA has smaller private key with a constant-size signature. All these advantages are achieved with the cost of a larger public key. This is a highly favorable trade-off for applications wherein the verifier is not memory-limited. We open-sourced our implementation of CEDA to enable its broad testing and adaptation.

In the setting of secure multiparty computation, a set of $n$ parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any $n$-party functionality can be computed with \emph{perfect security}, in the private channels model. When the adversary is semi-honest this holds as long as $t<n/2$ parties are corrupted, and when the adversary is malicious this holds as long as $t<n/3$ parties are corrupted. Unfortunately, a full proof of these results was never published. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. This includes a full description of the protocol for the malicious setting, including the construction of a new subprotocol for the perfect multiplication protocol that seems necessary for the case of $n/4\leq t<n/3$.

The first candidate indistinguishability obfuscator (iO) of Garg et al. (FOCS 2013) changed the previously pessimistic attitude towards general-purpose cryptographic obfuscation. The potential realizability of such a powerful tool motivated a plethora of applications, including solutions for long-standing open problems, from almost all areas of cryptography. At the same time, the question of whether iO is realizable under standard assumptions is still open. In this work, we review the rapid development of candidate constructions and organize the results of the first four years since the breakthrough. Our goal is to give a bird's-eye view of the infancy of cryptographic obfuscation, providing insight into the most important ideas and techniques.

Ishai, Kushilevitz, Ostrovsky and Sahai (STOC 2007, SIAM JoC 2009) introduced the powerful ``MPC-in-the-head'' technique that provided a general transformation of information-theoretic MPC protocols secure against passive adversaries to a ZK proof in a ``black-box'' way. In this work, we extend this technique and provide a generic transformation of any semi-honest secure two-party computation (2PC) protocol (with mild adaptive security guarantees) in the so called oblivious-transfer hybrid model to an adaptive ZK proof for any NP language, in a ``black-box'' way assuming only one-way functions. Our basic construction based on Goldreich-Micali-Wigderson's 2PC protocol yields an adaptive ZK proof with communication complexity proportional to quadratic in the size of the circuit implementing the NP relation. Previously such proofs relied on an expensive Karp reduction of the NP language to Graph Hamiltonicity (Lindell and Zarosim (TCC 2009, Journal of Cryptology 2011)).
As an application of our techniques, we show how to obtain a ZK proof with an ``input-delayed'' property for any NP language without relying on expensive Karp reductions that is black-box in the underlying one-way function. Namely, the input delayed property allows the honest prover's algorithm to receive the actual statement to be proved only in the final round. We further generalize this to obtain a ``commit and prove'' protocol with the same property where the prover commits to a witness w in the second message and proves a statement x regarding the witness w in zero-knowledge where the statement is determined only in the last round.
This improves a previous construction of Lapidot and Shamir (Crypto 1990) that was designed specifically for the Graph Hamiltonicity problem and relied on the underlying primitives in a non-black-box way.
Additionally, we provide a general transformation to construct a randomized encoding of a function f from any 2PC protocol that securely computes a related functionality (in a black-box way) from one-way functions. We show that if the 2PC protocol has mild adaptive security guarantees (which are satisfied by both the Yao's and GMW's protocol) then the resulting randomized encoding (RE) can be decomposed to an offline/online encoding.

We provide the first verifiable shuffle specifically for fully homomorphic schemes. A verifiable shuffle is a way to ensure that if a node receives and sends encrypted lists, the content will be the same, even though no adversary can trace individual list items through the node. Shuffles are useful in e-voting, traffic routing and other applications.
We build our shuffle on the ideas and techniques of Groth's 2010 shuffle, but make necessary modifications for a less ideal setting where the randomness and ciphertexts admit no group structure.
The protocol relies heavily on the properties of the so-called gadget matrices, so we have included a detailed introduction to these.

Zero-knowledge proofs of knowledge and fully-homomorphic encryption are two areas that have seen considerable advances in recent years, and these two techniques are used in conjunction in the context of verifiable decryption. Existing solutions for verifiable decryption are aimed at the batch setting, however there are many applications in which there will only be one ciphertext that requires a proof of decryption. The purpose of this paper is to provide a zero-knowledge proof of correct decryption on an FHE ciphertext, which for instance could hold the result of a cryptographic election.
We give two main contributions. Firstly, we present a bootstrapping-like protocol to switch from one FHE scheme to another. The first scheme has efficient homomorphic capabilities; the second admits a simple zero-knowledge protocol. To illustrate this, we use the Brakerski et al. (ITCS, 2012) scheme for the former, and Gentry's original scheme (STOC, 2009) for the latter. Secondly, we present a simple one-shot zero-knowledge protocol for verifiable decryption using Gentry's original FHE scheme.

Nowadays it is well known that randomness may fail due to bugs or deliberate randomness subversion. As a result, the security of traditional public-key encryption (PKE) cannot be guaranteed any more. Currently there are mainly three approaches dealing with the problem of randomness failures: deterministic PKE, hedged PKE, and nonce-based PKE. However, these three approaches only apply to different application scenarios respectively. Since the situations in practice are dynamic and very complex, it's almost impossible to predict the situation in which a scheme is deployed, and determine which approach should be used beforehand.
In this paper, we initiate the study of hedged security for nonce-based PKE, which adaptively applies to the situations whenever randomness fails, and achieves the best-possible security. Specifically, we lift the hedged security to the setting of nonce-based PKE, and formalize the notion of chosen-ciphertext security against chosen-distribution attacks (IND-CDA2) for nonce-based PKE. By presenting two counterexamples, we show a separation between our IND-CDA2 security for nonce-based PKE and the original NBP1/NBP2 security defined by Bellare and Tackmann (EUROCRYPT 2016). We show two nonce-based PKE constructions meeting IND-CDA2, NBP1 and NBP2 security simultaneously. The first one is a concrete construction in the random oracle model, and the second one is a generic construction based on a nonce-based PKE scheme and a deterministic PKE scheme.

Attribute-based signature (ABS), originally introduced by Maji et al. (CT-RSA'11), represents an essential mechanism to allow for fine-grained authentication. A user associated with an attribute $x$ can sign w.r.t. a given public policy $C$ only if his attribute satisfies $C$, i.e., $C(x)=1$. So far, much effort on constructing bilinear map-based ABS schemes have been made, where the state-of-the-art scheme of Sakai et al. (PKC'16) supports the very wide class of unbounded circuits as policies. However, construction of ABS schemes without bilinear maps are less investigated, where it was not until recently that Tsabary (TCC'17) showed a lattice-based ABS scheme supporting bounded circuits as policies, at the cost of weakening the security requirement.
In this work, we affirmatively close the gap between ABS schemes based on bilinear maps and lattices by constructing the first lattice-based ABS scheme for unbounded circuits in the random oracle model. We start our work by providing a generic construction of ABS schemes for unbounded-circuits in the random oracle model, which in turn implies that one-way functions are sufficient to construct ABS schemes. To prove security, we formalize and prove a generalization of the Forking Lemma, which we call "general multi-forking lemma with oracle access", capturing the situation where the simulator is interacting with some algorithms he cannot rewind, and also covering many features of the recent lattice-based ZKPs. This, in fact, was a formalization lacking in many existing anonymous signatures from lattices so far (e.g., group signatures). Therefore, this formalization is believed to be of independent interest. Finally, we provide a concrete instantiation of our generic ABS construction from lattices by introducing a new $\Sigma$-protocol, that highly departs from the previously known techniques, for proving possession of a valid signature of the lattice-based signature scheme of Boyen (PKC'10).

Key-encapsulation mechanisms (KEMs) are a common stepping stone for constructing public-key encryption. Secure KEMs can be built from diverse assumptions, including ones related to integer factorization, discrete logarithms, error correcting codes, or lattices. In light of the recent NIST call for post-quantum secure PKE, the zoo of KEMs that are believed to be secure continues to grow. Yet, on the question of which is the most secure KEM opinions are divided. While using the best candidate might actually not seem necessary to survive everyday life situations, placing a wrong bet can actually be devastating, should the employed KEM eventually turn out to be vulnerable.
We introduce KEM combiners as a way to garner trust from different KEM constructions, rather than relying on a single one: We present efficient black-box constructions that, given any set of `ingredient' KEMs, yield a new KEM that is (CCA) secure as long as at least one of the ingredient KEMs is.
As building blocks our constructions use cryptographic hash functions and blockciphers. Some corresponding security proofs require idealized models for these primitives, others get along on standard assumptions.

We initiate the study of public-key encryption (PKE) schemes and key-encapsulation mechanisms (KEMs) that retain security even when public parameters (primes, curves) they use may be untrusted and subverted. We define a strong security goal that we call ciphertext pseudo-randomness under parameter subversion attack (CPR-PSA). We also define indistinguishability (of ciphertexts for PKE, and of encapsulated keys from random ones for KEMs) and public-key hiding (also called anonymity) under parameter subversion attack, and show they are implied by CPR-PSA, for both PKE and KEMs. We show that hybrid encryption continues to work in the parameter subversion setting to reduce the design of CPR-PSA PKE to CPR-PSA KEMs and an appropriate form of symmetric encryption. To obtain efficient, elliptic-curve-based KEMs achieving CPR-PSA, we introduce efficiently-embeddable group families and give several constructions from elliptic-curves.