Protocols for password authenticated key exchange (PAKE) allow two parties who share only a weak password to agree on a cryptographically strong key. We revisit the notion of PAKE in the framework of universal composability, and propose a relaxation of the PAKE functionality of Canetti et al. that we call lazy-extraction PAKE (lePAKE). Roughly, our relaxation allows the ideal-world adversary to postpone its password guess even until after a session is complete. We argue that this relaxed notion still provides meaningful security in the password-only setting. As our main result, we show that several PAKE protocols that were previously only proven secure with respect to a "game-based" definition can in fact be shown to realize the lePAKE functionality in the random-oracle model. These include SPEKE, SPAKE2, and TBPEKE, the most efficient PAKE schemes currently known.

The $k$-nearest neighbors ($k$NN) classifier predicts a class of a query, $q$, by taking the majority class of its $k$ neighbors in an existing (already classified) database, $S$. In secure $k$NN, $q$ and $S$ are owned by two different parties and $q$ is classified without sharing data. In this work we present a classifier based on $k$NN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider $\kappa$ nearest neighbors for $\kappa\approx k$ with probability that increases as the statistical distance between Gaussian and the distribution of the distances from $q$ to $S$ decreases. We call our classifier $k$-ish Nearest Neighbors ($k$-ish NN). For the implementation we introduce {\em double-blinded coin-toss} where the bias and output of the toss are encrypted. We use it to approximate the average and variance of the distances from $q$ to $S$ in a scalable circuit whose depth is independent of $|S|$. We believe these to be of independent interest. We implemented our classifier in an open source library based on HElib and tested it on a breast tumor database. Our classifier has accuracy and running time comparable to current state of the art (non-HE) MPC solution that have better running time but worse communication complexity. It also has communication complexity similar to naive HE implementation that have worse running time.

We present a new general framework for constructing compact and adaptively secure attribute-based encryption (ABE) schemes from $k$-Lin in asymmetric bilinear pairing groups. Previously, the only construction [Kowalczyk and Wee, Eurocrypt '19] that simultaneously achieves compactness and adaptive security from static assumptions supports policies represented by Boolean formulae. Our framework enables supporting more expressive policies represented by arithmetic branching programs. Our framework extends to ABE for policies represented by uniform models of computation such as Turing machines. Such policies enjoy the feature of being applicable to attributes of arbitrary lengths. We obtain the first compact adaptively secure ABE for deterministic and non-deterministic finite automata (DFA and NFA) from $k$-Lin, previously unknown from any static assumptions. Beyond finite automata, we obtain the first ABE for large classes of uniform computation, captured by deterministic and non-deterministic logspace Turing machines (the complexity classes $\mathsf{L}$ and $\mathsf{NL}$) based on $k$-Lin. Our ABE scheme has compact secret keys of size linear in the description size of the Turing machine $M$. The ciphertext size grows linearly in the input length, but also linearly in the time complexity, and exponentially in the space complexity. Irrespective of compactness, we stress that our scheme is the first that supports large classes of Turing machines based solely on standard assumptions. In comparison, previous ABE for general Turing machines all rely on strong primitives related to indistinguishability obfuscation.

Mathematically-secure cryptographic algorithms leak significant side-channel information through their power supplies when implemented on a physical platform. These side-channel leakages can be exploited by an attacker to extract the secret key of an embedded device. The existing state-of-the-art countermeasures mainly focus on the power balancing, gate-level masking, or signal-to-noise (SNR) reduction using noise injection and signature attenuation, all of which suffer either from the limitations of high power/area overheads, performance degradation or are not synthesizable. In this article, we propose a generic low-overhead digital-friendly power SCA countermeasure utilizing physical Time-Varying Transfer Functions (TVTF) by randomly shuffling distributed switched capacitors to significantly obfuscate the traces in the time domain. System-level simulation results of the TVTF-AES implemented in TSMC 65nm CMOS technology show > 4000x MTD improvement over the unprotected implementation with ~ 1.25x power and ~ 1.2x area overheads, and without any performance degradation.

Software watermarking schemes allow a user to embed an identifier into a piece of code such that the resulting program is nearly functionally-equivalent to the original program, and yet, it is difficult to remove the identifier without destroying the functionality of the program. Such schemes are often considered for proving software ownership or for digital rights management. Existing constructions of watermarking have focused primarily on watermarking pseudorandom functions (PRFs). In this work, we revisit the definitional foundations of watermarking, and begin by highlighting a major flaw in existing security notions. Existing security notions for watermarking only require that the identifier be successfully extracted from programs that preserve the exact input/output behavior of the original program. In the context of PRFs, this means that an adversary that constructs a program which computes a quarter of the output bits of the PRF or that is able to distinguish the outputs of the PRF from random are considered to be outside the threat model. However, in any application (e.g., watermarking a decryption device or an authentication token) that relies on PRF security, an adversary that manages to predict a quarter of the bits or distinguishes the PRF outputs from random would be considered to have defeated the scheme. Thus, existing watermarking schemes provide very little security guarantee against realistic adversaries. None of the existing constructions of watermarkable PRFs would be able to extract the identifier from a program that only outputs a quarter of the bits of the PRF or one that perfectly distinguishes. To address the shortcomings in existing watermarkable PRF definitions, we introduce a new primitive called a traceable PRF. Our definitions are inspired by similar definitions from public-key traitor tracing, and aim to capture a very robust set of adversaries: namely, any adversary that produces a useful distinguisher (i.e., a program that can break PRF security), can be traced to a specific identifier. We provide a general framework for constructing traceable PRFs via an intermediate primitive called private linear constrained PRFs. Finally, we show how to construct traceable PRFs from a similar set of assumptions previously used to realize software watermarking. Namely, we obtain a single-key traceable PRF from standard lattice assumptions and a fully collusion-resistant traceable PRF from indistinguishability obfuscation (together with injective one-way functions).

We present a protocol for checking the values of a committed polynomial $f\in \mathbb{F}_{<n}[X]$ over a multiplicative subgroup $H\subset \mathbb{F}$ of size $n$, are contained in the values of a table $t\in \mathbb{F}^d$. Our protocol can be viewed as a simplification of one from Bootle et. al [BCGJM, ASIACRYPT 2018] for a similar problem, with potential efficiency improvements when $d\leq n$. In particular, [BCGJM]'s protocol requires comitting to several auxiliary polynomials of degree $d\cdot \log n$, whereas ours requires three commitments to auxiliary polynomials of degree $n$, which can be much smaller in the case $d\sim n$. One common use case of this primitive in the zk-SNARK setting is a ``batched range proof'', where one wishes to check all of $f$'s values on $H$ are in a range $[0,\ldots,M]$. We present a slightly optimized protocol for this special case, and pose improving it as an open problem.

We have proposed before a multivariate public key cryptosystem (MPKC) that does not rely on the difficulty of prime factorization, and whose modulus is the product of many small prime numbers. In this system, the prime factorization by the attackers is self-trivial, and the structure of the secret key is based on CRT (Chinese Remainder Theorem). In this paper we propose MPKC with security of IND-CPA by adding random numbers to central transformation vectors in the system proposed before.

We show that a slight variant of Protocol $\mathit{SPAKE2}+$, which was presented but not analyzed in Cash, Kiltz, and Shoup (2008) is a secure asymmetric password-authenticated key exchange protocol (PAKE), meaning that the protocol still provides good security guarantees even if a server is compromised and the password file stored on the server is leaked to an adversary. The analysis is done in the UC framework (i.e., a simulation-based security model), under the computational Diffie-Hellman (CDH) assumption, and modeling certain hash functions as random oracles. The main difference between our variant and the original Protocol~$\mathit{SPAKE2}+$ is that our variant includes standard key confirmation flows; also, adding these flows allows some slight simplification to the remainder of the protocol. Along the way, we also: provide the first proof (under the same assumptions) that a slight variant of Protocol $\mathit{SPAKE2}$ from Abdalla and Pointcheval (2005) is a secure symmetric PAKE in the UC framework (previous security proofs were all in the weaker BPR framework of Bellare, Pointcheval, and Rogaway (2000); provide a proof (under very similar assumptions) that a variant of Protocol $\mathit{SPAKE2}+$ that is currently being standardized is also a secure asymmetric PAKE; repair several problems in earlier UC formulations of secure symmetric and asymmetric PAKE.

Confidential transactions are used in distributed digital assets to demonstrate the balance of values hidden in commitments, while retaining signer ambiguity. Previous work describes a signer-ambiguous proof of knowledge of the opening of commitments to zero at the same index across multiple public commitment sets and the evaluation of a verifiable random function used as a linking tag, and uses this to build a linkable ring signature called Triptych that can be used as a building block for a confidential transaction model. In this work, we extend Triptych to build Arcturus, a proving system that proves knowledge of openings of multiple commitments to zero within a single set, correct construction of a verifiable random function evaluated at each opening, and value balance across a separate list of commitments within a single proof. While soundness depends on a novel dual discrete-logarithm hardness assumption, we use data from the Monero blockchain to show that Arcturus can be used in a confidential transaction model to provide faster total batch verification time than other state-of-the-art constructions without a trusted setup.

Many blockchain researches focus on the privacy protection. However, criminals can leverage strong privacy protection of the blockchain to do illegal crimes (such as ransomware) without being punished. These crimes have caused huge losses to society and users. Implementing identity tracing is an important step in dealing with issues arising from privacy protection. In this paper, we propose a blockchain traceable scheme with oversight function (BTSOF). The design of BTSOF builds on SkyEye (Tianjun Ma et al., Cryptology ePrint Archive 2020). In BTSOF, the regulator must obtain the consent of the committee to enable tracing. Moreover, we construct a non-interactive verifiable multi-secret sharing scheme (VMSS scheme) and leverage the VMSS scheme to design a distributed multi-key generation (DMKG) protocol for the Cramer-Shoup public key encryption scheme. The DMKG protocol is used in the design of BTSOF. We provide the security definition and security proof of the VMSS scheme and DMKG protocol.

Recent works in side-channel analysis have been fully relying on training classification models to recover sensitive information from traces. However, the knowledge of an attacker or an evaluator is not taken into account and poorly capturedby solely training a classifier on signals. This paper proposes to inject prior information in preprocessing and classification in order to increase the performance of side-channel attacks (SCA). First wepropose to use the Wavelet Scattering Transform, recently proposed by Mallat, for mapping traces into a time-frequency space which is stable under small translation and diffeomorphism. That way, we address the issues of desynchronization and deformation generally present in signals for SCA. The second part of our paper extends the canonical attacks over byteand Hamming weight by introducing a more general attack. Classifiers are trained on different labelings of the sensitive variable and combined by minimizing a cross-entropy criterion so as to find the best labeling strategy. With these two key ideas, we successfully increase the performance of Template Attacks on artificially desynchronized traces and signals from a jitter-protected implementation.

Spook is one of the 32 candidates that has made it to the second round of the NIST Lightweight Cryptography Standardization process, and is particularly interesting since it proposes differential side channel resistance. In this paper, we present practical distinguishers of the full 6-step version of the underlying permutations of Spook, namely Shadow-512 and Shadow-384, solving challenges proposed by the designers on the permutation. We also propose practical forgeries with 4-step Shadow for the S1P mode of operation in the nonce misuse scenario, which is allowed by the CIML2 security game considered by the authors. All the results presented in this paper have been implemented.

We present our integration of post-quantum cryptography (PQC), more specifically of the post-quantum KEM scheme Kyber for key establishment and the post-quantum signature scheme SPHINCS$^+$, into the embedded TLS library mbed TLS. We measure the performance of these post-quantum primitives on four different embedded platforms with three different ARM processors and an Xtensa LX6 processor. Furthermore, we compare the performance of our experimental PQC cipher suite to a classical TLS variant using elliptic curve cryptography (ECC). Post-quantum key establishment and signature schemes have been either integrated into TLS or ported to embedded devices before. However, to the best of our knowledge, we are the first to combine TLS, post-quantum schemes, and embedded systems and to measure and evaluate the performance of post-quantum TLS on embedded platforms. Our results show that post-quantum key establishment with Kyber performs well in TLS on embedded devices compared to ECC variants. The use of SPHINCS$^+$ signatures comes with certain challenges in terms of signature size and signing time, which mainly affects the use of embedded systems as PQC-TLS server but does not necessarily prevent embedded systems to act as PQC-TLS clients.

We characterize the ANF and the univariate representation of any vectorial function as parts of the ANF and bivariate representation of the Boolean function equal to its graph indicator. We show how this provides, when $F$ is bijective, the expression of $F^{-1}$ and/or allows deriving properties of $F^{-1}$. We illustrate this with examples and with a tight upper bound on the algebraic degree of $F^{-1}$ by means of that of $F$. We characterize by the Fourier-Hadamard transform, by the ANF, and by the bivariate representation, that a given Boolean function is the graph indicator of a vectorial function. We also give characterizations of those Boolean functions that are affine equivalent to graph indicators. We express the graph indicators of the sum, product, composition and concatenation of vectorial functions by means of the graph indicators of the functions. We deduce from these results a characterization of the bijectivity of a generic $(n,n)$-function by the fact that some Boolean function, which appears as a part of the ANF (resp. the bivariate representation) of its graph indicator, is equal to constant function 1. We also address the injectivity of $(n,m)$-functions. Finally, we study the characterization of the almost perfect nonlinearity of vectorial functions by means of their graph indicators.

Generic vulnerability assessment of cipher implementations against fault attacks (FA) is a largely unexplored research area to date. Security assessment against FA is particularly important in the context of FA countermeasures because, on several occasions, countermeasures fail to fulfil their sole purpose of preventing FA due to flawed design or implementation. In this paper, we propose a generic, simulation-based, statistical yes/no experiment for evaluating fault-assisted information leakage based on the principle of non-interference. The proposed exper- iment is oblivious to the structure of countermeasure/cipher under test and detects fault-induced leakage solely by observing the ciphertext dis- tributions. Unlike a recently proposed approach that utilizes t-test and its higher-order variants for detecting leakage at different moments of ciphertext distributions, in this work, we present a Deep Learning (DL) based leakage detection test. Our DL-based detection test is not specific to only moment-based leakages and thus can expose leakages in several cases where t-test based technique demands a prohibitively large number of ciphertexts. We also present a systematic approach to interpret the leakages from DL models. Apart from improving the leak- age detection test, we explore two generalizations of the leakage assess- ment experiment itself – one for evaluating against the Statistical ineffec- tive fault model (SIFA), and another for assessing fault-induced leakages originating from “non-cryptographic” peripheral components of a secu- rity module. Finally, we present techniques for efficiently covering the fault space of a block cipher by exploiting logic-level and cipher-level fault equivalences. The efficacy of DL-based leakage detection, as well as the proposed generalizations, has been evaluated on a rich test-suite of hardened implementations from several countermeasure classes, includ- ing open-source SIFA countermeasures and a hardware security module called Secured-Hardware-Extension (SHE).

While the digital technology spreads through the society, reliable personal authentication is becoming an urgent issue. As shown in digital taxation (e-Tax) and blockchain, etc., high reliable link between the private key of a public key and the owner who has it in card or smartphone etc. is required. This paper proposes 3 layer public key cryptosystem in which Individual Number (a.k.a. "My Number") and STR (Short Tandem Repeat) as personal identification data installed. "Individual Number" is a national identification number issued by government, like social security number in USA. STR is a kind of DNA data which does not contain any subtle personal information such as inherited character and has very accurate personal identification. The proposed system satisfies requirements of integrity, soundness and zero knowledge characteristics which analog biometrics such as face authentications cannot provide.

We propose and evaluate a secure-multiparty-computation (MPC) solution in the semi-honest model with dishonest majority that is based on multiparty homomorphic encryption (MHE). To support our solution, we introduce a multiparty version of the Brakerski-Fan-Vercauteren homomorphic cryptosystem and implement it in an open-source library. MHE-based MPC solutions have several advantages: Their transcript is public, their offline phase is compact, and their circuit-evaluation procedure is non-interactive. By exploiting these properties, the communication complexity of MPC tasks is reduced from quadratic to linear in the number of parties, thus enabling secure computation among potentially thousands of parties and in a broad variety of computing paradigms, from the traditional peer-to-peer setting to cloud-outsourcing and smart-contract technologies. MHE-based approaches can also outperform the state-of-the-art solutions, even for a small number of parties. We demonstrate this for three circuits: private input selection with application to private-information retrieval, component-wise vector multiplication with application to private-set intersection, and Beaver multiplication triples generation. For the first circuit, privately selecting one input among eight thousand parties' (of 32 KB each) requires only 1.31 MB of communication per party and completes in 61.7 seconds. For the second circuit with eight parties, our approach is 8.6 times faster and requires 39.3 times less communication than the current methods. For the third circuit and ten parties, our approach generates 20 times more triples per second while requiring 136 times less communication per-triple than an approach based on oblivious transfer. We implemented our scheme in the Lattigo library and open-sourced the code at https://github.com/ldsec/lattigo.

Payment channel networks have been introduced to mitigate the scalability issues inherent to permissionless decentralized cryptocurrencies such as Bitcoin. Launched in 2018, the Lightning Network (LN) has been gaining popularity and consists today of more than 5000 nodes and 30000 payment channels that jointly hold 895 bitcoins (7.6M USD as of February 2020). This adoption has motivated research from both academia and industry. Payment channels suffer from security vulnerabilities, such as the wormhole attack, anonymity issues, and scalability limitations related to the upper bound on the number of concurrent payments per channel, which have been pointed out by the scientific community but never quantitatively analyzed. In this work, we first analyze the proneness of the LN to the wormhole attack and attacks against anonymity. We observe that an adversary needs to control only 2% of LN nodes to learn sensitive payment information (e.g., sender, receiver and payment amount) or to carry out the wormhole attack. Second, we study the management of concurrent payments in the LN and quantify its negative effect on scalability. We observe that for micropayments, the forwarding capability of up to 50% of channels is restricted to a value smaller than the overall channel capacity. This phenomenon not only hinders scalability but also opens the door for DoS attacks: We estimate that a network-wide DoS attack costs within 1.5M USD, while isolating the biggest community from the rest of the network costs only 225k USD. Our findings should prompt the LN community to consider the security, privacy and scalability issues of the network studied in this work when educating users about path selection algorithms, as well as to adopt multi-hop payment protocols that provide stronger security, privacy and scalability guarantees.

We present a stochastic method for breaking general periodic polyalphabetic substitution ciphers using only the ciphertext and without using any additional constraints that might come from the cipher’s structure. The method employs a hill-climbing algorithm for individual key alphabets, with occasional slipping down the hill. We implement the method with a computer and achieve reliable results for a sufficiently long ciphertext (150 characters per key alphabet). Because no constraints among the key alphabets are used, this method applies to any periodic polyalphabetic substitution cipher.

We present a toy cipher that has two novel features: Two plaintexts are concealed by the same ciphertext in different schemes, and the enumeration of the permutations of ciphertext symbols (not the permutations of plaintext symbols, as used in transposition ciphers) forms the basis of one of the schemes. The other scheme uses mixed-radix numbers as substitutes for plaintext symbols. Both schemes use the same symbols, but with different interpretations, and this allows two plaintexts to be encrypted in the same ciphertext.

Protocols for secure multiparty computation (MPC) enable a set of parties to interact and compute a joint function of their private inputs while revealing nothing but the output. The potential applications for MPC are huge: privacy-preserving auctions, private DNA comparisons, private machine learning, threshold cryptography, and more. Due to this, MPC has been an intensive topic of research in academia ever since it was introduced in the 1980s by Yao for the two-party case (FOCS 1986), and by Goldreich, Micali and Wigderson for the multiparty case (STOC 1987). Recently, MPC has become efficient enough to be used in practice, and has made the transition from an object of theoretical study to a technology being used in industry. In this article, we will review what MPC is, what problems it solves, and how it is being currently used. We note that the examples and references brought in this review article are far from comprehensive, and due to the lack of space many highly relevant works are not cited.

State channels are an attractive layer-two solution for improving the throughput and latency of blockchains. They offer optimistic offchain settlement of payments and expedient offchain evolution of smart contracts between multiple parties without imposing any additional assumptions beyond those of the underlying blockchain. In the case of disputes, or if a party fails to respond, cryptographic evidence collected in the offchain channel is used to settle the last confirmed state onchain, such that in-progress contracts can be continued under mainchain consensus. A serious disadvantage present in current layer-two state channel protocols is that existing layer-one smart contract infrastructure and contract code cannot be reused offchain without change. In this paper, we introduce Hydra, an isomorphic multi-party state channel. Hydra simplifies offchain protocol and smart contract development by directly adopting the layer-one smart contract system, in this way allowing the same code to be used both on- and offchain. Taking advantage of the extended UTxO model, we develop a fast off-chain protocol for evolution of Hydra heads (our isomorphic state channels) that has smaller round complexity than all previous proposals and enables the state channel processing to advance on-demand, concurrently and asynchronously. We establish strong security properties for the protocol, and we present and evaluate extensive simulation results that demonstrate that Hydra approaches the physical limits of the network in terms of transaction confirmation time and throughput while keeping storage requirements at the lowest possible. Finally, our experimental methodology may be of independent interest in the general context of evaluating consensus protocols.

The NIST PQC standardization project evaluates multiple new designs for post-quantum Key Encapsulation Mechanisms (KEMs). Some of them present challenging tradeoffs between communication bandwidth and computational overheads. An interesting case is the set of QC-MDPC based KEMs. Here, schemes that use the Niederreiter framework require only half the communication bandwidth compared to schemes that use the McEliece framework. However, this requires costly polynomial inversion during the key generation, which is prohibitive when ephemeral keys are used. One example is BIKE, where the BIKE-1 variant uses McEliece and the BIKE-2 variant uses Niederreiter. This paper shows an optimized constant-time polynomial inversion method that makes the computation costs of BIKE-2 key generation tolerable. We report a speedup of 11.8x over the commonly used NTL library, and 55.5 over OpenSSL. We achieve additional speedups by leveraging the latest Intel's Vector-PCLMULQDQ instructions on a laptop machine, 14.3x over NTL and 96.8x over OpenSSL. With this, BIKE-2 becomes a competitive variant of BIKE.

Fixing a number field, the space of all ideal lattices, up to isometry, is naturally an Abelian group, called the *Arakelov class group*. This fact, well known to number theorists, has so far not been explicitly used in the literature on lattice-based cryptography. Remarkably, the Arakelov class group is a combination of two groups that have already led to significant cryptanalytic advances: the class group and the unit torus. In the present article, we show that the Arakelov class group has more to offer. We start with the development of a new versatile tool: we prove that, subject to the Riemann Hypothesis for Hecke $L$-functions, certain random walks on the Arakelov class group have a rapid mixing property. We then exploit this result to relate the average-case and the worst-case of the Shortest Vector Problem in ideal lattices. Our reduction appears particularly sharp: for Hermite-SVP in ideal lattices of certain cyclotomic number fields, it loses no more than a $\tilde O(\sqrt n)$ factor on the Hermite approximation factor. Furthermore, we suggest that this rapid-mixing theorem should find other applications in cryptography and in algorithmic number theory.

This work considers the security of systems that process encrypted multi-dimensional range queries with only access pattern leakage. Recent work of Kellaris et al. (CCS 2016) showed that in one dimension, an adversary could use the access patterns of several uniformly random range queries to reconstruct a plaintext column of numbers “up to reflection.” We extend this attack to two dimensions and find that the situation is much more complicated: Information theoretically it is complex to describe even what is possible to recover for the adversary in general. We provide a classification of these limits under certain technical conditions. We also give a faster algorithm that works for “dense” databases that contain at least one record for each possible value. Finally we explore the implications for our classification with real data sets.

In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (2018), when the starting function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for $n=8$ and produces fifteen new APN functions for $n=9$.

We revisit the problem of proving that a user algorithm selected and correctly used a truly random seed in the generation of her cryptographic key. A first approach was proposed in 2002 by Juels and Guajardo for the validation of RSA secret keys. We present a new security model and general tools to efficiently prove that a private key was generated at random according to a prescribed process, without revealing any further information about the private key. In addition to formalizing randomness verifiability in key generation, which turns out to be highly non-trivial, we give a generic protocol for all key-generation algorithms based on probabilistic circuits and prove its security. We also propose a new protocol for factoring-based cryptography that we prove secure in the aforementioned model, as well as a practical instantiation. This latter relies on a new efficient zero-knowledge argument for the double discrete logarithm problem that achieves an exponential improvement in communication complexity compared to the state of the art, and is of independent interest.

Anonymous Zether, proposed by Bünz, Agrawal, Zamani, and Boneh (FC'20), is a private payment design whose wallets demand little bandwidth and need not remain online; this unique property makes it a compelling choice for resource-constrained devices. In this work, we describe an efficient construction of Anonymous Zether. Our protocol features proofs which grow only logarithmically in the size of the "anonymity sets" used, improving upon the linear growth attained by prior efforts. It also features competitive transaction sizes in practice (on the order of 3 kilobytes). Our central tool is a new family of extensions to Groth and Kohlweiss's one-out-of-many proofs (Eurocrypt 2015), which efficiently prove statements about many messages among a list of commitments. These extensions prove knowledge of a secret subset of a public list, and assert that the commitments in the subset satisfy certain properties (expressed as linear equations). Remarkably, our communication remains logarithmic; our computation increases only by a logarithmic multiplicative factor. This technique is likely to be of independent interest. We present an open-source, Ethereum-based implementation of our Anonymous Zether construction.

We propose a framework for cryptanalysis of lattice-based schemes, when side information---in the form of ``hints''--- about the secret and/or error is available. Our framework generalizes the so-called primal lattice reduction attack, and allows the progressive integration of hints before running a final lattice reduction step. Our techniques for integrating hints include sparsifying the lattice, projecting onto and intersecting with hyperplanes, and/or altering the distribution of the secret vector. Our main contribution is to propose a toolbox and a methodology to integrate such hints into lattice reduction attacks and to predict the performance of those lattice attacks with side information. While initially designed for side-channel information, our framework can also be used in other cases: exploiting decryption failures, or simply exploiting constraints imposed by certain schemes (LAC, Round5, NTRU). We implement a Sage 9.0 toolkit to actually mount such attacks with hints when computationally feasible, and to predict their performances on larger instances. We provide several end-to-end application examples, such as an improvement of a single trace attack on Frodo by Bos et al (SAC 2018). In particular, our work can estimates security loss even given very little side information, leading to a smooth measurement/computation trade-off for side-channel attacks.

Defining unforgeability and designing cryptographic primitives that provide unforgeability in the quantum setting, i.e. where the adversary has quantum capabilities including quantum oracle access to the primitive, has proven to be a hard challenge. The classical notions and techniques do not transpose directly to the quantum setting. In this paper, we continue the line of work initiated by Boneh and Zhandry at CRYPTO 2013 and EUROCRYPT 2013 in which they formally define the notion of unforgeability against quantum adversaries specifically for Message Authentication Codes and Digital Signatures schemes. We develop a general and parameterized quantum game-based security framework for both classical and quantum primitives modelled by unitary transformations. We provide general possibility and impossibility results for such primitives. In particular, we show that no unitary primitive can provide existential unforgeability against quantum adversaries. Our main impossibility result relies on a new and generic quantum attack. We demonstrate this attack both on classical and quantum primitives to show its applicability as well as the completeness of our definitions of security. On the other hand, we show that selective unforgeability is satisfied by a specific class of unitaries that we term unknown unitaries.

We present attacks on 21-rounds of SIMON 32/64, 21-rounds of SIMON 48/96, 25-rounds of SIMON 64/128, 35-rounds of SIMON 96/144 and 43-rounds of SIMON 128/256, often with direct recovery of the full master key without repeating the attack over multiple rounds. These attacks result from the observation that, after four rounds of encryption, one bit of the left half of the state of 32/64 SIMON depends on only 17 key bits (19 key bits for the other variants of SIMON). Further, linear cryptanalysis requires the guessing of only 16 bits, the size of a single round key of SIMON 32/64. We partition the key into smaller strings by focusing on one bit of state at a time, decreasing the cost of the exhaustive search of linear cryptanalysis to 16 bits at a time for SIMON 32/64. We also present other example linear cryptanalysis, experimentally verified on 8, 10 and 12 rounds for SIMON 32/64.

Recent work using groups of unknown order to construct verifiable delay functions, polynomial commitment schemes and non interactive zero knowledge proofs have provoked fresh interest in the construction of efficient cryptographic groups of unknown order. It has been suggested that the Jacobian of hyperelliptic curves of genus 3 could be suitable for this purpose. Regrettably, efficient algorithms to compute the order of the Jacobian of a hyperelliptic curve are known. Concretely, it is unclear whether these groups are competitive with RSA groups or class groups at or above the 128 bit security level.

Light key schedule has found many applications in lightweight blockciphers, e.g. LED, PRINTcipher and LBlock. In this paper, we study an interesting question of how to design a as light as possible key schedule from the view of provable security and revisit the four-round key-alternating Feistel cipher by Guo and Wang in Asiacrypt 18. We optimize the construction by Guo and Wang and propose a four-round key-alternating Feistel cipher with an ultra-light (in fact non-existent) key schedule. We prove our construction retain the same security level as that of Guo and Wang's construction. To the best of our knowledge, this is the first provably secure key-alternating Feistel cipher using identical round function and one n-bit master key but with ultra-light (non-existent) key schedule. We also investigate whether the same refinement works for the three-round key-alternating Feistel cipher. This time we show a distinguishing attack on such three-round construction with only four encryption queries. On the positive side, we prove that three-round key-alternating Feistel cipher with a suitable key schedule is a pseudorandom permutation. This is also the first provable-security result for three-round key-alternating Feistel cipher.

This paper introduces a new cryptographic primitive called a private resource allocator (PRA) that can be used to allocate resources (e.g., network bandwidth, CPUs) to a set of clients without revealing to the clients whether any other clients received resources. We give several constructions of PRAs that provide guarantees ranging from information-theoretic to differential privacy. PRAs are useful in preventing a new class of attacks that we call allocation-based side-channel attacks. These attacks can be used, for example, to break the privacy guarantees of anonymous messaging systems that were designed specifically to defend against side-channel and traffic analysis attacks. Our implementation of PRAs in Alpenhorn, which is a recent anonymous messaging system, shows that PRAs increase the network resources required to start a conversation by up to 16X (can be made as low as 4X in some cases), but add no overhead once the conversation has been established.

We put forth a new framework for building pairing-based non-interactive zero- knowledge (NIZK) arguments for a wide class of algebraic languages, which are an extension of linear languages, containing disjunctions of linear languages and more. Our approach differs from the Groth-Sahai methodology, in that we rely on pairings to compile a $\Sigma$-protocol into a NIZK. Our framework enjoys a number of interesting features: – conceptual simplicity, parameters derive from the $\Sigma$-protocol; – proofs as short as resulting from the Fiat-Shamir heuristic applied to the underlying $\Sigma$-protocol; – fully adaptive soundness and perfect zero-knowledge in the common random string model with a single random group element as CRS; – yields simple and efficient two-round, public coin, publicly-verifiable perfect witness-indistinguishable (WI) arguments (ZAPs) in the plain model. To our knowledge, this is the first construction of two-rounds statistical witness-indistinguishable arguments from pairing assumptions. Our proof system relies on a new (static, falsifiable) assumption over pairing groups which generalizes the standard kernel Diffie-Hellman assumption in a natural way and holds in the generic group model (GGM) and in the algebraic group model (AGM). Replacing Groth-Sahai NIZKs with our new proof system allows to improve several important cryptographic primitives. In particular, we obtain the shortest tightly-secure structure-preserving signature scheme (which are a core component in anonymous credentials), the shortest tightly-secure quasi-adaptive NIZK with unbounded simulation soundness (which in turns implies the shortest tightly-mCCA-secure cryptosystem), and shorter ring signatures.

We revisit the security of various generalized Feistel networks. Concretely, for unbalanced, alternating, type-1, type-2, and type-3 Feistel networks built from random functions, we substantially improve the coupling analyzes of Hoang and Rogaway (CRYPTO 2010). For a tweakable blockcipher-based generalized Feistel network proposed by Coron et al. (TCC 2010), we present a coupling analysis and for the first time show that with enough rounds, it achieves 2n-bit security, and this provides highly secure, double-length tweakable blockciphers.

Access and search pattern leakage have been shown to be detrimental to the security of encrypted databases that allow for range queries, as shown by an extensive body of work on efficient attacks that reconstruct one-dimensional databases. We are the first to go beyond one dimension, exploring the threat of access and search pattern leakage in two dimensions. First, we unveil an intrinsic limitation of reconstruction attacks by showing that there can be an exponential number of distinct databases that produce the same access and search pattern leakage. Next, we present attacks that reconstruct (1) the horizontal and vertical order of the points from the access pattern leakage, and (2) the coordinates of the points from the access and search pattern leakage. Our algorithms run in polynomial time and return a linear-size encoding of all databases consistent with the given leakage profile.

In this paper, we put forth the problem of bequeathing cryptoassets. In this problem, a testator wishes to bequeath cryptoassets - e.g. secrets, static keys or cryptocurrency - to their heirs. Crucially, the testator should retain control of their assets before their passing. Additionally testator needs to maintain privacy, i.e. beneficiaries must not learn the bequest, moreover, beneficiaries must not be able to determine whether they will inherit at all before testator's decease. We formally define the security goals of a cryptographic will (cryptowill) protocol and subsequently present schemes fulfilling the required security properties.

We revisit recent works by Don, Fehr, Majenz and Schaffner and by Liu and Zhandry on the security of the Fiat-Shamir transformation of $\Sigma$-protocols in the quantum random oracle model (QROM). Two natural questions that arise in this context are: (1) whether the results extend to the Fiat-Shamir transformation of *multi-round* interactive proofs, and (2) whether Don et al.'s $O(q^2)$ loss in security is optimal. Firstly, we answer question (1) in the affirmative. As a byproduct of solving a technical difficulty in proving this result, we slightly improve the result of Don et al., equipping it with a cleaner bound and an even simpler proof. We apply our result to digital signature schemes showing that it can be used to prove strong security for schemes like MQDSS in the QROM. As another application we prove QROM-security of a non-interactive OR proof by Liu, Wei and Wong. As for question (2), we show via a Grover-search based attack that Don et al.'s quadratic security loss for the Fiat-Shamir transformation of $\Sigma$-protocols is optimal up to a small constant factor. This extends to our new multi-round result, proving it tight up to a factor that depends on the number of rounds only, i.e. is constant for any constant-round interactive proof.

Keeping cryptocurrency spending keys safe and being able to use them when signing a transaction is a well-known problem, addressed by hardware wallets. Our work focuses on a transaction signing process for privacy-centric cryptocurrency Monero, in the hardware wallets. We designed, implemented, and analyzed a privacy-preserving transaction signing protocol that runs on a hardware wallet and protects the spending keys. Moreover, we also implemented a privacy-preserving multi-party version of the Bulletproof zero-knowledge prover algorithm, which runs on a hardware wallet with constant memory. We present the protocols and evaluate their performance on a real hardware wallet.

In this work we study the leakage resilience of authenticated encryption schemes. We show that, if one settles for non-adaptive leakage, leakage-resilient authenticated encryption schemes can be built solely from leakage-resilient pseudorandom functions. Degabriele et al. (ASIACRYPT 2019) introduce the FGHF' construction which allows to build leakage-resilient authenticated encryption schemes from functions which, under leakage, retain both pseudorandomness and unpredictability. We revisit their construction and show the following. First, pseudorandomness and unpredictability do not imply one another in the leakage setting. Unfortunately, this entails that any instantiation of the FGHF' construction indeed seems to require a function that is proven both pseudorandom and unpredictable under leakage. Second, however, we show that the unpredictability requirement is an artefact that stems from the underlying composition theorem of the N2 construction given by Barwell et al. (ASIACRYPT 2017). By recasting this composition theorem, we show that the unpredictability requirement is unnecessary for the FGHF' construction. Thus, leakage-resilient AEAD schemes can be obtained by instantiating the FGHF' construction with functions that are solely pseudorandom under leakage.

Authenticated Encryption has emerged as a high-performance and resource-efficient solution to achieve message authentication in addition to encryption. This has motivated extensive study of algorithms for Authenticated Encryption with Associated Data (AEAD). While there have been significant efforts to benchmark these algorithms on hardware and software platforms, very little work has focused on the integration of these ciphers onto a System-on-Chip (SoC). This work looks at design alternatives for the SoC integration of few of the finalists of the Competition for Authenticated Encryption: Security, Applicability, and Robustness (CAESAR). We highlight the penalty on area and performance that is incurred during SoC integration, and analyze the impact of design choices on the same. Our observations indicate that integration onto a system significantly affects the lightweight and high-performance properties of these ciphers, and achieving a trade-off requires careful design decisions.

The last few years have witnessed increasing interest in the deployment of zero-knowledge proof systems, in particular ones with succinct proofs and efficient verification (zk-SNARKs). One of the main challenges facing the wide deployment of zk-SNARKs is the requirement of a trusted key generation phase per different computation to achieve practical proving performance. Existing zero-knowledge proof systems that do not require trusted setup or have a single trusted preprocessing phase suffer from increased proof size and/or additional verification overhead. On the other other hand, although universal circuit generators for zk-SNARKs (that can eliminate the need for per-computation preprocessing) have been introduced in the literature, the performance of the prover remains far from practical for real-world applications. In this paper, we first present a new zk-SNARK system that is well-suited for randomized algorithms---in particular it does not encode randomness generation within the arithmetic circuit allowing for more practical prover times. Then, we design a universal circuit that takes as input any arithmetic circuit of a bounded number of operations as well as a possible value assignment, and performs randomized checks to verify consistency. Our universal circuit is linear in the number of operations instead of quasi-linear like other universal circuits. By applying our new zk-SNARK system to our universal circuit, we build MIRAGE, a universal zk-SNARK with very succinct proofs---the proof contains just one additional element compared to the per-circuit preprocessing state-of-the-art zk-SNARK by Groth (Eurocrypt 2016). Finally, we implement MIRAGE and experimentally evaluate its performance for different circuits and in the context of privacy-preserving smart contracts.

Nakamoto consensus, arguably the most exciting development in decentralized computation in the last few years, is in a sense a recasting of the traditional state machine replication problem in an unauthenticated setting, where furthermore parties come and go without warning. The protocol relies on a cryptographic primitive known as proof of work (PoW) which is used to throttle message passing. Importantly, the PoW difficulty level is appropriately adjusted throughout the course of the protocol execution relying on the blockchain’s timekeeping ability. While the original formulation was only accompanied by rudimentary analysis, significant and steady progress has been made in abstracting the protocol’s properties and providing a formal analysis under various restrictions and protocol simplifications. Still, a full analysis of the protocol that includes its PoW target value recalculation and, notably, its timestamp adjustment mechanism, which equip it to operate in its intended setting of bounded communication delays, imperfect clocks and dynamic participation, has remained open. (Specifically, the protocol allows incoming block timestamps in the near future, as determined by a protocol parameter, and rejects blocks that have a timestamp in the past of the median time of a specific number of blocks on-chain [namely, 11].) The gap is that Nakamoto’s protocol fundamentally depends on the blockchain itself to be a consistent timekeeper that should advance roughly on par with real time. In order to tackle this question we introduce a new analytical tool we call `hot-hand executions,' which capture the regular occurrence of high concentration of honestly generated blocks, and correspondingly put forth and prove a new blockchain property called `concentrated chain quality,' which may be of independent interest. Utilizing these tools and techniques we demonstrate that Nakamoto’s protocol achieves, under suitable conditions, consistency, liveness as well as (consistent) timekeeping.

Quantum computers promise to solve hard mathematical problems such as integer factorization and discrete logarithms in polynomial time, making standardized public-key cryptography (such as digital signature and key agreement) insecure. Lattice-Based Cryptography (LBC) is a promising post-quantum public-key cryptographic protocol that could replace standardized public-key cryptography, thanks to the inherent post-quantum resistant properties, efficiency, and versatility. A key mathematical tool in LBC is the Number Theoretic Transform (NTT), a common method to compute polynomial multiplication that is the most compute-intensive routine, and which requires acceleration for practical deployment of LBC protocols. In this paper, we propose, a high-throughput Processing In-Memory (PIM) accelerator for NTT-based polynomial multiplier with the support of polynomials with degrees up to 32k. Compared to the fastest FPGA implementation of an NTT-based multiplier, achieves on average 31x throughput improvement with the same energy and only 28% performance reduction, thereby showing promise for practical deployment of LBC.

With the dawn of quantum computers, higher security than $128$ bits has become desirable for primitives and modes. During the past decade, highly secure hash functions, MACs, and encryption schemes have been built primarily on top of keyless permutations, which simplified their analyses and implementation due to the absence of a key schedule. However, the security of these modes is most often limited to the birthday bound of the state size, and their analysis may require a different security model than the easier-to-handle secret-permutation setting. Yet, larger state and key sizes are desirable not only for permutations but also for other primitives such as block ciphers. Using the additional public input of tweakable block ciphers for domain separation allows for exceptionally high security or performance as recently proposed modes have shown. Therefore, it appears natural to ask for such designs. While security is fundamental for cryptographic primitives, performance is of similar relevance. Since 2009, processor-integrated instructions have allowed high throughput for the AES round function, which already motivated various constructions based on it. Moreover, the four-fold vectorization of the AES instruction sets in Intel's Ice Lake architecture is yet another leap in terms of performance and gives rise to exploit the AES round function for even more efficient designs. This work tries to combine all aspects above into a primitive and to build upon years of existing analysis on its components. We propose Pholkos, a family of (1) highly efficient, (2) highly secure, and (3) tweakable block ciphers. Pholkos is no novel round-function design, but utilizes the AES round function, following design ideas of Haraka and AESQ to profit from earlier analysis results. It extends them to build a family of primitives with state and key sizes of $256$ and $512$ bits for flexible applications, providing high security at high performance. Moreover, we propose its usage with a $128$-bit tweak to instantiate high-security encryption and authentication schemes such as SCT, ThetaCB3, or ZAE. We study its resistance against the common attack vectors, including differential, linear, and integral distinguishers using a MILP-based approach and show an isomorphism from the AES to Pholkos-$512$ for bounding impossible-differential, or exchange distinguishers from the AES. Our proposals encrypt at around $1$--$2$ cycles per byte on Skylake processors, while supporting a much more general application range and considerably higher security guarantees than comparable primitives and modes such as PAEQ/AESQ, AEGIS, Tiaoxin346, or Simpira.

Recently, Kamara and Moataz described the first encrypted relational database solution with support for a non-trivial fraction of SQL that does not make use of property-preserving encryption (Asiacrypt, 2018). More precisely, their construction, called SPX, handles the set of conjunctive SQL queries. While SPX was shown to be optimal for the subset of uncorrelated conjunctive SQL queries, it did not handle correlated queries optimally. Furthermore, it only handles queries in heuristic normal form. In this work, we address these limitations by proposing an extension of SPX that handles all conjunctive SQL queries optimally no matter what form they are in.

Motivated by the impact of fast algebraic attacks on stream ciphers, and recent constructions using a threshold function as part of the filtering function, we study the fast algebraic immunity of threshold functions. As a first result, we determine exactly the fast algebraic immunity of all majority functions in more than $8$ variables. Then, For all $n\geq 8$ and all threshold value between $1$ and $n$ we exhibit the fast algebraic immunity for most of the thresholds, and we determine a small range for the value related to the few remaining cases. Finally, provided $m\geq 2$, we determine exactly the fast algebraic immunity of all threshold functions in $3\cdot 2^m$ or $3\cdot 2^m +1$ variables.

Privacy and machine learning are difficult to coexist due to their nature: parivacy should be kept from others while machine learning requires large amount of data. Among several possible solutions to this problem, Fully Homomorphic Encryption has been a center of intensive researches in this field. FHE enables linear operations of ciphertext. To take advantage of this property, many protocols to achieve statistical operaions have been proposed. On the other hand, many of them are impractical. Some of the approaches introduce cryptosystems that are not familiar. Moreover, most of their protocols are approximation which might sensitively depend on our choice of parameters. In this paper, we propose fast, simple, and exact privacy-preserving linear equation solver using FHE. Our two-party protocol is secure against at least semi-honest model, and we can exactly calculate the model even without the bootstrapping.

OR-proofs enable a prover to show that it knows the witness for one of many statements, or that one out of many statements is true. OR-proofs are a remarkably versatile tool, used to strengthen security properties, design group and ring signature schemes, and achieve tight security. The common technique to build OR-proofs is based on an approach introduced by Cramer, Damgård, and Schoenmakers (CRYPTO’94), where the prover splits the verifier’s challenge into random shares and computes proofs for each statement in parallel. In this work we study a different, less investigated OR-proof technique, put forward by Abe, Ohkubo, and Suzuki (ASIACRYPT’02). The difference is that the prover now computes the individual proofs sequentially. We show that such sequential OR-proofs yield signature schemes which can be proved secure in the non-programmable random oracle model. We complement this positive result with a black-box impossibility proof, showing that the same is unlikely to be the case for signatures derived from traditional OR-proofs. We finally argue that sequential-OR signature schemes can be proved secure in the quantum random oracle model, albeit with very loose bounds and by programming the random oracle.

Inner product encryption is a powerful cryptographic primitive, where a private key and a ciphertext are both associated with a predicate vector and an attribute vector, respectively. A successful decryption requires the inner product of the predicate vector and the attribute vector to be zero. Most of the existing inner product encryption schemes suffer either long private key or heavy decryption cost. In this manuscript, an efficient inner product encryption is proposed. The length for a private key is only an element in $\mathbb{G}$ and an element in $\mathbb{Z}_p$. Besides, only one pairing computation is needed for decryption. Moreover, both formal security proof and implementation result are demonstrated in this manuscript. To the best of our knowledge, our scheme is the most efficient one in terms of the private key length and the number of pairings computation for decryption.

Decades of research in both cryptography and distributed systems has extensively studied the problem of state machine replication, also known as Byzantine consensus. A consensus protocol must satisfy two properties: consistency and liveness. These properties ensure that honest participating nodes agree on the same log and dictate when fresh transactions get added. They fail, however, to ensure against adversarial manipulation of the actual ordering of transactions in the log. Indeed, in leader-based protocols (almost all protocols used today), malicious leaders can directly choose the final transaction ordering. To rectify this problem, we propose a third consensus property: transaction order-fairness. We initiate the first formal investigation of order-fairness and explain its fundamental importance. We provide several natural definitions for order-fairness and analyze the assumptions necessary to realize them. We also propose a new class of consensus protocols called Aequitas. Aequitas protocols are the first to achieve order-fairness in addition to consistency and liveness. They can be realized in a black-box way using existing broadcast and agreement primitives (or indeed using any consensus protocol), and work in both synchronous and asynchronous network models.

Since the introduction of the ring-learning with errors problem, the number theoretic transform (NTT) based polynomial multiplication algorithm has been studied extensively. Due to its faster quasilinear time complexity, it has been the preferred choice of cryptographers to realize ring-learning with errors cryptographic schemes. Compared to NTT, Toom-Cook or Karatsuba based polynomial multiplication algorithms, though being known for a long time, still have a fledgling presence in the context of post-quantum cryptography. In this work, we observe that the pre- and post-processing steps in Toom-Cook based multiplications can be expressed as linear transformations. Based on this observation we propose two novel techniques that can increase the efficiency of Toom-Cook based polynomial multiplications. Evaluation is reduced by a factor of 2, and we call this method precomputation, and interpolation is reduced from quadratic to linear, and we call this method lazy interpolation. As a practical application, we applied our algorithms to the Saber post-quantum key-encapsulation mechanism. We discuss in detail the various implementation aspects of applying our algorithms to Saber. We show that our algorithm can improve the efficiency of the computationally costly matrix-vector multiplication by12&#8722;37%compared to previous methods on their respective platforms. Secondly, we propose different methods to reduce the memory footprint of Saber for Cortex-M4microcontrollers. Our implementation shows between2.6 and 5.7KB reduction in memory usage with respect to the smallest implementation in the literature.

This work introduces the first differential side-channel analysis of the Picnic Signature Scheme, an alternate candidate in the ongoing competition for post-quantum cryptography by the National Institute of Standards and Technology (NIST). We present a successful side-channel analysis of the underlying multiparty implementation of the LowMC block cipher (MPC-LowMC) and show how side-channel information can be used to recover the entire secret key by exploiting two different parts of the algorithm. LowMC key recovery then allows to forge signatures for the calling Picnic post-quantum signature scheme. We target the NIST reference implementation executed on a FRDM-K66F development board. Key recovery succeeds with fewer than 1000 LowMC traces, which can be obtained from fewer than 30 observed Picnic signatures.

In this work we study the quantum security of public key encryption schemes (PKE). Boneh and Zhandry (CRYPTO'13) initiated this research area for PKE and symmetric key encryption (SKE), albeit restricted to a classical indistinguishability phase. Gagliardoni et al. (CRYPTO'16) advanced the study of quantum security by giving, for SKE, the first definition with a quantum indistinguishability phase. For PKE, on the other hand, no notion of quantum security with a quantum indistinguishability phase exists. Our main result is a novel quantum security notion (qIND-qCPA) for PKE with a quantum indistinguishability phase, which closes the aforementioned gap. We show a distinguishing attack against code-based schemes and against LWE-based schemes with certain parameters. We also show that the canonical hybrid PKE-SKE encryption construction is qIND-qCPA-secure, even if the underlying PKE scheme by itself is not. Finally, we classify quantum-resistant PKE schemes based on the applicability of our security notion. Our core idea follows the approach of Gagliardoni et al. by using so-called type-2 operators for encrypting the challenge message. At first glance, type-2 operators appear unnatural for PKE, as the canonical way of building them requires both the secret and the public key. However, we identify a class of PKE schemes - which we call recoverable - and show that for this class type-2 operators require merely the public key. Moreover, recoverable schemes allow to realise type-2 operators even if they suffer from decryption failures, which in general thwarts the reversibility mandated by type-2 operators. Our work reveals that many real-world quantum-resistant PKE schemes, including most NIST PQC candidates and the canonical hybrid construction, are indeed recoverable.

Non-interactive zero-knowledge proofs (NIZKs) are important primitives in cryptography. A major challenge since the early works on NIZKs has been to construct NIZKs with a statistical zero-knowledge guarantee against unbounded verifiers. In the common reference string (CRS) model, such "statistical NIZK arguments" are currently known from k-Lin in a pairing-group and from LWE. In the (reusable) designated-verifier model (DV-NIZK), where a trusted setup algorithm generates a reusable verification key for checking proofs, we also have a construction from DCR. If we relax our requirements to computational zero-knowledge, we additionally have NIZKs from factoring and CDH in a pairing group in the CRS model, and from nearly all assumptions that imply public-key encryption (e.g., CDH, LPN, LWE) in the designated-verifier model. Thus, there still remains a gap in our understanding of statistical NIZKs in both the CRS and the designated-verifier models. In this work, we develop new techniques for constructing statistical NIZK arguments. First, we construct statistical DV-NIZK arguments from the k-Lin assumption in pairing-free groups, the QR assumption, and the DCR assumption. These are the first constructions in pairing-free groups and from QR that satisfy statistical zero-knowledge. All of our constructions are secure even if the verification key is chosen maliciously (i.e., they are "malicious-designated-verifier" NIZKs), and moreover, they satisfy a "dual-mode" property where the CRS can be sampled from two computationally indistinguishable distributions: one distribution yields statistical DV-NIZK arguments while the other yields computational DV-NIZK proofs. We then show how to adapt our k-Lin construction in a pairing group to obtain new publicly-verifiable statistical NIZK arguments from pairings with a qualitatively weaker assumption than existing constructions of pairing-based statistical NIZKs. Our constructions follow the classic paradigm of Feige, Lapidot, and Shamir (FLS). While the FLS framework has traditionally been used to construct computational (DV)-NIZK proofs, we newly show that the same framework can be leveraged to construct dual-mode (DV)-NIZKs.

Homomorphic encryption primitives have the potential to be the main enabler of privacy preserving computation delegation to cloud environments. One of the avenues which has been explored to reduce their significant computational overhead with respect to cleartext computation is the one of the so-called noise-free homomorphic encryption schemes. In this work, we present an attack against fully homomorphic encryption primitives where a distinguisher for a single plaintext value exists. We employ two noise-free homomorphic encryption schemes where such a property holds as our case studies, providing detailed attack procedure against them. We validate the effectiveness and performance of our attacks on prototype implementations of the said schemes, and suggest two countermeasures to our attack tailored to the schemes at hand.

In this work, we propose a new table-based block cipher structure, dubbed $\mathsf{FPL}$, that can be used to build white-box secure block ciphers. Our construction is a balanced Feistel cipher, where the input to each round function determines multiple indices for the underlying table via a probe function, and the sum of the values from the table becomes the output of the round function. We identify the properties of the probe function that make the resulting block cipher white-box secure in terms of weak and strong space hardness against known-space and non-adaptive chosen-space attacks. Our construction, enjoying rigorous provable security without relying on any ideal primitive, provides flexibility to the block size and the table size, and permits parallel table look-ups. We also propose a concrete instantiation of $\mathsf{FPL}$, dubbed $\mathsf{FPL}_{\mathsf{AES}}$, using (round-reduced) $\mathsf{AES}$ for the underlying table and probe functions. Our implementation shows that $\mathsf{FPL}_{\mathsf{AES}}$ provides stronger security without significant loss of efficiency, compared to existing schemes including $\mathsf{SPACE}$, $\mathsf{WhiteBlock}$ and $\mathsf{WEM}$.

It has been suspected that in supersingular isogeny-based cryptosystems the two ending elliptic curves computed by the participants are exactly equal. Resolving this open problem has not been pressing because the elliptic curves are known to be isomorphic, and therefore share a $j$-invariant which can be used as a shared secret. However, this is still an interesting independent problem as other values of the elliptic curves may be valuable as shared information as well. This note answers this open problem in the affirmative.

This paper presents Foxtail+, a new shared-key protocol to securely authenticate resource constrained devices, such as Internet of things (IoT) devices. Foxtail+ is based on a previously proposed protocol to authenticate unaided humans, called the Foxtail protocol, which we modify for authenticating resource constrained devices. It uses a computationally lightweight function, called the Foxtail function, which makes it ideal for IoT nodes with low memory, computational, and/or battery resources. We introduce a new family of functions based on the Foxtail function, analyze its security in terms of the number of samples required to obtain the secret, and demonstrate how it is connected with the learning with rounding (LWR) problem. We then build the Foxtail+ protocol from this function family, secure against active adversaries. Finally, we implement and experimentally evaluate the performance of Foxtail+ against a similar alternate protocol, i.e., the modified version of the Hopper and Blum protocol called HB+, and a block cipher based protocol instantiated with AES. The experiments are run on an IoT device connected to a LoRa network which is an IoT specific Low-Power Wide-Area Network (LPWAN). We show that Foxtail+ outperforms HB+ in terms of overall communication and energy cost, and its parallel implementation is comparable to the AES-based protocol in terms of time and energy consumption. To our knowledge, we provide the first implementation of any member of the HB+ family of protocols that directly compares its performance against an AES-based protocol in terms of time and power consumption. Our experiments shed new light on some of the limitations of identification protocols based on lightweight primitives, of which Foxtail+ is a member, over block cipher based protocols.

We present in this paper a blind signature and its partially blind variant based on lattices assumptions. Blind signature is a cornerstone in privacy-oriented cryptography and we propose the first lattice based scheme without restart. Compare to related work, the key idea of our construction is to provide a trapdoor to the signer in order to let him perform some gaussian pre-sampling during the signature generation process, preventing this way to restart from scratch the whole protocol. We prove the security of our scheme under the ring k-SIS assumption, in the random oracle model. We also explain security issues in the other existing lattice-based blind signature schemes. Finally, we propose a partially blind variant of our scheme, which is done with no supplementary cost, as the number of elements generated and exchanged during the signing protocol is exactly the same.

Two-source non-malleable extractors are pseudorandom objects which extract randomness even when an adversary is allowed to learn the behavior of the extractor on tamperings of the input weak sources, and they have found important applications in non-malleable coding and secret sharing. We begin by asking how hard it is to improve upon the best known constructions of such objects (Chattopadhyay, Goyal, Li, STOC 2016, and Li, STOC 2017). We show that even small improvements to these constructions lead to explicit low-error two-source extractors for very low linear min-entropy, a longstanding open problem in pseudorandomness. Given the result above in the information-theoretic setting, we turn to studying two-source non-malleable extractors in the computational setting, namely in the CRS model first considered in (Garg, Kalai, Khurana, Eurocrypt 2020). We enforce that both the sampling process for the input sources and the tampering functions must be efficient, but we do not necessarily put such a constraint on the adversary distinguishing the output of the extractor from uniform. We obtain results about two-source non-malleable extractors in the CRS model under different types of hardness assumptions: - Under standard assumptions, we show that small improvements upon state-of-the-art statistical two-source non-malleable extractors also yield explicit low-error two-source non-malleable extractors in the CRS model for low min-entropy against computationally unbounded distinguishers. Remarkably, all previous results on computational extractors require much stronger assumptions; - Under a quasi-polynomial hardness assumption, we give explicit constructions of low-error two-source non-malleable extractors in the CRS model with much lower min-entropy requirements than their best statistical counterparts, against a computationally bounded distinguisher; - Assuming the existence of nearly optimal collision-resistant hash functions, we give a simple explicit construction of a low-error two-source non-malleable extractors in the CRS model for very low min-entropy, against a computationally unbounded distinguisher.

We present new non-interactive zero-knowledge argument systems (NIZK), based on standard assumptions that were previously not known to imply it. In particular, we rely on the hardness of both the learning parity with noise (LPN) assumption, and the existence of trapdoor hash functions (TDH, defined by Döttling et al., Crypto 2019). Such TDH can be based on a number of standard assumptions, including DDH, QR, DCR, and LWE. We revisit the correlation intractability (CI) framework for converting $\Sigma$-protocols into NIZK, and present a different strategy for instantiating it by putting together two new components. First, while prior works considered the search-complexity of the relations for which CI is sought,we consider their probabilistic representation. Namely, a distribution over lower-complexity functions that bitwise-computes the target function with all but small (constant) probability. The second component is a new perspective for quantifying the class of relations for which CI is achieved. We show that it is instructive to consider CI for approximable relations (CI-Apx) which is quantified by a class of relations, but requires CI to hold against any approximation of any relation in this class. We show that CI-Apx for just constant-degree polynomials suffices for NIZK, if the under-lying $\Sigma$-protocol is implemented using a suitable commitment scheme. We show that such a commitment scheme can be constructed based on LPN. We then show how to construct CI-Apx for constant-degree polynomials from any suitable TDH (with an enhanced correctness property that is satisfied by all existing TDH constructions).

The problem of secret-key based authentication under privacy and storage constraints on the source sequence is considered. The identifier measurement channels during authentication are assumed to be controllable via a cost-constrained action sequence. Single-letter inner and outer bounds for the key-leakage-storage-cost regions are derived for a generalization of a classic two-terminal key agreement model with an eavesdropper that observes a sequence that is correlated with the sequences observed by the legitimate terminals. The additions to the model are that the encoder observes a noisy version of a remote source, and the noisy output and the remote source output together with an action sequence are given as inputs to the measurement channel at the decoder. Thus, correlation is introduced between the noise components on the encoder and decoder measurements. The model with a secret-key generated by an encoder is extended to the randomized models, where a secret-key is embedded to the encoder. The results are relevant for several user and device authentication scenarios including physical and biometric identifiers with multiple measurements that provide diversity and multiplexing gains. To illustrate the behavior of the rate region, achievable (secret-key rate, storage-rate, cost) tuples are given for binary identifiers and measurement channels that can be represented as a set of binary symmetric subchannels. The gains from using an action sequence such as a large secret-key rate at a significantly small hardware cost, are illustrated to motivate the use of low-complexity transform-coding algorithms with cost-constrained actions.

Dwork and Naor (FOCS '00) defined ZAPs as 2-message witness-indistinguishable proofs that are public-coin. We relax this to ``ZAPs with private randomness'' (ZAPRs), where the verifier can use private coins to sample the first message (independently of the statement being proved), but the proof must remain publicly verifiable given only the protocol transcript. In particular, ZAPRs are reusable, meaning that the first message can be reused for multiple proofs without compromising security. Known constructions of ZAPs from trapdoor permutations or bilinear maps are only computationally WI (and statistically sound). Two recent results of Badrinarayanan-Fernando-Jain-Khurana-Sahai and Goyal-Jain-Jin-Malavolta [EUROCRYPT '20] construct the first statistical ZAP arguments, which are statistically WI (and computationally sound), from the quasi-polynomial LWE assumption. Here, we construct statistical ZAPR arguments from the quasi-polynomial decision-linear (DLIN) assumption on groups with a bilinear map. Our construction relies on a combination of several tools, including the Groth-Ostrovsky-Sahai NIZK and NIWI [EUROCRYPT '06, CRYPTO '06, JACM '12], ``sometimes-binding statistically hiding commitments'' [Kalai-Khurana-Sahai, EUROCRYPT '18] and the ``MPC-in-the-head'' technique [Ishai-Kushilevitz-Ostrovsky-Sahai, STOC '07].

To maintain the availability of industrial control systems (ICS), it is important to robustly detect malware infection that spreads within the ICS network. In ICS, a host often communicates with the determined hosts; for instance, a supervisory control host observes and controls the same devices routinely via the network. Therefore, a communication request to the unused internet protocol (IP) address space, i.e. darknet, in the ICS network is likely to be caused by malware in the compromised host in the network. That is, darknet monitoring may enable us to detect malware that tries to spread indiscriminately within the network. On the other hand, advanced malware, such as malware determining target hosts of infection with reference to host lists in the networks, infects the confined hosts in the networks, and consequently evades detection by security sensors or honeypots. In this paper, we propose novel deception techniques that lure such malware to our sensor, by embedding the sensor information continuously in the lists of hosts in the ICS networks. In addition, the feasibility of the proposed deception techniques is shown through our simplified implementation by using actual malware samples: WannaCry and Conficker.

The right of an individual to request the deletion of their personal data by an entity that might be storing it -- referred to as the right to be forgotten -- has been explicitly recognized, legislated, and exercised in several jurisdictions across the world, including the European Union, Argentina, and California. However, much of the discussion surrounding this right offers only an intuitive notion of what it means for it to be fulfilled -- of what it means for such personal data to be deleted. In this work, we provide a formal definitional framework for the right to be forgotten using tools and paradigms from cryptography. In particular, we provide a precise definition of what could be (or should be) expected from an entity that collects individuals' data when a request is made of it to delete some of this data. Our framework captures several, though not all, relevant aspects of typical systems involved in data processing. While it cannot be viewed as expressing the statements of current laws (especially since these are rather vague in this respect), our work offers technically precise definitions that represent possibilities for what the law could reasonably expect, and alternatives for what future versions of the law could explicitly require. Finally, with the goal of demonstrating the applicability of our framework and definitions, we consider various natural and simple scenarios where the right to be forgotten comes up. For each of these scenarios, we highlight the pitfalls that arise even in genuine attempts at implementing systems offering deletion guarantees, and also describe technological solutions that provably satisfy our definitions. These solutions bring together techniques built by various communities.

A two-party fair coin-tossing protocol guarantees output delivery to the honest party even when the other party aborts during the protocol execution. Cleve (STOC--1986) demonstrated that a computationally bounded fail-stop adversary could alter the output distribution of the honest party by (roughly) $1/r$ (in the statistical distance) in an $r$-message coin-tossing protocol. An optimal fair coin-tossing protocol ensures that no adversary can alter the output distribution beyond $1/r$. In a seminal result, Moran, Naor, and Segev (TCC--2009) constructed the first optimal fair coin-tossing protocol using (unfair) oblivious transfer protocols. Whether the existence of oblivious transfer protocols is a necessary hardness of computation assumption for optimal fair coin-tossing remains among the most fundamental open problems in theoretical cryptography. The results of Impagliazzo and Luby (FOCS–1989) and Cleve and Impagliazzo (1993) prove that optimal fair coin-tossing implies the necessity of one-way functions' existence; a significantly weaker hardness of computation assumption compared to the existence of secure oblivious transfer protocols. However, the sufficiency of the existence of one-way functions is not known. Towards this research endeavor, our work proves a black-box separation of optimal fair coin-tossing from the existence of one-way functions. That is, the black-box use of one-way functions cannot enable optimal fair coin-tossing. Following the standard Impagliazzo and Rudich (STOC--1989) approach of proving black-box separations, our work considers any $r$-message fair coin-tossing protocol in the random oracle model where the parties have unbounded computational power. We demonstrate a fail-stop attack strategy for one of the parties to alter the honest party's output distribution by $1/\sqrt r$ by making polynomially-many additional queries to the random oracle. As a consequence, our result proves that the $r$-message coin-tossing protocol of Blum (COMPCON--1982) and Cleve (STOC--1986), which uses one-way functions in a black-box manner, is the best possible protocol because an adversary cannot change the honest party's output distribution by more than $1/\sqrt r$. Several previous works, for example, Dachman--Soled, Lindell, Mahmoody, and Malkin (TCC--2011), Haitner, Omri, and Zarosim (TCC--2013), and Dachman--Soled, Mahmoody, and Malkin (TCC--2014), made partial progress on proving this black-box separation assuming some restrictions on the coin-tossing protocol. Our work diverges significantly from these previous approaches to prove this black-box separation in its full generality. The starting point is the recently introduced potential-based inductive proof techniques for demonstrating large gaps in martingales in the information-theoretic plain model. Our technical contribution lies in identifying a global invariant of communication protocols in the random oracle model that enables the extension of this technique to the random oracle model.

A natural solution to increase the efficiency of secure computation will be to non-interactively and securely transform diverse inexpensive-to-generate correlated randomness, like, joint samples from noise sources, into correlations useful for the secure computation while incurring low computational overhead. Motivated by this general application for secure computation, our work introduces the notion of \textit{secure non-interactive simulation} (SNIS). Parties receive samples of correlated randomness, and they, without any interaction, securely convert them into samples from another correlated randomness. SNIS is an extension of \textit{non-interactive simulation of joint distributions} (NIS), and \textit{non-interactive correlation distillation} (NICD) to the cryptographic context. It is a non-interactive version of \textit{one-way secure computation} (OWSC). Our work presents a simulation-based security definition for SNIS and initiates the study of the feasibility and efficiency of SNIS. We also study SNIS among fundamental correlated randomnesses like random samples from the binary symmetric and binary erasure channels, represented by BSS and BES, respectively. The impossibility of realizing a BES sample from BSS samples in NIS and OWSC extends to SNIS. Additionally, we prove that a SNIS of BSS sample from BES samples is impossible, which remains an open problem in NIS and OWSC. Next, we prove that a SNIS of a BES$(\varepsilon')$ sample (a BES with noise characteristic $\varepsilon'$) from BES$(\varepsilon)$ is feasible if and only if $(1-\varepsilon')=(1-\varepsilon)^k$, for some $k\in N$. In this context, we prove that all SNIS constructions must be linear. Furthermore, if $(1-\varepsilon') = (1-\varepsilon)^k$, then the rate of simulating multiple independent BES$(\varepsilon')$ samples is at most $1/k$, which is also achievable using (block) linear constructions. Finally, we show that a SNIS of a BSS$(\varepsilon')$ sample from BSS$(\varepsilon)$ samples is feasible if and only if $(1-2\varepsilon')=(1-2\varepsilon)^k$, for some $k\in N$. Interestingly, there are linear as well as non-linear SNIS constructions. When $(1-2\varepsilon')=(1-2\varepsilon)^k$, we prove that the rate of a \textit{perfectly secure} SNIS is at most $1/k$, which is achievable using linear and non-linear constructions. Our results leave open the fascinating problem of determining the rate of \textit{statistically secure} SNIS among BSS samples. Our technical approach algebraizes the definition of SNIS and proceeds via Fourier analysis. Our work develops general analysis methodologies for Boolean functions, explicitly incorporating cryptographic security constraints. Our work also proves strong forms of \textit{statistical-to-perfect security} transformations: one can error-correct a statistically secure SNIS to make it perfectly secure. We show a connection of our research with \textit{homogeneous Boolean functions} and \textit{distance-invariant codes}, which may be of independent interest.

We prove a lower bound on the communication complexity of perfect maliciously secure multiparty computation, in the standard model with $n=3t+1$ parties of which $t$ are corrupted. We show that for any $n$ and all large enough $g \in \mathbb{N}$ there exists a Boolean circuit $C$ with $g$ gates, where any perfectly secure protocol implementing $C$ must communicate $\Omega(n g)$ bits. The results easily extends to constructing similar circuits over any fixed finite field. Our results also extend to the case where the threshold $t$ is suboptimal. Namely if $n= 3t+s$ the bound is $\Omega(ng/s)$, which corresponds to known optimizations via packed secret-sharing. Using known techniques, we also show an upper bound that matches the lower bound up to a constant factor (existing upper bounds are a factor $\log n$ off for Boolean circuits).

As IoT applications are increasingly being deployed, there comes along an ever increasing need for the security and privacy of the involved data. Since cryptographic implementations are used to achieve these goals, it is important for embedded software developers to take into consideration hardware attacks. Side Channel Analysis (SCA) and Fault Attacks (FA) are the main classes of such attacks, which can either reduce or even eliminate the security levels of an em-bedded design. Therefore, cryptographic implementations must address both of them at the same time. To this end, multiple solutions have been proposed to address both attacks in one solution, such as Dual Pre-charge Logic (DPL) and Encoding countermeasures. In this work, we discuss the advantages and disadvantages of the state of the art, concurrent SCA and FA countermeasures. Additionally, we propose a software countermeasure in order to provide protection against both types of attacks. The proposed countermeasure is a general approach, applicable to any byte-sliced cipher and any modern MCUs (32- and 64-bit). The proposed countermeasure is ap-plied to an AES S-BOX implementation, for a 32-bit MCU (ARM Cortex-M3). The countermeasure has been experimen-tally evaluated against Correlation Power Analysis (CPA) attacks for both platforms while its fault detection capabilities are theoretically described.

CONFISCA is the first generic SIMD-based software countermeasure that can concurrently resist against Side-Channel Attack (SCA) and Fault Injection (FI). Its promising strength is presented in a PRESENT cipher case study and compared to software-based Dual-rail with Pre-charge Logic concurrent countermeasure. It has lower overhead, wider usability, and higher protection. Its protection has been compared using Correlation Power Analysis, Welch’s T-Test, Signal- to- Noise Ratio and Normalized Inter-Class Variance testing methods. CONFISCA can on-the-fly switch between its two modes of operation: The High-Performance and High-Security by having only one instance of the cipher. This gives us the flexibility to trade performance/energy with security, based on the actual critical needs.

Anonymous Committed Broadcast is a functionality that extends DC-nets and allows a set of clients to privately commit a message to set of servers, which can then simultaneously open all committed messages in a random ordering. Anonymity holds since no one can learn the ordering or the content of the client’s committed message. We present Blinder, the first system that provides a scalable and fully robust solution for anonymous committed broadcast. Blinder maintains both properties of security (anonymity) and robustness (aka. ‘guaranteed output delivery’ or ‘availability’) in the face of a global active (malicious) adversary. Moreover, Blinder is censorship resistant, meaning that a honest client cannot be blocked from participating. Blinder obtains its security and scalability by carefully combining classical and state-of-the-art techniques from the fields of anonymous communication and secure multiparty computation (MPC). In order to demonstrate scalability, we evaluate Blinder with up to 1 million clients, up to 100 servers and a message size of up to 10 kilobytes. In addition, we show that it is a perfect fit to be implemented on a GPU. A GPU based implementation of Blinder with 5 servers, which accepts 1 million clients, incurs a latency of less than 8 minutes; faster by a factor of > 100 than the 3-servers Riposte protocol (SOSP ’15), which is not robust and not censorship resistant; we get an even larger factor when comparing to AsynchroMix and PowerMix (CCS ’19), which are the only constructions that guarantee fairness (or robustness in the online phase).

In CRYPTO 2018, Russell et al. introduced the notion of crooked indifferentiability to analyze the security of a hash function when the underlying primitive is subverted. They showed that the $n$-bit to $n$-bit function implemented using enveloped XOR construction ($\mathsf{EXor}$) with $3n+1$ many $n$-bit functions and $3n^2$- bit random initial vectors (iv) can be proven secure asymptotically in the crooked indifferentiability setting. -We identify several major issues and gaps in the proof by Russel et al. We show that their proof does not work when the adversary makes queries related to multiple messages or in the case of intricate function dependent subversion. -We formalize new technique to prove crooked indifferentiability for multiple messages. Our technique can handle function dependent subversion. We apply our technique to provide a concrete proof for the $\mathsf{EXor}$ construction. -We analyze crooked indifferentiability of the classical sponge construction. We show, using a simple proof idea, the sponge construction is a crooked-indifferentiable hash function using only $n$-bit random iv.

Supersingular isogeny key encapsulation (SIKE) protocol delivers promising public and secret key sizes over other post-quantum candidates. However, the huge computations form the bottleneck and limit its practical applications. The modular multiplication operation, which is one of the most computationally demanding operations in the fundamental arithmetics, takes up a large part of the computations in the protocol. In this paper, we propose an improved unconventional-radix finite-field multiplication (IFFM) algorithm which reduces the computational complexity by about 20% compared to previous algorithms. We then devise a new high-speed modular multiplier architecture based on the IFFM. It is shown that the proposed architecture can be extensively pipelined to achieve a very high clock speed due to its complete feedforward scheme, which demonstrates significant advantages over conventional designs. The FPGA implementation results show the proposed multiplier has about 67 times faster throughput than the state-of-the-art designs and more than 12 times better area efficiency than previous works. Therefore, we think that these achievements will greatly contribute to the practicability of this protocol.

The $e$-th power residue symbol $\left(\frac{\alpha}{\mathfrak{p}}\right)_e$ is a useful mathematical tool in cryptography, where $\alpha$ is an integer, $\mathfrak{p}$ is a prime ideal in the prime factorization of $p\mathbb{Z}[\zeta_e]$ with a large prime $p$ satisfying $e \mid p-1$, and $\zeta_e$ is an $e$-th primitive root of unity. One famous case of the $e$-th power symbol is the first semantic secure public key cryptosystem due to Goldwasser and Micali (at STOC 1982). In this paper, we revisit the $e$-th power residue symbol and its applications. In particular, we prove that computing the $e$-th power residue symbol is equivalent to solving the discrete logarithm problem. By this result, we give a natural extension of the Goldwasser-Micali cryptosystem, where $e$ is an integer only containing small prime factors. Compared to another extension of the Goldwasser-Micali cryptosystem due to Joye and Libert (at EUROCRYPT 2013), our proposal is more efficient in terms of bandwidth utilization and decryption cost. With a new complexity assumption naturally extended from the one used in the Goldwasser-Micali cryptosystem, our proposal is provable IND-CPA secure. Furthermore, we show that our results on the $e$-th power residue symbol can also be used to construct lossy trapdoor functions and circular and leakage resilient public key encryptions with more efficiency and better bandwidth utilization.

The k-SIDH protocol is a static-static isogeny-based key agreement protocol. At Mathcrypt 2018, Jao and Urbanik introduced a variant of this protocol which uses non-scalar automorphisms of special elliptic curves to improve its efficiency. In this paper, we provide a new adaptive attack on Jao-Urbanik's protocol. The attack is a non-trivial adaptation of Galbraith-Petit-Shani-Ti's attack on SIDH (Asiacrypt 2016) and its extension to k-SIDH by Dobson-Galbraith-LeGrow-Ti-Zobernig (IACR eprint 2019). Our attack provides a speedup compared to a naïve application of Dobson et al.'s attack to Jao-Urbanik's scheme, exploiting its inherent structure. Estimating the security of k-SIDH and Jao-Urbanik's variant with respect to these attacks, k-SIDH provides better efficiency.

Hybrid Public Key Encryption (HPKE) is a cryptographic primitive being standardized by the Crypto Forum Research Group (CFRG) within the Internet Research Task Force (IRTF). HPKE schemes combine asymmetric and symmetric cryptographic primitives for efficient authenticated encryption of arbitrary-sized plaintexts under a given recipient public key. This document presents a mechanized cryptographic analysis done with CryptoVerif, of all four HPKE modes, instantiated with a prime-order-group Diffie-Hellman Key Encapsulation Mechanism (KEM).

With the location-based services booming, the volume of spatial data inevitably explodes. In order to reduce local storage and computational overhead, users tend to outsource data and initiate queries to the cloud. However, sensitive data or queries may be compromised if cloud server has access to raw data and plaintext token. To cope with this problem, searchable encryption for geometric range is applied. Geometric range search has wide applications in many scenarios, especially the circular range search. In this paper, we propose a practical and secure circular range search scheme (PSCS) to support searching for spatial data in a circular range. With Our scheme, a semi-honest cloud server will return the data for a given circular range correctly without revealing index privacy or query privacy. We propose a polynomial split algorithm which can decompose the inner product calculation neatly. Then, We formally define the security of our scheme and theoretically prove that it is secure under same-closeness-pattern chosen-plaintext attacks (CLS-CPA). In addition, we demonstrate the efficiency and accuracy through analysis and experiments compared with existing schemes.

It is convenient and common for schemes in the random oracle model to assume access to multiple random oracles (ROs), leaving to implementations the task (we call it oracle cloning) of constructing them from a single RO. The first part of the paper is a case study of oracle cloning in KEM submissions to the NIST Post-Quantum Cryptography standardization process. We give key-recovery attacks on some submissions arising from mistakes in oracle cloning, and find other submissions using oracle cloning methods whose validity is unclear. Motivated by this, the second part of the paper gives a theoretical treatment of oracle cloning. We give a definition of what is an "oracle cloning method" and what it means for such a method to "work," in a framework we call read-only indifferentiability, a simple variant of classical indifferentiability that yields security not only for usage in single-stage games but also in multi-stage ones. We formalize domain separation, and specify and study many oracle cloning methods, including common domain-separating ones, giving some general results to justify (prove read-only indifferentiability of) certain classes of methods. We are not only able to validate the oracle cloning methods used in many of the unbroken NIST PQC KEMs, but also able to specify and validate oracle cloning methods that may be useful beyond that.

Massively Parallel Computation (MPC) is a model of computation widely believed to best capture realistic parallel computing architectures such as large-scale MapReduce and Hadoop clusters. Motivated by the fact that many data analytics tasks performed on these platforms involve sensitive user data, we initiate the theoretical exploration of how to leverage MPC architectures to enable efficient, privacy-preserving computation over massive data. Clearly if a computation task does not lend itself to an efficient implementation on MPC even without security, then we cannot hope to compute it efficiently on MPC with security. We show, on the other hand, that any task that can be efficiently computed on MPC can also be securely computed with comparable efficiency. Specifically, we show the following results: • any MPC algorithm can be compiled to a communication-oblivious counterpart while asymp- totically preserving its round and space complexity, where communication-obliviousness ensures that any network intermediary observing the communication patterns learn no information about the secret inputs; • assuming the existence of Fully Homomorphic Encryption with a suitable notion of compact- ness and other standard cryptographic assumptions, any MPC algorithm can be compiled to a secure counterpart that defends against an adversary who controls not only intermediate network routers but additionally up to 1/3 &#8722; &#951; fraction of machines (for an arbitrarily small constant &#951;) — moreover, this compilation preserves the round complexity tightly, and preserves the space complexity upto a multiplicative security parameter related blowup. As an initial exploration of this important direction, our work suggests new definitions and proposes novel protocols that blend algorithmic and cryptographic techniques.

Viktoria hash is a compression function that generates a set of 512 bits from an arbitrary size input (limit of 2^480-1 bytes). This hash function contains some internal routines clearly inspired by AES and RC4 symmetric algorithms [14]. The new paradigm presents two major innovations: a fast preprocessing that initiates an internal state of 256!^2 permutations and a post-processing that guarantees a minimum number of executed rounds of 2^13. The pre-processing allows to differentiate very similar messages in the first runs of the algorithm. In the post-processing we have a safety barrier provided by a large number of rounds through a different structure of the main processing. The Viktoria algorithm seems to inaugurate a new design model in the construction of robust hash functions for some reasons, among them we highlight: the customization of the internal state according to each message, the elegance and efficiency of its main function and also a supposed high margin of safety provided by its post-processing function. Viktoria hash can also process bit oriented messages (whose last byte size is not complete) and generate larger hashes (1024, 1536, 2048 or larger) always as multiples of 512.

The Lyness map is a birational map in the plane which provides one of the simplest discrete analogues of a Hamiltonian system with one degree of freedom, having a conserved quantity and an invariant symplectic form. As an example of a symmetric Quispel-Roberts-Thompson (QRT) map, each generic orbit of the Lyness map lies on a curve of genus one, and corresponds to a sequence of points on an elliptic curve which is one of the fibres in a pencil of biquadratic curves in the plane. We present a version of the elliptic curve method (ECM) for integer factorization, which is based on iteration of the Lyness map with a particular choice of initial data. More precisely, we give an algorithm for scalar multiplication of a point on an elliptic curve, which is represented by one of the curves in the Lyness pencil. In order to avoid field inversion, and require only field multiplication (M), squaring (S) and addition, projective coordinates in P^1 x P^1 are used. Neglecting multiplication by curve constants (assumed small), each addition of the chosen point uses 2M, while each doubling step requires 15M. We further show that the doubling step can be implemented efficiently in parallel with four processors, dropping the effective cost to 4M. In contrast, the fastest algorithms in the literature, using twisted Edwards curves with small curve constants, use 8M for point addition and 4M+4S for point doubling, both of which can be run in parallel with four processors to yield effective costs of 2M and 1M+1S, respectively. Thus our scalar multiplication algorithm should require, on average, roughly twice as many multiplications per bit as state of the art methods using twisted Edwards curves, but it can be applied to any elliptic curve over Q, whereas twisted Edwards curves (equivalent to Montgomery curves) correspond to only a subset of all elliptic curves. Hence, if implemented in parallel, our method may have potential advantages for integer factorization or elliptic curve cryptography.

Indistinguishability against adaptive chosen-ciphertext attacks (IND-CCA2) is usually considered the most desirable security notion for classical encryption. In this work, we investigate its adaptation in the quantum world, when an adversary can perform superposition queries. The security of quantum-secure classical encryption has first been studied by Boneh and Zhandry (CRYPTO'13), but they restricted the adversary to classical challenge queries, which makes the indistinguishability only hold for classical messages (IND-qCCA2). We extend their work by giving the first security notions for fully quantum indistinguishability under quantum adaptive chosen-ciphertext attacks, where the indistinguishability holds for superposition of plaintexts (qIND-qCCA2).

In an early version of CRYPTO’17, Mennink and Neves pro- posed EWCDMD, a dual of EWCDM, and showed n-bit security, where n is the block size of the underlying block cipher. In CRYPTO’19, Chen et al. proposed permutation based design SoKAC21 and showed 2n/3- bit security, where n is the input size of the underlying permutation. In this paper we show birthday bound attacks on EWCDMD and SoKAC21, invalidating their security claims. Both attacks exploit an inherent com- position nature present in the constructions. Motivated by the above two attacks exploiting the composition nature, we consider some generic relevant composition based constructions of ideal primitives (possibly in the ideal permutation and random oracle model) and present birthday bound distinguishers for them. In particular, we demonstrate a birthday bound distinguisher against (1) a secret random permutation followed by a public random function and (2) composition of two secret random functions. Our distinguishers for SoKAC21 and EWCDMD are direct con- sequences of (1) and (2) respectively.

We study the problem of achieving statistical privacy in interactive proof systems and oblivious transfer -- two of the most well studied two-party protocols -- when limited rounds of interaction are available. Statistical Zaps: We give the first construction of statistical Zaps, namely, two-round statistical witness-indistinguishable (WI) protocols with a public-coin verifier. Our construction achieves computational soundness based on the quasi-polynomial hardness of learning with errors. Three-Round Statistical Receiver-Private Oblivious Transfer: We give the first construction of a three-round oblivious transfer (OT) protocol -- in the plain model -- that achieves statistical privacy for receivers and computational privacy for senders against malicious adversaries, based on polynomial-time assumptions. The round-complexity of our protocol is optimal. We obtain our first result by devising a public-coin approach to compress sigma protocols, without relying on trusted setup. To obtain our second result, we devise a general framework via a new notion of statistical hash commitments that may be of independent interest.

The goal of this investigation is effective method of key exchange which based on non-commutative group $G$. The results of Ko et al. \cite{kolee} is improved and generalized. The size of a minimal generating set for the commutator subgroup of Sylow 2-subgroups of alternating group is found. The structure of the commutator subgroup of Sylow 2-subgroups of the alternating group ${A_{{2^{k}}}}$ is investigated and used in key exchange protocol which based on non-commutative group. We consider non-commutative generalization of CDH problem \cite{gu2013new, bohli2006towards} on base of metacyclic group of Miller-Moreno type (minimal non-abelian group). We show that conjugacy problem in this group is intractable. Effectivity of computation is provided due to using groups of residues by modulo $n$. The algorithm of generating (designing) common key in non-commutative group with 2 mutually commuting subgroups is constructed by us.

Pseudorandom functions (PRFs) are fundamental objects in cryptography that play a central role in symmetric-key cryptography. Although PRFs can be constructed from one-way functions generically, these black-box constructions are usually inefficient and require deep circuits to evaluate compared to direct PRF constructions that rely on specific algebraic assumptions. From lattices, one can directly construct PRFs from the Learning with Errors (LWE) assumption (or its ring variant) using the result of Banerjee, Peikert, and Rosen (Eurocrypt 2012) and its subsequent works. However, all existing PRFs in this line of work rely on the hardness of the LWE problem where the associated modulus is super-polynomial in the security parameter. In this work, we provide two new PRF constructions from the LWE problem that each focuses on either minimizing the depth of its evaluation circuit or providing key-homomorphism while relying on the hardness of the LWE problem with either a polynomial modulus or nearly polynomial modulus. Along the way, we introduce a new variant of the LWE problem called the Learning with Rounding and Errors (LWRE) problem. We show that for certain settings of parameters, the LWRE problem is as hard as the LWE problem. We then show that the hardness of the LWRE problem naturally induces a pseudorandom synthesizer that can be used to construct a low-depth PRF. The techniques that we introduce to study the LWRE problem can then be used to derive variants of existing key-homomorphic PRFs whose security can be reduced from the hardness of the LWE problem with a much smaller modulus.

The Authenticated Encryption with Associated Data (AEAD) primitive, which integrates confidentiality and integrity services under a single roof, found wide-spread adoption in industry and became indispensable in practical protocol design. Recognizing this, academic research put forward a large number of candidate constructions, many of which come with provable security guarantees. Nevertheless, the recent past has shaken up with the discovery of vulnerabilities, some of them fatal, in well-regarded schemes, stemming from weak underlying primitives, flawed security arguments, implementation-level vulnerabilities, and so on. Simply reacting to such findings by replacing broken candidates by better(?) ones is in many cases unduly, costly, and sometimes just impossible. On the other hand, as attack techniques and opportunities change over time, it seems venturous to propose any specific scheme if the intended lifetime of its application is, say, twenty years. In this work we study a workable approach towards increasing the resilience against unforeseen breaks of AEAD primitives. Precisely, we consider the ability to combine two AEAD schemes into one such that the resulting AEAD scheme is secure as long as at least one of its components is (or: as long as at most one component is broken). We propose a series of such combiners, some of which work with fully generic AEAD components while others assume specific internal structures of the latter (like an encrypt-then-MAC design). We complement our results by proving the optimality of our constructions by showing the impossibility of combiners that get along with less invocations of the component algorithms.

At Eurocrypt'19, Attrapadung presented several transformations that dynamically compose a set of attribute-based encryption (ABE) schemes for simpler predicates into a new ABE scheme for more expressive predicates. Due to the powerful unbounded and modular nature of his compositions, many new ABE schemes can be obtained in a systematic manner. However, his approach heavily relies on $q$-type assumptions, which are not standard. Devising such powerful compositions from standard assumptions was left as an important open problem. In this paper, we present a new framework for constructing ABE schemes that allow unbounded and dynamic predicate compositions among them, and show that the adaptive security of these composed ABE will be preserved by relying only on the standard matrix Diffie-Hellman (MDDH) assumption. This thus resolves the open problem posed by Attrapadung. As for applications, we obtain various ABEs that are the first such instantiations of their kinds from standard assumptions.These include the following adaptively secure large-universe ABEs for Boolean formulae under MDDH: - The first completely unbounded monotone key-policy (KP)/ciphertext-policy (CP) ABE. Such ABE was recently proposed, but only for the KP and small-universe flavor (Kowalczyk and Wee, Eurocrypt'19). - The first completely unbounded non-monotone KP/CP-ABE. Especially, our ABEs support a new type of non-monotonicity that subsumes previous two types of non-monotonicity, namely, by Ostrovsky et al. (CCS'07) and by Okamoto and Takashima (CRYPTO'10). - The first (non-monotone) KP and CP-ABE with constant-size ciphertexts and secret keys, respectively. - The first KP and CP-ABE with constant-size secret keys and ciphertexts, respectively. At the core of our framework lies a new partially symmetric design of the core 1-key 1-ciphertext oracle component called Key Encoding Indistinguishability, which exploits the symmetry so as to obtain compositions.

In ASIACRYPT 2019, Genise et al. describe GGH+19 a new somewhat homomorphic encryption scheme. The security relies on an inhomogeneous and non-structured variant of the NTRU assumption that they call MiNTRU. To allow for meaningful homomorphic computations, they use overstretched parameters, but they do not provide an analysis of their new assumption against the state-of-the-art attack of Kirchner and Fouque KF17 for overstretched modulus. We show that the parameters of GGH+19 do not satisfy the desired security by actually conducting the known analysis. We also report a successful break of the smallest set of parameters in around 15 hours of computations while they are claimed to reach 100 bits of security.

We consider a collision search problem (CSP), where given a parameter $C$, the goal is to find $C$ collision pairs in a random function $f:[N] \rightarrow [N]$ (where $[N] = \{0,1,\ldots,N-1\})$ using $S$ bits of memory. Algorithms for CSP have numerous cryptanalytic applications such as space-efficient attacks on double and triple encryption. The best known algorithm for CSP is parallel collision search (PCS) published by van Oorschot and Wiener, which achieves the time-space tradeoff $T^2 \cdot S = \tilde{O}(C^2 \cdot N)$ for $S = \tilde{O}(C)$. In this paper, we prove that any algorithm for CSP satisfies $T^2 \cdot S = \tilde{\Omega}(C^2 \cdot N)$ for $S = \tilde{O}(C)$, hence the best known time-space tradeoff is optimal (up to poly-logarithmic factors in $N$). On the other hand, we give strong evidence that proving similar unconditional time-space tradeoff lower bounds on CSP applications (such as breaking double and triple encryption) may be very difficult, and would imply a breakthrough in complexity theory. Hence, we propose a new restricted model of computation and prove that under this model, the best known time-space tradeoff attack on double encryption is optimal.

Boneh, Waters and Zhandry (CRYPTO 2014) used multilinear maps to provide a solution to the long-standing problem of public-key broadcast encryption (BE) where all parameters in the system are small. In this work, we improve their result by providing a solution that uses only bilinear maps and Learning With Errors (LWE). Our scheme is fully collusion-resistant against any number of colluders, and can be generalized to an identity-based broadcast system with short parameters. Thus, we reclaim the problem of optimal broadcast encryption from the land of “Obfustopia”. Our main technical contribution is a ciphertext policy attribute based encryption (CP-ABE) scheme which achieves special efficiency properties – its ciphertext size, secret key size, and public key size are all independent of the size of the circuits supported by the scheme. We show that this special CP-ABE scheme implies BE with optimal parameters; but it may also be of independent interest. Our constructions rely on a novel interplay of bilinear maps and LWE, and are proven secure in the generic group model.

Let $k \ge 2$ be an integer, define $$ S_t^k:=\Bigg\{(a,b)\in \mathbb{Z}^2\ \Big| \ { 0 \le a,b \le 2^{k}-2,\ a+b\equiv t ~(\text{mod} \ 2^k-1),\ \w(a)+\w(b)\le{k-1}}\Bigg\},$$ where $t \in \mathbb{Z}, 1 \le t \le 2^k-2$. This paper gives the upper bound of cardinality of $S_t^k$ when $\w(t)\le 10$, proving that a conjecture proposed by Tu and Deng in the case.

In this paper, a multivariate polynomial and exponential mappings based password protocol is presented. The method can be utilized in public domains. The key generator generates a vector, intended to be used as a password by the authentication protocol subsequently, such that when the vector is substituted and evaluated in certain fixed multivariate polynomials -- that may be listed in a public domain -- the value $0$ is found as a result of proper authentication. The public domain in this context could be internal to a large, and possibly distributed, system. The key generator can take hints from the owner of the password to generate the particular zero vector to suit the user. It may take into consideration biometric and any other user specific information at the time of key generation. The information collected by the key generator can be saved by the owner of the password for its possible retrieval upon requisition by the user, during the period of its validity, in case it is forgotten by the user.

Despite the fundamental importance of delay functions, underlying both the classic notion of a time-lock puzzle and the more recent notion of a verifiable delay function, the only known delay function that offers both sufficient structure for realizing these two notions and a realistic level of practicality is the ``iterated squaring'' construction of Rivest, Shamir and Wagner. This construction, however, is based on rather strong assumptions in groups of hidden orders, such as the RSA group (which requires a trusted setup) or the class group of an imaginary quadratic number field (which is still somewhat insufficiently explored from the cryptographic perspective). For more than two decades, the challenge of constructing delay functions in groups of known orders, admitting a variety of well-studied instantiations, has eluded the cryptography community. In this work we prove that there are no constructions of generic-group delay functions in cyclic groups of known orders: We show that for any delay function that does not exploit any particular property of the representation of the underlying group, there exists an attacker that completely breaks the function's sequentiality when given the group's order. As any time-lock puzzle and verifiable delay function give rise to a delay function, our result holds for these two notions we well, and explains the lack of success in resolving the above-mentioned long-standing challenge. Moreover, our result holds even if the underlying group is equipped with a $d$-linear map, for any constant $d \geq 2$ (and even for super-constant values of $d$ under certain conditions).

At the core of Apple's iMessage is a signcryption scheme that involves symmetric encryption of a message under a key that is derived from the message itself. This motivates us to formalize a primitive we call Encryption under Message-Derived Keys (EMDK). We prove security of the EMDK scheme underlying iMessage. We use this to prove security of the signcryption scheme itself, with respect to definitions of signcryption we give that enhance prior ones to cover issues peculiar to messaging protocols. Our provable-security results are quantitative, and we discuss the practical implications for iMessage.

A non-interactive zero-knowledge (NIZK) protocol enables a prover to convince a verifier of the truth of a statement without leaking any other information by sending a single message. The main focus of this work is on exploring short pairing-based NIZKs for all NP languages based on standard assumptions. In this regime, the seminal work of Groth, Ostrovsky, and Sahai (J.ACM'12) (GOS-NIZK) is still considered to be the state-of-the-art. Although fairly efficient, one drawback of GOS-NIZK is that the proof size is multiplicative in the circuit size computing the NP relation. That is, the proof size grows by $O(|C|\lambda)$, where $C$ is the circuit for the NP relation and $\lambda$ is the security parameter. By now, there have been numerous follow-up works focusing on shortening the proof size of pairing-based NIZKs, however, thus far, all works come at the cost of relying either on a non-standard knowledge-type assumption or a non-static $q$-type assumption. Specifically, improving the proof size of the original GOS-NIZK under the same standard assumption has remained as an open problem. Our main result is a construction of a pairing-based NIZK for all of NP whose proof size is additive in $|C|$, that is, the proof size only grows by $|C| +\poly(\lambda)$, based on the decisional linear (DLIN) assumption. Since the DLIN assumption is the same assumption underlying GOS-NIZK, our NIZK is a strict improvement on their proof size. As by-products of our main result, we also obtain the following two results: (1) We construct a perfectly zero-knowledge NIZK (NIPZK) for NP relations computable in NC1 with proof size $|w| \cdot \poly(\lambda)$ where $|w|$ is the witness length based on the DLIN assumption. This is the first pairing-based NIPZK for a non-trivial class of NP languages whose proof size is independent of $|C|$ based on a standard assumption. (2)~We construct a universally composable (UC) NIZK for NP relations computable in NC1 in the erasure-free adaptive setting whose proof size is $|w| \cdot \poly(\lambda)$ from the DLIN assumption. This is an improvement over the recent result of Katsumata, Nishimaki, Yamada, and Yamakawa (CRYPTO'19), which gave a similar result based on a non-static $q$-type assumption. The main building block for all of our NIZKs is a constrained signature scheme with decomposable online-offline efficiency. This is a property which we newly introduce in this paper and construct from the DLIN assumption. We believe this construction is of an independent interest.

Periodic key rotation is a common practice designed to limit the long-term power of cryptographic keys. Key rotation refers to the process of re-encrypting encrypted content under a fresh key, and overwriting the old ciphertext with the new one. When encrypted data is stored in the cloud, key rotation can be very costly: it may require downloading the entire encrypted content from the cloud, re-encrypting it on the client's machine, and uploading the new ciphertext back to the cloud. An updatable encryption scheme is a symmetric-key encryption scheme designed to support efficient key rotation in the cloud. The data owner sends a short \emph{update token} to the cloud. This update token lets the cloud rotate the ciphertext from the old key to the new key, without learning any information about the plaintext. Recent work on updatable encryption has led to several security definitions and proposed constructions. However, existing constructions are not yet efficient enough for practical adoption, and the existing security definitions can be strengthened. In this work we make three contributions. First, we introduce stronger security definitions for updatable encryption (in the ciphertext-dependent setting) that capture desirable security properties not covered in prior work. Second, we construct two new updatable encryption schemes. The first construction relies only on symmetric cryptographic primitives, but only supports a bounded number of key rotations. The second construction supports a (nearly) unbounded number of updates, and is built from the Ring Learning with Errors (RLWE) assumption. Due to complexities of using RLWE, this scheme achieves a slightly weaker notion of integrity compared to the first. Finally, we implement both constructions and compare their performance to prior work. Our RLWE-based construction is 200x faster than a prior proposal for an updatable encryption scheme based on the hardness of elliptic curve DDH. Our first construction, based entirely on symmetric primitives, has the highest encryption throughput, approaching the performance of AES, and the highest decryption throughput on ciphertexts that were re-encrypted fewer than fifty times. For ciphertexts re-encrypted over fifty times, the RLWE construction dominates it in decryption speed.

Reducing interaction in Multiparty Computation (MPC) is a highly desirable goal in cryptography. It is known that 2-round MPC can be based on the minimal assumption of 2-round Oblivious Transfer (OT) [Benhamouda and Lin, Garg and Srinivasan, EC 2018], and 1-round MPC is impossible in general. In this work, we propose a natural ``hybrid'' model, called \textbf{multiparty reusable Non-Interactive Secure Computation Market (mrNISC)}. In this model, parties publish encodings of their private inputs $x_i$ at the beginning, once and for all. Later, any subset $I$ of them can compute \emph{on-the-fly} a function $f$ on their inputs $\vec x_I = {\{x_i\}}_{i \in I}$ by just sending a single message to a stateless evaluator, conveying the result $f(\vec x_I)$ and nothing else. Importantly, the input encodings can be \emph{reused} in any number of on-the-fly computations, and the same classical simulation security guaranteed by multi-round MPC, is achieved. In short, mrNISC has minimal yet ``tractable'' interaction pattern. We initiate the study of mrNISC on several fronts. First, we formalize the security of mrNISC protocols in both a UC definition and a game-based definition. Second, we construct mrNISC protocols in the plain model with semi-honest and semi-malicious security based on bilinear groups. Third, we demonstrate the power of mrNISC by showing two applications: non-interactive MPC (NIMPC) with reusable setup and a distributed version of program obfuscation. In addition, at the core of our construction of mrNISC is a witness encryption scheme for a special language that verifies Non-Interactive Zero-Knowledge (NIZK) proofs of the validity of computations over committed values, which we believe is of independent interest.