This paper presents an attack against common procedures for comparing the size-security tradeoffs of proposed cryptosystems. The attack begins with size-security tradeoff data, and then manipulates the presentation of the data in a way that favors a proposal selected by the attacker, while maintaining plausible deniability for the attacker. As concrete examples, this paper shows two manipulated comparisons of size-security tradeoffs of lattice-based encryption proposals submitted to the NIST Post-Quantum Cryptography Standardization Project. One of these manipulated comparisons appears to match public claims made by NIST, while the other does not, and the underlying facts do not. This raises the question of whether NIST has been subjected to this attack. This paper also considers a weak defense and a strong defense that can be applied by standards-development organizations and by other people comparing cryptographic algorithms. The weak defense does not protect the integrity of comparisons, although it does force this type of attack to begin early. The strong defense stops this attack.

New Number Field Sieves (NFS) attacks on the discrete logarithm problem have led to increase the key size of pairing-based cryptography and more precisely pairings on most popular curves like BN. To ensure 128-bit security level, recent costs estimations recommand to switch for BLS24 curves. However, using BLS24 curves for pairing requires to have an efficient arithmetic in Fp4. In this paper, we transposed previous work on multiplication over extesnsion fields using Newton's interpolation to construct a new formula for multiplication in Fp4 and propose time x area efficient hardware implementation of this operation. This co-processor is implemented on Kintex-7 Xilinx FPGA. The efficiency of our design in terms of time x area is almost 3 times better than previous specific architecture for multiplication in Fp4. Our architecture is used to estimate the efficiency of hardware implementations of full pairings on BLS12 and BLS24 curves with a 128-bit security level. This co-processeur can be easily modified to anticipate further curve changes.

Point randomization is an important countermeasure to protect Elliptic Curve Cryptography (ECC) implementations against side-channel attacks. In this paper, we revisit its worst-case security in front of advanced side-channel adversaries taking advantage of analytical techniques in order to exploit all the leakage samples of an implementation. Our main contributions in this respect are the following: first, we show that due to the nature of the attacks against the point randomization (which can be viewed as Simple Power Analyses), the gain of using analytical techniques over simpler divide-and-conquer attacks is limited. Second, we take advantage of this observation to evaluate the theoretical noise levels necessary for the point randomization to provide strong security guarantees and compare different elliptic curve coordinates systems. Then, we turn this simulated analysis into actual experiments and show that reasonable security levels can be achieved by implementations even on low-cost (e.g. 8-bit) embedded devices. Finally, we are able to bound the security on 32-bit devices against worst-case adversaries.

Bitcoin is a blockchain whose immutability relies on Proof-of-Work: Before appending a new block, some so-called miner has to solve a cryptographic challenge by brute force. The blockchain is spread over a network of faithful miners, whose cumulated computing power is assumed to be so large that, among other things, it should be too expensive for an attacker to mine a secret fork $n$ blocks longer than the main blockchain, provided that $n$ is big enough. For a given targeted advance of $n$ blocks, we investigate the expected time for the attacker to mine such a secret fork, the underlying cumulative distribution function, and some related optimization problems.

By design, TLS (Transport Layer Security) is a 2-party, end-to-end protocol. Yet, in practice, TLS delegation is often deployed: that is, middlebox proxies inspect and even modify TLS traffic between the endpoints. Recently, industry-leaders (e.g., Akamai, Cloudflare, Telefonica, Ericcson), standardization bodies (e.g., IETF, ETSI), and academic researchers have proposed numerous ways of achieving safer TLS delegation. We present LURK the LURK (Limited Use of Remote Keys) extension for TLS~1.2, a suite of designs for TLS delegation, where the TLS-server is aware of the middlebox. We implement and test LURK. We also cryptographically prove and formally verify, in Proverif, the security of LURK. Finally, we comprehensively analyze how our designs balance (provable) security and competitive performance.

The security of cryptosystems based on Chebyshev recursive relation, T_n(x)=2xT_{n-1}(x)-T_{n-2}(x), relies on the difficulty of finding the large degree of Chebyshev polynomials from given parameters. The relation cannot be used to evaluate T_n(x) if n is very large. We will investigate other three methods: matrix-multiplication-based evaluation, halve-and-square evaluation, and root-extraction-based evaluation. Though they have the same theoretical complexity O(\log n\log^2p), we find in some cases the root-extraction-based method is more efficient than the others, which is as fast as the general modular exponentiation. The result indicates that the hardness of some cryptosystems based on modular Chebyshev polynomials is almost equivalent to that of solving general discrete logarithm.

In a hybrid key encapsulation construction, multiple independent key encapsulation mechanisms are combined in a way that ensures the resulting key is secure according to the strongest mechanism. Such constructions can combine mechanisms that are secure in different settings and achieve the combined security of all mechanisms. For example classical and post-quantum mechanisms can be combined in order to secure communication against current threats as well as future quantum adversaries. This paper contains proofs of security for two hybrid key encapsulation mechanisms along with the relevant security definitions. Practical interpretation of these results is also provided in order to guide the use of these mechanisms in applications and standards.

We use biometrics like fingerprints and facial images to identify ourselves to our mobile devices and log on to applications everyday. Such authentication is internal-facing: we provide measurement on the same device where the template is stored. If our personal devices could participate in external-facing authentication too, where biometric measurement is captured by a nearby external sensor, then we could also enjoy a frictionless authentication experience in a variety of physical spaces like grocery stores, convention centers, ATMs, etc. The open setting of a physical space brings forth important privacy concerns though. We design a suite of secure protocols for external-facing authentication based on the cosine similarity metric which provide privacy for both user templates stored on their devices and the biometric measurement captured by external sensors in this open setting. The protocols provide different levels of security, ranging from passive security with some leakage to active security with no leakage at all. With the help of new packing techniques and zero-knowledge proofs for Paillier encryption - and careful protocol design, our protocols achieve very practical performance numbers. For templates of length 256 with elements of size 16 bits each, our fastest protocol takes merely 0.024 seconds to compute a match, but even the slowest one takes no more than 0.12 seconds. The communication overhead of our protocols is very small too. The passive and actively secure protocols (with some leakage) need to exchange just 16.5KB and 27.8KB of data, respectively. The first message is designed to be reusable and, if sent in advance, would cut the overhead down to just 0.5KB and 0.8KB, respectively.

Proof of Work (PoW) protocols, originally proposed to circumvent DoS and email spam attacks, are now at the heart of the majority of recent cryptocurrencies. Current popular PoW protocols are based on hash puzzles. These puzzles are solved via a brute force search for a hash output with particular properties, such as a certain number of leading zeros. By considering the hash as a random function, and fixing a priori a sufficiently large search space, Grover's search algorithm gives an asymptotic quadratic advantage to quantum machines over classical machines. In this paper, as a step towards a fuller understanding of post quantum blockchains, we propose a PoW protocol for which quantum machines have a smaller asymptotic advantage. Specifically, for a lattice of rank \(n\) sampled from a particular class, our protocol provides as the PoW an instance of the Hermite Shortest Vector Problem (Hermite-SVP) in the Euclidean norm, to a small approximation factor. Asymptotically, the best known classical and quantum algorithms that directly solve SVP type problems are heuristic lattice sieves, which run in time \(2^{0.292n + o(n)}\) and \(2^{0.265n + o(n)}\) respectively. We discuss recent advances in SVP type problem solvers and give examples of where the impetus provided by a lattice based PoW would help explore often complex optimization spaces.

The random oracle model (ROM) enjoys widespread popularity, mostly because it tends to allow for tight and conceptually simple proofs where provable security in the standard model is elusive or costly. While being the adequate replacement of the ROM in the post-quantum security setting, the quantum-accessible random oracle model (QROM) has thus far failed to provide these advantages in many settings. In this work, we focus on adaptive reprogrammability, a feature of the ROM enabling tight and simple proofs in many settings. We show that the straightforward quantum-accessible generalization of adaptive reprogramming is feasible by proving a bound on the adversarial advantage in distinguishing whether a random oracle has been reprogrammed or not. We show that our bound is tight by providing a matching attack. We go on to demonstrate that our technique recovers the mentioned advantages of the ROM in three QROM applications: 1) We give a tighter proof of security of the message compression routine as used by XMSS. 2) We show that the standard ROM proof of chosen-message security for Fiat-Shamir signatures can be lifted to the QROM, straightforwardly, achieving a tighter reduction than previously known. 3) We give the first QROM proof of security against fault injection and nonce attacks for the hedged Fiat-Shamir transform.

This paper gives the first definitions and constructions for incremental pseudo-random functions (IPRFs). The syntax is nonce based. (Algorithms are deterministic but may take as input a non-repeating quantity called a nonce.) The design approach is modular. First, given a scheme secure only in the single-document setting (there is just one document on which incremental updates are being performed) we show how to generically build a scheme that is secure in the more realistic multi-document setting (there are many documents, and they are simultaneously being incrementally updated). Then we give a general way to build an IPRF from (1) an incremental hash function with weak collision resistance properties and (2) a symmetric encryption scheme. (This adapts the classic Carter-Wegman paradigm used to build message authentication schemes in the non-incremental setting.) This leads to many particular IPRFs. Our work has both practical and theoretical motivation and value: Incremental PRFs bring the benefits of incrementality to new applications (such as incremental key derivation), and the movement from randomized or stateful schemes to nonce based ones, and from UF (unforgeability) to PRF security, bring incremental symmetric cryptography up to speed with the broader field of symmetric cryptography itself.

The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open problem is that of the Walsh spectrum of the Dobbertin power family, for which it still remains unknown. We derive alternative representations for theinfinite APN monomial families. We show how the Niho, Welch, and Dobbertin functions can be represented as the composition $x^i \circ x^{1/j}$ of two power functions, and prove that our representations are optimal, i.e. no two power functions of lesser algebraic degree can produce the same composition. We investigate compositions $x^i \circ L \circ x^{1/j}$ for a linear polynomial $L$, and compute all APN functions of this form for $n \le 9$ and for $L$ with binary coefficients, thereby confirming that our theoretical constructions exhaust all possible cases. We present observations and data on power functions with exponent $\sum_{i = 1}^{k-1} 2^{2ni} - 1$ which generalize the inverse and Dobbertin families. We present data on the Walsh spectrum of the Dobbertin function for $n \le 35$, and conjecture its exact form. As an application of our results, we determine the exact values of the Walsh transform of the Kasami function at all points of a special form. Computations performed for $n \le 21$ show that these points cover about 2/3 of the field.

The existence of a provable one-way function is a long-standing open problem. This short note presents an example towards the existence a provable one-way function, example in which both directions are polynomial. Namely, we prove that given a sorted array it takes O(n) operations to randomly permute the array values uniformly over the permutation space, while (comparison based) sorting of the permuted array (of big enough values) requires in the worst case (and in the average case) Omega(n log n) compare operations . We also present a candidate cryptosystem based on permutations of random polynomial values.

Recent research in Dynamic Searchable Symmetric Encryption (DSSE) focuses on efficient search over encrypted data while allowing updates. Unfortunately, as demonstrated by many attacks, updates can be a source of information leakage that can compromise DSSE privacy. To mitigate these attacks, forward and backward privacy of DSSE schemes have been introduced. A concerted effort of the research community has resulted in the publication of many DSSE schemes. To the best of our knowledge, however, there is no DSSE scheme supporting conjunctive queries, which achieves both forward and backward privacy. We give two DSSE schemes with forward and backward privacy, which support conjunctive queries, and they are suitable for different applications. In particular, we first introduce a new data structure termed the extended bitmap index. Then we describe our forward and backward private DSSE schemes, which support conjunctive queries. Our security analysis proves the claimed privacy characteristics, and experiments show that our schemes are practical. Compared to the state-of-the-art DSSE VBTree supporting conjunctive queries (but not backward privacy), our schemes offer search time that is a few orders of magnitude faster. Besides, our schemes claim better security (called Type-C backward privacy).

In this paper we introduce new algorithms that, based only on the independent round keys assumption, allow to practically compute the exact expected differential probability of (truncated) differentials and the expected linear potential of (multidimensional) linear hulls. That is, we can compute the exact sum of the probability or the potential of all characteristics that follow a given activity pattern. We apply our algorithms to various recent SPN ciphers and discuss the results.

We introduce a novel variant of Lagrange interpolation called modular Lagrange interpolation that allows us to obtain and prove error bounds for explicit low-degree polynomial approximations of a function on a union of equally-spaced small intervals even if the function overall is not continuous. We apply our technique to the mod function and obtain explicit low-degree polynomial approximations with small error. In particular, for every $k$ and $N >>k$, we construct low-degree polynomials that approximate $f(x) = x \mod N$, for $|f(x)| \leq 1$ and $|x| \leq kN$, to within O($1/N$) additive approximation. For $k= O(\log N)$, the result is generalized to give O($d$)-degree polynomial approximations to within O($N^{-d}$) error for any $d \geq 1$. Literature in approximation theory allows for arbitrary precision polynomial approximation of only smooth functions, whereas the mod function is only piecewise linear. These polynomials can be used in bootstrapping for approximate homomorphic encryption, which requires computing the mod function near multiples of the modulus. Our work bypasses the fundamental error of approximation in prior works caused by first approximating the mod function by a scaled sine function. We implement the bootstrapping of $\mathsf{HEAAN}$ using our polynomials and profile various parameter settings. For example, we demonstrate bootstrapping that can achieve 67 bit message precision, larger than the precision of a $\mathsf{double}$ variable, whereas the most advanced prior work was only capable of up to 40 bit message precision.

We present two new related families of lattice trapdoors based on the inhomogeneous NTRU problem (iNTRU) defined in Genise et. al (ASIACRYPT 2019). Our constructions are ``gadget-based'' and offer compact secret keys and preimages and compatibility with existing, efficient preimage sampling algorithms. Our trapdoors can be used as a fundamental building block in lattice-based schemes relying lattice trapdoors. In addition, we implemented our trapdoors using the PALISADE library.

There are lots of applications of inner-product functional encryption (IPFE). In this paper, we consider two important extensions of it. One is to enhance IPFE with access control such that only users with a pre-defined identity are allowed to compute the inner product, referred as identity-based inner-product functional encryption (IBIPFE). We formalize the definition of IBIPFE, and propose the first adaptive-secure IBIPFE scheme from Decisional Bilinear Diffie-Hellman (DBDH) assumption. In an IBIPFE scheme, the ciphertext is related to a vector $\vec{x}$ and a new parameter, identity ID. Each secret key is also related to a vector $\vec{y}$ and an identity ID'. The decryption algorithm will output the inner-product value $<\vec{x}, \vec{y}>$ only if ID $=$ ID'. The other extension is to make IBIPFE leakage resilient. We consider the bounded-retrieval model (BRM) in which an adversary can learn at most $l$ bits information from each secret key. Here, $l$ is the leakage bound determined by some external parameters, and it can be set arbitrarily large. After giving the security definition of leakage-resilient IBIPFE, we extend our IBIPFE scheme into a leakage-resilient IBIPFE scheme in the BRM by hash proof system (HPS).

Byzantine Broadcast is an important topic in distributed systems and improving its round complexity has long been a focused challenge. Under honest majority, the state of the art for Byzantine Broadcast is 10 rounds for a static adversary and 16 rounds for an adaptive adversary. In this paper, we present a Byzantine Broadcast protocol with expected 8 rounds under a static adversary and expected 10 rounds under an adaptive adversary. We also generalize our idea to the dishonest majority setting and achieve an improvement over existing protocols.

Most efficient zero-knowledge arguments lack a concrete security analysis, making parameter choices and efficiency comparisons challenging. This is even more true for non-interactive versions of these systems obtained via the Fiat-Shamir transform, for which the security guarantees generically derived from the interactive protocol are often too weak, even when assuming a random oracle. This paper initiates the study of state-restoration soundness in the algebraic group model (AGM) of Fuchsbauer, Kiltz, and Loss (CRYPTO '18). This is a stronger notion of soundness for an interactive proof or argument which allows the prover to rewind the verifier, and which is tightly connected with the concrete soundness of the non-interactive argument obtained via the Fiat-Shamir transform. We propose a general methodology to prove tight bounds on state-restoration soundness, and apply it to variants of Bulletproofs (Bootle et al, S&P '18) and Sonic (Maller et al., CCS '19). To the best of our knowledge, our analysis of Bulletproofs gives the first non-trivial concrete security analysis for a non-constant round argument combined with the Fiat-Shamir transform.

Many organizations stand to benefit from pooling their data together in order to draw mutually beneficial insights -- e.g., for fraud detection across banks, better medical studies across hospitals, etc. However, such organizations are often prevented from sharing their data with each other by privacy concerns, regulatory hurdles, or business competition. We present Senate, a system that allows multiple parties to collaboratively run analytical SQL queries without revealing their individual data to each other. Unlike prior works on secure multi-party computation (MPC) that assume that all parties are semi-honest, Senate protects the data even in the presence of malicious adversaries. At the heart of Senate lies a new MPC decomposition protocol that decomposes the cryptographic MPC computation into smaller units, some of which can be executed by subsets of parties and in parallel, while preserving its security guarantees. Senate then provides a new query planning algorithm that decomposes and plans the cryptographic computation effectively, achieving a performance of up to 145$\times$ faster than the state-of-the-art.

In this paper, we investigate the key dependency of differentials in block ciphers by examining the results of numerous experiments applied to the substitution-permutation network (SPN) structure using 4-bit S-boxes. In particular, we consider two cipher structures: a toy 16-bit SPN and a realistic 64-bit SPN. For both ciphers, we generate many different experimental results by inserting the S-boxes used in many lightweight cipher proposals and applying different forms of round key generation. It is demonstrated that, in most circumstances, with enough rounds in the cipher, the probability distribution (across all keys) of the differential probability follows the distribution expected in the theoretically ideal scenario. However, this does not occur consistently for all S-boxes and all approaches to round key generation. Consequently, it is possible that a cipher may have more susceptibility to differential cryptanalysis for some subset of the cipher keys than is implied when employing the standard assumptions used in analyzing a cipher’s security.

We introduce Vetted Encryption (VE), a novel cryptographic primitive, which addresses the following scenario: a receiver controls, or vets, who can send them encrypted messages. We model this as a filter publicly checking ciphertext validity, where the overhead does not grow with the number of senders. The filter receives one public key for verification, and every user receives one personal encryption key. We present three versions: Anonymous, Identifiable, and Opaque VE (AVE, IVE and OVE), and concentrate on formal definitions, security notions and examples of instantiations based on preexisting primitives of the latter two. For IVE, the sender is identifiable both to the filter and the receiver, and we make the comparison with identity-based signcryption. For OVE, a sender is anonymous to the filter, but is identified to the receiver. OVE is comparable to group signatures with message recovery, with the important additional property of confidentiality of messages.

In this paper we examine the central question that is how well do side channel evaluation regimes capture the true security level of a product. Concretely, answering this question requires considering the optimality of the attack/evaluation strategy selected by the evaluator, and the various steps to instantiate it. We draw on a number of published works and discuss whether state-of-the-art solutions for the different steps of a side-channel security evaluation offer bounds or guarantees of optimality, or if they are inherently heuristic. We use this discussion to provide an informal rating of the steps' optimality and to put forward where risks of overstated security levels remain.

SodsMPC is a quantum-safe smart contract system. SodsMPC permissioned servers (verification nodes) execute contracts by secure multi-party computation (MPC) protocols. MPC ensures the contract execution correctness while trivially keeping the \textit{data privacy}. Moreover, SodsMPC accomplishes the contract \textit{business logic privacy} while protecting the contract user \textit{anonymous identity} simultaneously. We express the logic of a contract by a finite state machine (FSM). A state transition of the FSM is represented by a \textit{blind polynomial} with secret-shared coefficients. When using MPC to compute this blind polynomial, the contract business logic privacy is obtained. These coefficients which control the logic are binary secret shares. We also propose a base conversion method among binary and integer secret shares by MPC. Our contract anonymity comes from the ``mixing-then-contract'' paradigm. The online phase of the SodsMPC mixing is a multiplication between a preprocessed permutation matrix and an input vector in the form of secret sharing, which accomplishes a fully randomized shuffle of the inputs and keeps the secret share form for the following contract execution. All SodsMPC components, including a verifiable secret sharing scheme, are quantum-safe, asynchronous, coping with $t<n/3$ compromised servers, and robust (tolerates Byzantine servers) in both preprocessing and online phases.

Adaptor signatures (AS) are an extension of digital signatures that enable the encoding of a cryptographic hard problem (e.g., discrete logarithm) within the signature itself. An AS scheme ensures that (i) the signature can be created only by the user knowing the solution to the cryptographic problem; (ii) the signature reveals the solution itself; (iii) the signature can be verified with the standard verification algorithm. These properties have made AS a salient building block for many blockchain applications, in particular, off-chain payment systems such as payment-channel networks, payment-channel hubs, atomic swaps or discrete log contracts. Current AS constructions, however, are not secure against adversaries with access to a quantum computer. In this work, we present IAS, a construction for adaptor signatures that relies on standard cryptographic assumptions for isogenies, and builds upon the isogeny-based signature scheme CSI-FiSh. We formally prove the security of IAS against a quantum adversary. We have implemented IAS and our evaluation shows that IAS can be incorporated into current blockchains while requiring $\sim1500$ bytes of storage size on-chain and $\sim140$ milliseconds for digital signature verification. We also show how IAS can be seamlessly leveraged to build post-quantum off-chain payment applications without harming their security and privacy.

We provide a formal proof for the indifferentiability of SKINNY-HASH internal function from a random oracle. SKINNY-HASH is a family of function-based sponge hash functions, and it was selected as one of the second round candidates of the NIST lightweight cryptography competition. Its internal function is constructed from the tweakable block cipher SKINNY. The construction of the internal function is very simple and the designers claim $n$-bit security, where $n$ is the block length of SKINNY. However, a formal security proof of this claim is not given in the original specification of SKINNY-HASH. In this paper, we formally prove that the internal function of SKINNY-HASH has $n$-bit security, i.e., it is indifferentiable from a random oracle up to $O(2^n)$ queries, substantiating the security claim of the designers.

The contributions of this paper are twofold. First, we simplify the description of the Unbalanced Oil and Vinegar scheme (UOV) and its Rainbow variant, which makes it easier to understand the scheme and the existing attacks. We hope that this will make UOV and Rainbow more approachable for cryptanalysts. Secondly, we give two new attacks against the UOV and Rainbow signature schemes; the intersection attack that applies to both UOV and Rainbow and the rectangular MinRank attack that applies only to Rainbow. Our attacks are more powerful than existing attacks. In particular, we estimate that compared to previously known attacks, our new attacks reduce the cost of a key recovery by a factor of $2^{17}$, $2^{53}$, and $2^{73}$ for the parameter sets submitted to the second round of the NIST PQC standardization project targeting the security levels I, III, and V respectively. For the third round parameters, the cost is reduced by a factor of $2^{20}$, $2^{40}$, and $2^{55}$ respectively. This means all these parameter sets fall short of the security requirements set out by NIST.

Dynamic searchable symmetric encryption (SSE) supports updates and keyword searches in tandem on outsourced symmetrically encrypted data, while aiming to minimize the information revealed to the (untrusted) host server. The literature on dynamic SSE has identified two crucial security properties in this regard - forward and backward privacy. Forward privacy makes it hard for the server to correlate an update operation with previously executed search operations. Backward privacy limits the amount of information learnt by the server about documents that have already been deleted from the database. To date, work on forward and backward private SSE has focused mainly on single keyword search. However, for any SSE scheme to be truly practical, it should at least support conjunctive keyword search. In this setting, most prior SSE constructions with sub-linear search complexity do not support dynamic databases. The only exception is the scheme of Kamara and Moataz (EUROCRYPT'17); however it only achieves forward privacy. Achieving both forward and backward privacy, which is the most desirable security notion for any dynamic SSE scheme, has remained open in the setting of conjunctive keyword search. In this work, we develop the first forward and backward private SSE scheme for conjunctive keyword searches. Our proposed scheme, called Oblivious Dynamic Cross Tags (or ODXT in short) scales to very large arbitrarily-structured databases (including both attribute-value and free-text databases). ODXT provides a realistic trade-off between performance and security by efficiently supporting fast updates and conjunctive keyword searches over very large databases, while incurring only moderate access pattern leakages to the server that conform to existing notions of forward and backward privacy. We precisely define the leakage profile of ODXT, and present a detailed formal analysis of its security. We then demonstrate the practicality of ODXT by developing a prototype implementation and evaluating its performance on real world databases containing millions of documents.

We introduce a new primitive in information-theoretic cryptography, namely zero-communication reductions (ZCR), with different levels of security. We relate ZCR to several other important primitives, and obtain new results on upper and lower bounds. In particular, we obtain new upper bounds for PSM, CDS and OT complexity of functions, which are exponential in the information complexity of the functions. These upper bounds complement the results of Beimel et al. (2014) which broke the circuit-complexity barrier for ``high complexity'' functions; our results break the barrier of input size for ``low complexity'' functions. We also show that lower bounds on secure ZCR can be used to establish lower bounds for OT-complexity. We recover the known (linear) lower bounds on OT-complexity by Beimal and Malkin (2004) via this new route. We also formulate the lower bound problem for secure ZCR in purely linear-algebraic terms, by defining the invertible rank of a matrix. We present an Invertible Rank Conjecture, proving which will establish super-linear lower bounds for OT-complexity (and if accompanied by an explicit construction, will provide explicit functions with super-linear circuit lower bounds).

We report the homomorphic evaluation of the SM4 symmetric block-cipher based on BGV homomorphic encryption scheme. We implement bootstrapping and non-bootstrapping homomorphic evaluation of the 32-rounds SM4 based on HELib with about 128-bit security level. Our ways refer to and are similar as the AES homomorphic evaluation. The implementation uses packed ciphertexts and bytes in slots. The S-Box evaluation is similar as the AES evaluation method, and the Linear Transform layer uses the permutation of the bytes in states. Since the rounds are more than the AES and the SM4's feistel structer is different with the AES, the depths and levels of homomorphic evaluation of the SM4 are much more than AES, so need larger parameter(non-bootstrapping) and more bootstrapping. Our bootstrapping implementaion(3 ciphertexts, 360 blocks) runs about 1.5 hours on Macbook Pro(MacOS catalina 10.15, 16G), and the non-bootstrapping(1 ciphertext, 480 block) implementation runs about 6 hours on Macbook Pro(MacOS catalina 10.15, 16G).

Quantum copy protection uses the unclonability of quantum states to construct quantum software that provably cannot be pirated. Copy protection would be immensely useful, but unfortunately little is known about how to achieve it in general. In this work, we make progress on this goal, by giving the following results: –We show how to copy protect any program that cannot be learned from its input/output behavior, relative to a classical oracle. This improves on Aaronson [CCC’09], which achieves the same relative to a quantum oracle. By instantiating the oracle with post-quantum candidate obfuscation schemes, we obtain a heuristic construction of copy protection. –We show, roughly, that any program which can be watermarked can be copy detected, a weaker version of copy protection that does not prevent copying, but guarantees that any copying can be detected. Our scheme relies on the security of the assumed watermarking, plus the assumed existence of public key quantum money. Our construction is general, applicable to many recent watermarking schemes.

Abstract. In this paper, we present different implementations of point multiplication over Curve448. Curve448 has recently been recommended by NIST to provide 224-bit security over elliptic curve cryptography. Although implementing high-security cryptosystems should be considered due to recent improvements in cryptanalysis, hardware implementation of Curve488 has been investigated in a few studies. Hence, in this study, we propose three variable-base-point FPGA-based Curve448 implementations, i.e., lightweight, area-time efficient, and high-performance architectures, which aim to be used for different applications. Synthesized on a Xilinx Zynq 7020 FPGA, our proposed high-performance design increases 12% throughput with executing 1,219 point multiplication per second and increases 40% efficiency in terms of required clock cycles\timesutilized area compared to the best previous work. Furthermore, the proposed lightweight architecture works in 250 MHz and saves 96% of resources with the same performance. Additionally, our area-time efficient design considers a trade-off between time and required resources, which shows a 48% efficiency improvement with 52% fewer resources. Finally, effective side-channel countermeasures are added to our proposed designs, which also outperform previous works.

An extensive research of MPC protocols in different adversarial settings over the past few years has led to various improvements. Goyal et al.\cite{goyal2019communication} in their paper addressed the issue of an efficient MPC protocol in active adversarial setting by removing the dependency on multiplication depth $D_m$ in the arithmetic circuit. This development was followed by Hirt et al. in ITC 2020, which proposed an efficient MPC protocol tolerating mixed adversary with communication complexity of $O((c_i + c_m + c_o)n\kappa + c_iBA(\kappa) + D_m(n^3\kappa + nBA(\kappa)))$ bits, where $D_m$ is the multiplicative depth of the circuit and $\kappa$ is the size of an element in the field. Additionally, Hirt et al.\cite{hirt2020efficient}, proposed an open problem to construct a protocol for the mixed adversarial setting, independent of the multiplicative depth $D_m$, with linear communication complexity. In this paper, we resolve this problem in the affirmative by providing an efficient MPC protocol in the mixed adversarial setting independent of the multiplicative depth of the circuit.

Efficient computation of polynomial multiplication for characteristic three fields, $\mathbb{F}_{3^{n}}$ for $n\geq1$, is an important attribute for many cryptographic protocols. In this paper, we propose three new polynomial multiplication algorithms over $\mathbb{F}_{3}[x]$ and show that they are more efficient than the current state-of-the-art algorithms. We first examine through the well-known multiplication algorithms in $\mathbb{F}_{3}[x]$ including Karatsuba-2-way and 3-way split formulas along with the recent enhancements. Then, we propose a new 4-way split polynomial multiplication algorithm and an improved version of it which are both derived by using interpolation in $\mathbb{F}_{9}$. Moreover, we propose a 5-way split multiplication algorithm, and then compare the efficiencies of these algorithms altogether. We apply the proposed algorithms to the NTRU Prime protocol, a post-quantum key encapsulation mechanism (KEM), submitted to the NIST PQC Competition by Bernstein et al., performing polynomial multiplication in characteristic three fields in its decapsulation phase. We observe that the new hybrid algorithms provide a $12.9\%$ reduction in the arithmetic complexity. Furthermore, we implement these new hybrid methods on Intel (R) Core (TM) i7-9750H architecture using C and obtain a $37.3\%$ reduction in the implementation cycle count.

Homomorphic encryption (HE) is a promising cryptographic primitive that enables computation over encrypted data, with a variety of applications including medical, genomic, and financial tasks. In Asiacrypt 2017, Cheon et al. proposed the CKKS scheme to efficiently support approximate computation over encrypted data of real numbers. HE schemes including CKKS, nevertheless, still suffer from slow encryption speed and large ciphertext expansion compared to symmetric cryptography. In this paper, we propose a novel hybrid framework, dubbed RtF (Real-to-Finite-field) framework, that supports CKKS. The main idea behind this construction is to combine the CKKS and the FV homomorphic encryption schemes, and use a stream cipher using modular arithmetic in between. As a result, real numbers can be encrypted without significant ciphertext expansion or computational overload on the client side. As an instantiation of the stream cipher in our framework, we propose a new HE-friendly cipher, dubbed HERA, and extensively analyze its security and efficiency. The main feature of HERA is that it uses a simple randomized key schedule. Compared to recent HE-friendly ciphers such as FLIP and Rasta using randomized linear layers, HERA requires a smaller number of random bits. For this reason, HERA significantly outperforms existing HE-friendly ciphers on both the client and the server sides. With the RtF transciphering framework combined with HERA at the 128-bit security level, we achieve small ciphertext expansion ratio with a range of 1.23 to 1.54, which is at least 23 times smaller than using (symmetric) CKKS-only, assuming the same precision bits and the same level of ciphertexts at the end of the framework. We also achieve 1.6 $\mu$s and 21.7 MB/s for latency and throughput on the client side, which are 9085 times and 17.8 times faster than the CKKS-only environment, respectively.

The standard model security of the Fiat-Shamir transform has been an active research area for many years. In breakthrough results, Canetti et al. (STOC'19) and Peikert-Shiehian (Crypto'19) showed that, under the Learning-With-Errors (LWE) assumption, it provides soundness by applying correlation-intractable (CI) hash functions to so-called trapdoor $\Sigma$-protocols. In order to be compatible with CI hash functions based on standard LWE assumptions with polynomial approximation factors, all known such protocols have been obtained via parallel repetitions of a basic protocol with binary challenges. In this paper, we consider languages related to Paillier's composite residuosity assumption (DCR) for which we give the first trapdoor $\Sigma$-protocols providing soundness in one shot, via exponentially large challenge spaces. This improvement is analogous to the one enabled by Schnorr over the original Fiat-Shamir protocol in the random oracle model. Using the correlation-intractable hash function paradigm, we then obtain simulation-sound NIZK arguments showing that an element of $\mathbb{Z}_{N^2}^\ast$ is a composite residue, which opens the door to space-efficient applications in the standard model. As a concrete example, we build logarithmic-size ring signatures (assuming a common reference string) with the shortest signature length among schemes based on standard assumptions in the standard model. We prove security under the DCR and LWE assumptions, while keeping the signature size comparable with that of random-oracle-based schemes.

We propose an improvement for the inner product argument of Bootle et al. (EUROCRYPT’16). The new argument replaces the unstructured common reference string (the commitment key) by a structured one. We give two instantiations of this argument, for two different distributions of the CRS. In the designated verifier setting, this structure can be used to reduce verification from linear to logarithmic in the circuit size. The argument can be compiled to the publicly verifiable setting in asymmetric bilinear groups. The new common reference string can easily be updateable. The argument can be directly used to improve verification of Bulletproofs range proofs (IEEE SP’18). On the other hand, to use the improved argument to prove circuit satisfiability with logarithmic verification, we adapt recent techniques from Sonic (ACM CCS’19) to work with the new common reference string. The resulting argument is secure under standard assumptions (in the Random Oracle Model), in contrast with Sonic and recent works that improve its efficiency (Plonk, Marlin, AuroraLight), which, apart from the Random Oracle Model, need either the Algebraic Group Model or Knowledge Type assumptions.

Protecting the privacy of voters is a basic requirement of any electronic voting scheme, and formal definitions can be used to prove that a scheme satisfies privacy. In this work, we provide new game-based definitions of ballot secrecy for electronic voting schemes. First, we propose an intuitive definition in the honest model, i.e., a model in which all election officials are honest. Then, we show that this definition can be easily extended to the malicious ballot box setting and a setting that allows for a distributed tallier. In fact, to the best of our knowledge, we provide the first game-based definition of ballot secrecy that models both a malicious ballot box and a malicious subset of talliers. We demonstrate that our definitions of ballot secrecy are satisfiable, defining electronic voting scheme constructions which we prove satisfy our definitions. Finally, we revisit existing definitions, exploring their limitations and contextualising our contributions to the field.

The long term privacy of voting systems is of increasing concern as quantum computers come closer to reality. Everlasting privacy schemes offer the best way to manage these risks at present. While homomorphic tallying schemes with everlasting privacy are well developed, most national elections, using electronic voting, use mixnets. Currently the best candidate encryption scheme for making these kinds of elections everlastingly private is PPATC, but it has not been shown to work with any mixnet of comparable efficiency to the current ElGamal mixnets. In this work we give a paper proof, and a machine checked proof, that the variant of Wikstrom's mixnet commonly in use is safe for use with the PPATC encryption scheme.

In this work we introduce a novel four-party honest-majority MPC protocol with active security that achieves comparable efficiency to equivalent protocols in the same setting, while having a much simpler design and not relying on function-dependent preprocessing. Our initial protocol satisfies security with abort, but we present some extensions to achieve guaranteed output delivery. Unlike previous works, we do not achieve this by delegating the computation to one single party that is identified to be honest, which is likely to hinder the adoption of these technologies as it centralizes sensitive data. Instead, our novel approach guarantees termination of the protocol while ensuring that no single party (honest or corrupt) learns anything beyond the output. We implement our four-party protocol with abort in the MP-SPDZ framework for multiparty computation and benchmark multiple applications like MNIST classification training and ImageNet inference. Our results show that our four-party protocol performs similarly to an efficient honest-majority three-party protocol that only provides semi-honest/passive security, which suggest that adding a fourth party can be an effective method to achieve active security without harming performance.

In a threshold symmetric-key encryption (TSE) scheme, encryption/decryption is performed by interacting with any threshold number of parties who hold parts of the secret-keys. Security holds as long as the number of corrupt (possibly colluding) parties stay below the threshold. Recently, Agrawal et al. [CCS 2018] (alternatively called DiSE) initiated the study of TSE. They proposed a generic TSE construction based on any distributed pseudorandom function (DPRF). Instantiating with DPRF constructions by Naor, Pinkas and Reingold [Eurocrypt 1999] (also called NPR) they obtained several efficient TSE schemes with various merits. However, their security models and corresponding analyses consider only static (and malicious) corruption, in that the adversary fixes the set of corrupt parties in the beginning of the execution before acquiring any information (except the public parameters) and is not allowed to change that later. In this work we augment the DiSE TSE definitions to the fully adaptive (and malicious) setting, in that the adversary is allowed to corrupt parties dynamically at any time during the execution. The adversary may choose to corrupt a party depending on the information acquired thus far, as long as the total number of corrupt parties stays below the threshold. We also augment DiSE’s DPRF definitions to support adaptive corruption. We show that their generic TSE construction, when plugged-in with an adaptive DPRF (satisfying our definition), meets our adaptive TSE definitions. We provide an efficient instantiation of the adaptive DPRF, proven secure assuming decisional Diffie-Hellman assumption (DDH), in the random oracle model. Our construction borrows ideas from Naor, Pinkas and Reingold’s [Eurocrypt 1999] statically secure DDH-based DPRF (used in DiSE) and Libert, Joye and Yung’s [PODC 2014] adaptively secure threshold signature. Similar to DiSE, we also give an extension satisfying a strengthened adaptive DPRF definition, which in turn yields a stronger adaptive TSE scheme. For that, we construct a simple and efficient adaptive NIZK protocol for proving a specific commit-and-prove style statement in the random oracle model assuming DDH.

This paper initiates a new direction in the design and analysis of searchable symmetric encryption (SSE) schemes. We provide the first comprehensive security model and definition for SSE that takes into account leakage from the entirety of the SSE system, including not only from access to encrypted indices but also from access to the encrypted database documents themselves. Such system-wide leakage is intrinsic in end-to-end SSE systems, and can be used to break almost all state-of-the-art SSE schemes (Gui et al., IEEE S&P 2023). We then provide static and dynamic SSE constructions targeting our new notions. Our constructions involve a combination of novel techniques: bucketization to hide volumes of responses to queries; delayed, pseudorandom write-backs to disrupt access patterns; and indistinguishable search and update operations. The oblivious operations make it easy to establish strong versions of forward and backward security for our dynamic SSE scheme and rule out file-injection attacks. We implement our schemes and demonstrate that they offer very strong security against general classes of (system-wide) leakage-abuse attacks with moderate overhead. Our schemes scale smoothly to databases containing hundreds of thousand of documents and millions of keyword-document pairs. To the best of our knowledge, these are the first end-to-end SSE schemes that effectively suppress system-wide leakage while maintaining practical efficiency.

The Messaging Layer Security (MLS) protocol is an open standard for end-to-end (E2E) secure group messaging being developed by the IETF poised for deployment to consumers, industry, and government. It is designed to provide E2E privacy and authenticity for messages in long lived sessions whenever possible despite the participation (at times) of malicious insiders that can adaptively interact with the PKI at will, actively deviate from the protocol, leak honest parties' states, and fully control the network. The core of the MLS protocol (from which it inherits essentially all of its efficiency and security properties) is a Continuous Group Key Agreement (CGKA) protocol. It provides asynchronous E2E group management by allowing group members to agree on a fresh independent symmetric key after every change to the group's state (e.g. when someone joins/leaves the group). In this work, we make progress towards a precise understanding of the insider security of MLS (Draft 12). On the theory side, we overcome several subtleties to formulate the first notion of insider security for CGKA (or group messaging). Next, we isolate the core components of MLS to obtain a CGKA protocol we dub Insider Secure TreeKEM (ITK). Finally, we give a rigorous security proof for ITK. In particular, this work also initiates the study of insider secure CGKA and group messaging protocols. Along the way we give three new (very practical) attacks on MLS and corresponding fixes. (Those fixes have now been included into the standard.) We also describe a second attack against MLS-like CGKA protocols proven secure under all previously considered security notions (including those designed specifically to analyze MLS). These attacks highlight the pitfalls in simplifying security notions even in the name of tractability.

Constructing one-way functions from average-case hardness is a long-standing open problem. A positive result would exclude Pessiland (Impagliazzo ’95) and establish a highly desirable win-win situation: either (symmetric) cryptography exists unconditionally, or all NP problems can be solved efficiently on the average. Motivated by the lack of progress on this seemingly very hard question, we initiate the investigation of weaker yet meaningful candidate win-win results of the following type: either there are fine-grained one-way functions (FGOWF), or nontrivial speedups can be obtained for all NP problems on the average. FGOWFs only require a fixed polynomial gap (as opposed to superpolynomial) between the running time of the function and the running time of an inverter. We obtain three main results: Construction. We show that if there is an NP language having a very strong form of average-case hardness, which we call block finding hardness, then FGOWF exist. We provide heuristic support for this very strong average-case hardness notion by showing that it holds for a random language. Then, we study whether weaker (and more natural) forms of average-case hardness could already suffice to obtain FGOWF, and obtain two negative results: Separation I. We provide a strong oracle separation for the implication (∃ exponentially average-case hard NP language ⇒ ∃ FGOWF). Separation II. We provide a second strong negative result for an even weaker candidate win-win result. Namely, we rule out a relativizing proof for the implication (∃ exponentially average-case NP hard language whose hardness amplifies optimally through parallel repetitions ⇒ ∃ FGOWF). This separation forms the core technical contribution of our work.

All academic methods to secure software implementations of block ciphers against adversaries with full control of the device have been broken. Despite the huge progress in the cryptanalysis of these white-box implementations, no recent progress has been made on the design side. Most of the white-box designs follow the CEJO framework, where each round is encoded by composing it with small random permutations. While several generic attacks have been proposed on the CEJO framework, no generic analysis has been performed on self-equivalence encodings, a different design where only the affine layer of each round is encoded with random self-equivalences of the S-box layer, that is, affine permutations commuting with the non-linear layer. In this work, we analyse the security of white-box implementations based on self-equivalence encodings for a broad class of SPN ciphers. First, we characterize the self-equivalence groups of S-box layers, and we prove that all the self-equivalences of a cryptographically strong S-box layer have a diagonal shape. Then, we propose the first generic attack on self-equivalence encodings. Our attack, based on affine equivalence problems, identifies the connection between the security of self-equivalence encodings and the self-equivalence structure of the cipher components. While we show that traditional SPN ciphers with cryptographically strong S-box layers cannot be secured with self-equivalence encodings, our analysis shows that self-equivalence encodings resist the generic attack if the cipher components satisfy several conditions, revealing the potential of self-equivalence encodings to secure other types of ciphers.

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In particular, we show (almost) separation of several classes of Boolean functions which have been studied in the coding theory and cryptography from classes which have been studied in combinatorics and complexity theory.

We present an honest-majority Distributed Key Generation protocol (DKG) based on Shamir's $(k,n)$-threshold secret sharing in the setting of Very Hard Homogenous Spaces (VHHS). DKG's in the DLOG setting use Pedersen commitments, for which there is no known analogue in the VHHS setting. As a replacement, we introduce a new primitive called piecewise verifiable proofs, which allow a prover to prove that a list of NP-statements is valid with respect to a common witness, and such that the different statements can be verified individually. Our protocol is robust and actively secure in the Quantum Random Oracle Model. For $n$ participants, the total runtime of our protocol is\break $2+\lambda+n(1+4\lambda)$ group action evaluations, where $\lambda$ is the underlying security parameter, and is thus independent of the threshold $k$. When instantiated with CSIDH-512, this amounts to approximately $4.5+18n$ seconds.

The threat of a cryptographically relevant quantum computer contributes to an increasing interest in the field of post-quantum cryptography (PQC). Compared to existing research efforts regarding the integration of PQC into the Transport Layer Security (TLS) protocol, industrial communication protocols have so far been neglected. Since industrial cyber-physical systems (CPS) are typically deployed for decades, protection against such long-term threats is needed. In this work, we propose two novel solutions for the integration of post-quantum (PQ) primitives (digital signatures and key establishment) into the industrial protocol Open Platform Communications Unified Architecture (OPC UA): a hybrid solution combining conventional cryptography with PQC and a solution solely based on PQC. Both approaches provide mutual authentication between client and server and are realized with certificates fully compliant to the X.509 standard. Moreover, we implement the two solutions and measure and evaluate their performance across three different security levels. All selected algorithms (Kyber, Dilithium, and Falcon) are candidates for standardization by the National Institute of Standards and Technology (NIST). We show that Falcon is a suitable option—especially—when using floating-point hardware provided by our ARM-based evaluation platform. Our proposed hybrid solution provides PQ security for early adopters but comes with additional performance and communication requirements. Our solution solely based on PQC shows superior performance across all evaluated security levels in terms of handshake duration compared to conventional OPC UA but comes at the cost of increased sizes for handshake messages.

Recent results on quantum cryptanalysis show that some symmetric key schemes can be broken in polynomial time even if they are proven to be secure in the classical setting. Liskov, Rivest, and Wagner showed that secure tweakable block ciphers can be constructed from secure block ciphers in the classical setting. However, Kaplan et al.~showed that their scheme can be broken by polynomial time quantum superposition attacks, even if underlying block ciphers are quantum-secure. Since then, it remains open if there exists a mode of block ciphers to build quantum-secure tweakable block ciphers. This paper settles the problem in the reduction-based provable security paradigm. We show the first design of quantum-secure tweakable block ciphers based on quantum-secure block ciphers, and present a provable security bound. Our construction is simple, and when instantiated with a quantum-secure $n$-bit block cipher, it is secure against attacks that query arbitrary quantum superpositions of plaintexts and tweaks up to $O(2^{n/6})$ quantum queries. Our security proofs use the compressed oracle technique introduced by Zhandry. More precisely, we use an alternative formalization of the technique introduced by Hosoyamada and Iwata.

In this article, we present WARP, a lightweight 128-bit block cipher with a 128-bit key. It aims at small-footprint circuit in the field of 128-bit block ciphers, possibly for a unified encryption and decryption functionality. The overall structure of WARP is a variant of 32-nibble Type-2 Generalized Feistel Network (GFN), with a permutation over nibbles designed to optimize the security and efficiency. We conduct a thorough security analysis and report comprehensive hardware and software implementation results. Our hardware results show that WARP is the smallest 128-bit block cipher for most of typical hardware implementation strategies. A serialized circuit of WARP achieves around 800 Gate Equivalents (GEs), which is much smaller than previous state-of-the-art implementations of lightweight 128-bit ciphers (they need more than $1,000$ GEs). While our primary metric is hardware size, WARP also enjoys several other features, most notably low energy consumption. This is somewhat surprising, since GFN generally needs more rounds than substitution permutation network (SPN), and thus GFN has been considered to be less advantageous in this regard. We show a multi-round implementation of WARP is quite low-energy. Moreover, WARP also performs well on software: our SIMD implementation is quite competitive to known hardware-oriented 128-bit lightweight ciphers for long input, and even much better for small inputs due to the small number of parallel blocks. On 8-bit microcontrollers, the results of our assembly implementations show that WARP is flexible to achieve various performance characteristics.

Succinct non-interactive arguments (SNARGs) enable proofs of NP statements with very low communication. Recently, there has been significant work in both theory and practice on constructing SNARGs with very short proofs. Currently, the state-of-the-art in succinctness is due to Groth (Eurocrypt 2016) who constructed a SNARG from bilinear maps where the proof consists of just 3 group elements. In this work, we first construct a concretely-efficient designated-verifier (preprocessing) SNARG with inverse polynomial soundness, where the proof consists of just 2 group elements in a standard (generic) group. This leads to a 50% reduction in concrete proof size compared to Groth's construction. We follow the approach of Bitansky et al. (TCC 2013) who describe a compiler from linear PCPs to SNARGs in the preprocessing model. Our improvement is based on a new linear PCP packing technique that allows us to construct 1-query linear PCPs which can then be compiled into a SNARG (using ElGamal encryption over a generic group). An appealing feature of our new SNARG is that the verifier can precompute a statement-independent lookup table in an offline phase; verifying proofs then only requires 2 exponentiations and a single table lookup. This makes our new designated-verifier SNARG appealing in settings that demand fast verification and minimal communication. We then turn to the question of constructing arguments where the proof consists of a single group element. Here, we first show that any (possibly interactive) argument for a language L where the verification algorithm is "generic" (i.e., only performs generic group operations) and the proof consists of a single group element, implies a witness encryption scheme for L. We then show that under a yet-unproven, but highly plausible, hypothesis on the hardness of approximating the minimal distance of linear codes, we can construct a 2-message laconic argument for NP where the proof consists of a single group element. Under the same hypothesis, we obtain a witness encryption scheme for NP in the generic group model. Along the way, we show that under a conceptually-similar but proven hardness of approximation result, there is a 2-message laconic argument for NP with negligible soundness error where the prover's message consists of just 2 group elements. In both settings, we obtain laconic arguments (and linear PCPs) with linear decision procedures. Our constructions circumvent a previous lower bound by Groth on such argument systems with linear decision procedures by relying on imperfect completeness. Namely, our constructions have vanishing but not negligible completeness error, while the lower bound of Groth implicitly assumes negligible completeness error of the underlying argument. Our techniques thus highlight new avenues for designing linear PCPs, succinct arguments, and witness encryption schemes.

We present Poppins, a direct construction of a zero-knowledge argument system for general computation that features an $O_{\lambda}(n)$ time prover and an $O_{\lambda}(1)$ time verifier (after a single $O_{\lambda}(n)$ public setup) for computations of size $n$. Our scheme utilizes a universal linear-size structured reference string (SRS) that allows a single trusted setup to be used across all computation instances of a bounded size. Concretely, for computations of size $n$, our prover's cost is dominated by $35$ multi-exponentiations of size $n$ and our verifier's cost is dominated by $34$ pairings. To achieve the stated asymptotics, we first construct a nearly-optimal zkSNARK with a logarithmic verifier in the random oracle model. We then show how to achieve a constant-time verifier using (single-layer) proof composition. Along the way we design (1) a new polynomial commitment scheme for evaluation-based representations of polynomials, (2) an asymptotically optimal inner-product argument system, (3) an asymptotically optimal multi-Hadamard-product argument system, and (4)~a new constraint system for NP that is particularly well-suited for our bundle of techniques.

The boomerang and rectangle attacks are adaptions of differential cryptanalysis that regard the target cipher $E$ as a composition of two sub-ciphers, i.e., $E = E_{1}\circ E_{0}$, to construct a distinguisher for $E$ with probability $p^{2}q^{2}$ by concatenating two short differential trails for $E_{0}$ and $E_{1}$ with probability $p$ and $q$ respectively. According to the previous research, the dependency between these two differential characteristics has a great impact on the probability of boomerang and rectangle distinguishers. Dunkelman et al. proposed the sandwich attack to formalise such dependency that regards $E$ as three parts, i.e., $E = E_{1}\circ E_{m}\circ E_{0}$, where $E_{m}$ contains the dependency between two differential trails, satisfying some differential propagation with probability $r$. Accordingly, the entire probability is $p^{2}q^{2}r$. Recently, Song et al. have proposed a general framework to identify the actual boundaries of $E_{m}$ and systematically evaluate the probability of $E_{m}$ with any number of rounds, and applied their method to accurately evaluate the probabilities of the best SKINNY's boomerang distinguishers. In this paper, using a more advanced method to search for boomerang distinguishers, we show that the best previous boomerang distinguishers for SKINNY can be significantly improved in terms of probability and number of rounds. More precisely, we propose related-tweakey boomerang distinguishers for up to 19, 21, 23, and 25 rounds of SKINNY-64-128, SKINNY-128-256, SKINNY-64-192 and SKINNY-128-384 respectively, which improve the previous boomerang distinguishers of these variants of SKINNY by 1, 2, 1, and 1 round respectively. Based on the improved boomerang distinguishers for SKINNY, we provide related-tweakey rectangle attacks on 23 rounds of SKINNY-64-128, 24 rounds of SKINNY-128-256, 29 rounds of SKINNY-64-192, and 30 rounds of SKINNY-128-384. It is worth noting that our improved related-tweakey rectangle attacks on SKINNY-64-192, SKINNY-128-256 and SKINNY-128-384 can be directly applied for the same number of rounds of ForkSkinny-64-192, ForkSkinny-128-256 and ForkSkinny-128-384 respectively. CRAFT is another SKINNY-like tweakable block cipher for which we provide the security analysis against rectangle attack for the first time. As a result, we provide a 14-round boomerang distinguisher for CRAFT in the single-tweak model based on which we propose a single-tweak rectangle attack on 18 rounds of this cipher. Moreover, following the previous research regarding the evaluation of switching in multiple rounds of boomerang distinguishers, we also introduce new tools called Double Boomerang Connectivity Table $\tt{DBCT}$, $\tt{LBCT}^{\scriptsize{=}|}$, and $\tt{UBCT}^{\vDash}$ to evaluate the boomerang switch through the multiple rounds more accurately.

Ciphertext indistinguishability under chosen plaintext attacks is a standard security notion for public key encryption. It crucially relies on the usage of good randomness and is trivially unachievable if the randomness is known by the adversary. Yilek (CT-RSA'10) defined security against resetting attacks, where randomness might be reused but remains unknown to the adversary. Furthermore, Yilek claimed that security against adversaries making a single query to the challenge oracle implies security against adversaries making multiple queries to the challenge oracle. This is a typical simplification for indistinguishability security notions proven via a standard hybrid argument. The given proof, however, was pointed out to be flawed by Paterson, Schuldt, and Sibborn (PKC'14). Prior to this work, it has been unclear whether this simplification of the security notion also holds in case of resetting attacks. We remedy this state of affairs as follows. First, we show the strength of resetting attacks by showing that many public key encryption schemes are susceptible to these attacks. As our main contribution, we show that the simplification to adversaries making only one query to the challenge oracle also holds in the light of resetting attacks. More precisely, we show that the existing proof can not be fixed and give a different proof for the claim. Finally, we define real-or-random security against resetting attacks and prove it equivalent to the notion by Yilek which is of the form left-or-right.

In this paper we further the study of index calculus methods for solving the elliptic curve discrete logarithm problem (ECDLP). We focus on the index calculus for subfield curves, also called Koblitz curves, defined over $\mathbb{F}_q$ with ECDLP in $\mathbb{F}_{q^n}$. Instead of accelerating the solution of polynomial systems during index calculus as was predominantly done in previous work, we define factor bases that are invariant under the $q$-power Frobenius automorphism of the field $\mathbb{F}_{q^n}$, reducing the number of polynomial systems that need to be solved. A reduction by a factor of $1/n$ is the best one could hope for. We show how to choose factor bases to achieve this, while simultaneously accelerating the linear algebra step of the index calculus method for Koblitz curves by a factor $n^2$. Furthermore, we show how to use the Frobenius endomorphism to improve symmetry breaking for Koblitz curves. We provide constructions of factor bases with the desired properties, and we study their impact on the polynomial system solving costs experimentally. This work gives an answer to the problem raised in the literature on how the Frobenius endomorphism can be used to speed-up index calculus on subfield curves.

Secure software leasing (SSL) is a quantum cryptographic primitive that enables an authority to lease software to a user by encoding it into a quantum state. SSL prevents users from generating authenticated pirated copies of leased software, where authenticated copies indicate those run on legitimate platforms. Although SSL is a relaxed variant of quantum copy protection that prevents users from generating any copy of leased softwares, it is still meaningful and attractive. Recently, Ananth and La Placa proposed the first SSL scheme. It satisfies a strong security notion called infinite-term security. On the other hand, it has a drawback that it is based on public key quantum money, which is not instantiated with standard cryptographic assumptions so far. Moreover, their scheme only supports a subclass of evasive functions. In this work, we present SSL schemes that satisfy a security notion called finite-term security based on the learning with errors assumption (LWE). Finite-term security is weaker than infinite-term security, but it still provides a reasonable security guarantee. Specifically, our contributions consist of the following. - We construct a finite-term secure SSL scheme for pseudorandom functions from the LWE assumption against quantum adversaries. - We construct a finite-term secure SSL scheme for a subclass of evasive functions from the LWE assumption against sub-exponential quantum adversaries. - We construct finite-term secure SSL schemes for the functionalities above with classical communication from the LWE assumption against (sub-exponential) quantum adversaries. SSL with classical communication means that entities exchange only classical information though they run quantum computation locally. Our crucial tool is two-tier quantum lightning, which is introduced in this work and a relaxed version of quantum lighting. In two-tier quantum lightning schemes, we have a public verification algorithm called semi-verification and a private verification algorithm called full-verification. An adversary cannot generate possibly entangled two quantum states whose serial numbers are the same such that one passes the semi-verification, and the other also passes the full-verification. We show that we can construct a two-tier quantum lightning scheme from the LWE assumption.

The security of blockchain based decentralized ledgers relies on consensus protocols executed between mutually distrustful parties. Such protocols incur delays which severely limit the throughput of such ledgers. Payment and state channels enable execution of offchain protocols that allow interaction between parties without involving the consensus protocol. Protocols such as Hashed Timelock Contracts (HTLC) and Sprites (FC'19) connect channels into Payment Channel Networks (PCN) allowing payments across a path of payment channels. Such a payment requires each party to lock away funds for an amount of time. The product of funds and locktime is the collateral of the party, i.e., their cost of opportunity to forward a payment. In the case of HTLC, the locktime is linear to the length of the path, making the total collateral invested across the path quadratic in size of its length. Sprites improved on this by reducing the locktime to a constant by utilizing smart contracts. Atomic Multi-Channel Updates (AMCU), published at CCS'19, introduced constant collateral payments without smart contracts. In this work we present the Channel Closure attack on AMCU that allows a malicious adversary to make honest parties lose funds. Furthermore, we propose the Payment Trees protocol that allows payments across a PCN with linear total collateral without the aid of smart contracts; a competitive performance similar to Sprites, and yet compatible to Bitcoin.

We develop an individual simulation technique that explicitly makes use of particular properties/structures of a given adversary's functionality. Using this simulation technique, we obtain the following results. 1. We construct the first protocols that \emph{break previous black-box barriers} of [Xiao, TCC'11 and Alwen et al., Crypto'05] under the standard hardness of factoring, both of which are polynomial time simulatable against all a-priori bounded polynomial size distinguishers: -- Two-round selective opening secure commitment scheme. -- Three-round concurrent zero knowledge and concurrent witness hiding argument for NP in the bare public-key model. 2. We present a simpler two-round weak zero knowledge and witness hiding argument for NP in the plain model under the sub-exponential hardness of factoring. Our technique also yields a significantly simpler proof that existing distinguisher-dependent simulatable zero knowledge protocols are also polynomial time simulatable against all distinguishers of a-priori bounded polynomial size. The core conceptual idea underlying our individual simulation technique is an observation of the existence of nearly optimal extractors for all hard distributions: For any NP-instance(s) sampling algorithm, there exists a polynomial-size witness extractor (depending on the sampler's functionality) that almost outperforms any circuit of a-priori bounded polynomial size in terms of the success probability.

Format-Preserving Encryption (FPE) is a method to encrypt non-standard domains, thus allowing for securely encrypting not only binary strings, but also special domains, e.g., social security numbers into social security numbers. The need for those resulted in a few standardized constructions such as the NIST standardized FF1 and FF3-1 and the Korean Standards FEA-1 and FEA-2. Moreover, there are currently efforts both in ANSI and in ISO to include such block ciphers to standards (e.g., the ANSI X9.124 discussing encryption for financial services). Most of the proposed FPE schemes, such as the NIST standardized FF1 and FF3-1 and the Korean Standards FEA-1 and FEA-2, are based on a Feistel construction with pseudo-random round functions. Moreover, to mitigate enumeration attacks against the possibly small domains, they all employ tweaks, which enrich the actual domain sizes. In this paper we present distinguishing attacks against Feistel-based FPEs. We show a distinguishing attack against the full FF1 with data complexity of $2^{60}$ 20-bit plaintexts, against the full FF3-1 with data complexity of $2^{40}$ 20-bit plaintexts. For FEA-1 with 128-bit, 192-bit and 256-bit keys, the data complexity of the distinguishing attack is $2^{32}$, $2^{40}$, and $2^{48}$ 8-bit plaintexts, respectively. The data complexity of the distinguishing attack against the full FEA-2 with 128-bit, 192-bit and 256-bit is $2^{56}$, $2^{68}$, and $2^{80}$ 8-bit plaintexts, respectively. Moreover, we show how to extend the distinguishing attack on FEA-1 and FEA-2 using 192-bit and 256-bit keys into key recovery attacks with time complexity $2^{136}$ (for both attacks).

In this short note we analyze the low order assumption in the imaginary quadratic number fields. We show how this assumption is broken for Mersenne primes. We also provide a description on how to possible attack this assumption for other class of prime numbers leveraging some new mathematical tool coming from higher (cubic) number fields.

Automated contact tracing leverages the ubiquity of smartphones to warn users about an increased exposure risk to COVID-19. In the course of only a few weeks, several cryptographic protocols have been proposed that aim to achieve such contract tracing in a decentralized and privacy-preserving way. Roughly, they let users' phones exchange random looking pseudonyms that are derived from locally stored keys. If a user is diagnosed, her phone uploads the keys which allows other users to check for any contact matches. Ultimately this line of work led to Google and Apple including a variant of these protocols into their phones which is currently used by millions of users. Due to the obvious urgency, these schemes were pushed to deployment without a formal analysis of the achieved security and privacy features. In this work we address this gap and provide the first formal treatment of such decentralized cryptographic contact tracing. We formally define three main properties in a game-based manner: pseudonym and trace unlinkability to guarantee the privacy of users during healthy and infectious periods, and integrity ensuring that triggering false positive alarms is infeasible. A particular focus of our work is on the timed aspects of these schemes, as both keys and pseudonyms are rotated regularly, and we specify different variants of the aforementioned properties depending on the time granularity for which they hold. We analyze a selection of practical protocols (DP-3T, TCN, GAEN) and prove their security under well-defined assumptions.

As lattice-based key encapsulation, digital signature, and fully homomorphic encryption schemes near standardisation, ever more focus is being directed to the precise estimation of the security of these schemes. The primal attack reduces key recovery against such schemes to instances of the unique Shortest Vector Problem (uSVP). Dachman-Soled et al. (Crypto 2020) recently proposed a new approach for fine-grained estimation of the cost of the primal attack when using Progressive BKZ for lattice reduction. In this paper we review and extend their technique to BKZ 2.0 and provide extensive experimental evidence of its accuracy. Using this technique we also explain results from previous primal attack experiments by Albrecht et al. (Asiacrypt 2017) where attacks succeeded with smaller than expected block sizes. Finally, we use our simulators to reestimate the cost of attacking the three lattice KEM finalists of the NIST Post Quantum Standardisation Process.

Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than $n-t$, where $n$ is the size of the sets and $t$ is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold $t$ and not on the sizes of the input sets. Current Threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of Threshold PSI is the former part. In this work, we present a new Cardinality Testing protocol that allows $N$ parties to check if the intersection of their input sets is larger than $n-t$. The protocol incurs in $\tilde{ \mathcal{O}} (Nt^2)$ communication complexity. We thus obtain a Threshold PSI scheme for $N$ parties with communication complexity $\tilde{ \mathcal{O}}(Nt^2)$.

Zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) are the most efficient proof systems in terms of proof size and verification. Currently, Groth's scheme from EUROCRYPT 2016, $\textsf{Groth16}$, is the state-of-the-art and is widely deployed in practice. $\mathsf{Groth16}$ is originally proven to achieve knowledge soundness, which does not guarantee the non-malleability of proofs. There has been considerable progress in presenting new zk-SNARKs or modifying $\mathsf{Groth16}$ to efficiently achieve $\textit{strong}$ Simulation Extractability (SE), which is shown to be a necessary requirement in some applications. In this paper, we revise the Random Oracle (RO) based variant of $\mathsf{Groth16}$ proposed by Bowe and Gabizon, BG18, the most efficient one in terms of prover efficiency and CRS size among the candidates, and present a more efficient variant that saves $2$ pairings in the verification and $1$ group element in the proof. This supersedes our preliminary construction, presented in CANS 2020 [BPR20], which saved 1 pairing in the verification, and was proven in the Generic Group Model (GGM). Our new construction also improves on BG18 in that our proofs are in the Algebraic Group Model (AGM) with Random Oracles and reduces security to standard computational assumptions in bilinear groups (as opposed to using the full power of the GGM). We implement our proposed SE zk-SNARK along with BG18 in the $\textsf{Arkworks}$ library and compare the efficiency of our scheme with some related works. Our empirical experiences confirm that our SE zk-SNARK is more efficient than all previous SE schemes in most dimensions and it has very close efficiency to the original $\mathsf{Groth16}$.

We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). This technique has proven to be very powerful for reproving known lower bound results, but also for proving new results that seemed to be out of reach before. Despite being very useful, it is however still quite cumbersome to actually employ the compressed oracle technique. To start off with, we offer a concise yet mathematically rigorous exposition of the compressed oracle technique. We adopt a more abstract view than other descriptions found in the literature, which allows us to keep the focus on the relevant aspects. Our exposition easily extends to the parallel-query QROM, where in each query-round the considered quantum oracle algorithm may make several queries to the QROM in parallel. This variant of the QROM allows for a more fine-grained query-complexity analysis of quantum oracle algorithms. Our main technical contribution is a framework that simplifies the use of (the parallel-query generalization of) the compressed oracle technique for proving query complexity results. With our framework in place, whenever applicable, it is possible to prove quantum query complexity lower bounds by means of purely classical reasoning. More than that, we show that, for typical examples, the crucial classical observations that give rise to the classical bounds are sufficient to conclude the corresponding quantum bounds. We demonstrate this on a few examples, recovering known results (like the optimality of parallel Grover), but also obtaining new results (like the optimality of parallel BHT collision search). Our main application is to prove hardness of finding a $q$-chain, i.e., a sequence $x_0,x_1,\ldots,x_q$ with the property that $x_i = H(x_{i-1})$ for all $1 \leq i \leq q$, with fewer than $q$ parallel queries. The above problem of producing a hash chain is of fundamental importance in the context of proofs of sequential work. Indeed, as a concrete application of our new bound, we prove that the ``Simple Proofs of Sequential Work" proposed by Cohen and Pietrzak remain secure against quantum attacks. Such a proof is not simply a matter of plugging in our new bound; the entire protocol needs to be analyzed in the light of a quantum attack, and substantial additional work is necessary. Thanks to our framework, this can now be done with purely classical reasoning.

It was long thought that symmetric cryptography was only mildly affected by quantum attacks, and that doubling the key length was sufficient to restore security. However, recent works have shown that Simon's quantum period finding algorithm breaks a large number of MAC and authenticated encryption algorithms when the adversary can query the MAC/encryption oracle with a quantum superposition of messages. In particular, the OCB authenticated encryption mode is broken in this setting, and no quantum-secure mode is known with the same efficiency (rate-one and parallelizable). In this paper we generalize the previous attacks, show that a large class of OCB-like schemes is unsafe against superposition queries, and discuss the quantum security notions for authenticated encryption modes. We propose a new rate-one parallelizable mode named QCB inspired by TAE and OCB and prove its security against quantum superposition queries.

There are currently over 30 billion IoT (Internet of Things) devices installed worldwide. To secure these devices from various threats one often relies on public-key cryptographic primitives whose operations can be costly to compute on resource-constrained IoT devices. To support such operations these devices often include a dedicated co-processor for cryptographic procedures, typically in the form of a big integer arithmetic unit. Such existing arithmetic co-processors do not offer the functionality that is expected by upcoming post-quantum cryptographic primitives. Regardless, contemporary systems may exist in the field for many years to come. In this paper we propose the Kronecker+ algorithm for polynomial multiplication in rings of the form Z[X]/(X^n+1): the arithmetic foundation of many lattice-based cryptographic schemes. We discuss how Kronecker+ allows for re-use of existing co-processors for post-quantum cryptography, and in particular directly applies to the various finalists in the post-quantum standardization effort led by NIST. We demonstrate the effectiveness of our algorithm in practice by integrating Kronecker+ into Saber: one of the finalists in the ongoing NIST standardization effort. On our target platform, a RV32IMC with access to a dedicated arithmetic co-processor designed to accelerate RSA and ECC, Kronecker+ performs the matrix multiplication 2.8 times faster than regular Kronecker substitution and 1.7 times faster than Harvey's negated-evaluation-points method.

Lattice-based NIST PQC finalists need efficient multiplication in $\mathbb{Z}_q[x]/(f(x))$. Multiplication in this ring can be performed very efficiently via number theoretic transform (NTT) as done in CRYSTALS-Kyber if the parameters of the scheme allow it. If NTT is not supported, other multiplication algorithms must be employed. For example, if the modulus $q$ of the scheme is a power of two, as in Saber and NTRU, then NTT can not be used directly. In this case, Karatsuba and Toom-Cook methods together with modular reduction, are commonly used for multiplication in this ring. In this paper, we show that the Toeplitz matrix-vector product (TMVP) representation of modular polynomial multiplication yields better results than Karatsuba and Toom-Cook methods. We present three- and four-way TMVP formulas derived from three- and four-way Toom-Cook algorithms, respectively. We use the four-way TMVP formula to develop an algorithm for multiplication in the ring $\mathbb{Z}_{2^m}[x]/(x^{256}+1)$. We implement the proposed algorithm on the ARM Cortex-M4 microcontroller and apply it to Saber, one of the lattice-based finalists of the NIST PQC competition. We compare the results to previous implementations. The TMVP-based multiplication algorithm we propose is $20.83\%$ faster than the previous algorithm that uses a combination of Toom-Cook, Karatsuba, and schoolbook methods. Our algorithm also speeds up key generation, encapsulation, and decapsulation algorithms of all variants of Saber. The speedups vary between $4.3-39.8\%$. Moreover, our algorithm requires less memory than the others, except for the memory-optimized implementation of Saber.

Robust property-preserving hash (PPH) functions, recently introduced by Boyle, Lavigne, and Vaikuntanathan [ITCS 2019], compress large inputs $x$ and $y$ into short digests $h(x)$ and $h(y)$ in a manner that allows for computing a predicate $P$ on $x$ and $y$ while only having access to the corresponding hash values. In contrast to locality-sensitive hash functions, a robust PPH function guarantees to correctly evaluate a predicate on $h(x)$ and $h(y)$ even if $x$ and $y$ are chosen adversarially after seeing $h$. Our main result is a robust PPH function for the exact hamming distance predicate $$\mathsf{HAM}^t(x, y) = \begin{cases}1 &\text{if } d( x, y) \geq t \\0 & \text{Otherwise}\\\end{cases}$$ where $d(x, y)$ is the hamming-distance between $x$ and $y$. Our PPH function compresses $n$-bit strings into $\mathcal{O}(t \lambda)$-bit digests, where $\lambda$ is the security parameter. The construction is based on the q-strong bilinear discrete logarithm assumption. Along the way, we construct a robust PPH function for the set intersection predicate $$ \mathsf{INT}^t(X, Y) = \begin{cases} 1 &\text{if } \vert X \cap Y\vert > n - t \\ 0 & \text{Otherwise}\\ \end{cases} $$ which compresses sets $X$ and $Y$ of size $n$ with elements from some arbitrary universe $U$ into $\mathcal{O}(t\lambda)$-bit long digests. This PPH function may be of independent interest. We present an almost matching lower bound of $\Omega(t \log t)$ on the digest size of any PPH function for the intersection predicate, which indicates that our compression rate is close to optimal. Finally, we also show how to extend our PPH function for the intersection predicate to more than two inputs.

The specific order of commands agreed upon when running state machine replication (SMR) is immaterial to fault-tolerance: all that is required is for all correct deterministic replicas to follow it. In the permissioned blockchains that rely on Byzantine fault tolerant (BFT) SMR, however, nodes have a stake in the specific sequence that ledger records, as well as in preventing other parties from manipulating the sequencing to their advantage. The traditional specification of SMR correctness, however, has no language to express these concerns. This paper introduces Byzantine ordered consensus, a new primitive that augments the correctness specification of BFT SMR to include specific guarantees on the total orders it produces; and a new architecture for BFT SMR that, by factoring out ordering from consensus, can enforce these guarantees and prevent Byzantine nodes from controlling ordering decisions (a Byzantine oligarchy). These contributions are instantiated in Pompe, a BFT SMR protocol that is guaranteed to order commands in a way that respects a natural extension of linearizability.

Attribute-based encryption received widespread attention as soon as it was proposed. However, due to its specific characteristics, some restrictions on attribute set in attribute-based encryption are not flexible enough in actual operation. In addition, since access authorities are determined according to users' attributes, users sharing the same attributes are difficult to be distinguished. Once a malicious user makes illicit gains by their decryption authorities, it is difficult to track down specific users. This paper follows practical demands to propose a more flexible key-policy attribute-based encryption scheme with black-box traceability. The scheme has a constant size of public parameters which can be utilized to construct attribute-related parameters flexibly, and the method of traitor tracing in broadcast encryption is introduced to achieve effective malicious user tracing. In addition, the security and feasibility can be proved by the security proofs and performance evaluation in this paper.

FIDO’s U2F is a web-authentication mechanism designed to mitigate real-time phishing—an attack that undermines multi-factor authentication by allowing an attacker to relay second-factor one-time tokens from the victim user to the legitimate website in real-time. A U2F dongle is simple to use, and is designed to restrain users from using it incorrectly. We show that social engineering attacks allow an adversary to downgrade FIDO’s U2F to alternative authentication mechanisms. Websites allow such alternatives to handle dongle malfunction or loss. All FIDO-supporting websites in Alexa’s top 100 allow choosing alternatives to FIDO, and are thus potentially vulnerable to real-time phishing attacks. We crafted a phishing website that mimics Google login’s page and implements a FIDO-downgrade attack. We then ran a carefully-designed user study to test the effect on users. We found that, when using FIDO as their second authentication factor, 55% of participants fell for real-time phishing, and another 35% would potentially be susceptible to the attack in practice.

There are many examples of how to assess the side-channel resistance of a hardware implementation for a given order, where one has to take into account all transitions and glitches produced by a given design. However, microprocessors do not conform with the ideal circuit model which is typically used to gain confidence in the security of masking against side-channel attacks. As a result, masked software implementations in practice do not exhibit the security one would expect in theory. In this paper, we generalize and extend work by Papagiannopoulos and Veshchikov to describe the ways in which a microprocessor may leak. We show that the sources of leakage are far more numerous than previously considered and highly dependent on the platform. We further describe how to write high-level code in the C programming language that allows one to work around common micro-architectural features. In particular, we introduce implementation techniques to reduce sensitive combinations made by the CPU and which are devised so as to be preserved through the optimizations made by the compiler. However, these techniques cannot be proven to be secure. In this paper, we seek to highlight leakage not considered in current models used in proofs and describe some potential solutions. We apply our techniques to two case studies (DES and AES) and show that they are able to provide a modest level of security on several platforms.

This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines. The main optimization target is the size of the quantum computer, i.e., the number of logical qubits required, as this appears to be the main obstacle to implementing Shor's polynomial-time discrete-logarithm algorithm. The secondary optimization target is the number of logical Toffoli gates. For an elliptic curve over a field of 2^n elements, this paper reduces the number of qubits to 7n+[log_2(n)]+9. At the same time this paper reduces the number of Toffoli gates to 48n^3+8n^(log_2(3)+1)+352n^2 log_2(n)+512n^2+O(n^(log_2(3))) with double-and-add scalar multiplication, and a logarithmic factor smaller with fixed-window scalar multiplication. The number of CNOT gates is also O(n^3). Exact gate counts are given for various sizes of elliptic curves currently used for cryptography.

In this work we develop optimized software implementationsfor ForkAE, a second round candidate in the ongoing NIST lightweight cryptography standardization process. Moreover, we analyze the perfor-mance and efficiency of different ForkAE implementations on two em-bedded platforms: ARM Cortex-A9 and ARM Cortex-M0.First, we study portable ForkAE implementations. We apply a decryption optimization technique which allows us to accelerate decryption by up to 35%. Second, we go on to explore platform-specific software op-timizations. In platforms where cache-timing attacks are not a risk, we present a novel table-based approach to compute the SKINNY round function. Compared to the existing portable implementations, this technique speeds up encryption and decryption by 20% and 25%, respectively. Additionally, we propose a set of platform-specific optimizations for processors with parallel hardware extensions such as ARM NEON. Without relying on parallelism provided by long messages (cf. bit-sliced implementations), we focus on the primitive-level ForkSkinny parallelism provided by ForkAE to reduce encryption and decryption latency by up to 30%. We benchmark the performance of our implementations on the ARM Cortex-M0 and ARM Cortex-A9 processors and give a comparison withthe other SKINNY-based schemes in the NIST lightweight competition– SKINNY-AEAD and Romulus

The protection of cryptographic implementations against power analysis attacks is of critical importance for many applications in embedded systems. The typical approach of protecting against these attacks is to implement algorithmic countermeasures, like masking. However, implementing these countermeasures in a secure and correct manner is challenging. Masking schemes require the independent processing of secret shares, which is a property that is often violated by CPU microarchitectures in practice. In order to write leakage-free code, the typical approach in practice is to iteratively explore instruction sequences and to empirically verify whether there is leakage caused by the hardware for this instruction sequence or not. Clearly, this approach is neither efficient, nor does it lead to rigorous security statements. In this paper, we overcome the current situation and present the first approach for co-design and co-verification of masked software implementations on CPUs. First, we present Coco, a tool that allows us to provide security proofs at the gate-level for the execution of a masked software implementation on a concrete CPU. Using Coco , we analyze the popular 32-bit RISC-V Ibex core, identify all design aspects that violate the security of our tested masked software implementations and perform corrections, mostly in hardware. The resulting secured Ibex core has an area overhead around 10%, the runtime of software on this core is largely unaffected, and the formal verification with Coco of an, e.g., first-order masked Keccak S-box running on the secured Ibex core takes around 156 seconds. To demonstrate the effectiveness of our suggested design modifications, we perform practical leakage assessments using an FPGA evaluation board.

Deep learning-based SCA represents a powerful option for profiling side-channel analysis. Numerous results in the last few years indicate neural networks can break targets protected with countermeasures even with a relatively small number of attack traces. Intuitively, the more powerful neural network architecture we require, the more effort we need to spend in its hyperparameter tuning. Current results commonly use random search and reach good performance. Yet, we remain with the question of how good are such architectures if compared with the architectures that are carefully designed by following a specific methodology. Unfortunately, the works considering methodologies are sparse and difficult to ease without prior knowledge about the target. This work proposes an automated way for deep learning hyperparameter tuning that is based on Bayesian Optimization. We build a custom framework denoted as AutoSCA that supports both machine learning and side-channel metrics. Our experimental analysis shows that Bayesian optimization performs well regardless of the dataset, leakage model, or neural network type. What is more, we find a number of neural network architectures outperforming state-of-the-art attacks. Finally, we note that random search, despite being considered not particularly powerful, manages to reach top performance for a number of considered settings. We postulate this happens since the datasets are relatively easy to break, and there are many neural network architectures reaching top performance.

An oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (STOC '87 and J. ACM '96), is a technique for hiding RAM's access pattern. That is, for every input the distribution of the observed locations accessed by the machine is essentially independent of the machine's secret inputs. Recent progress culminated in a work of Asharov et al. (EUROCRYPT '20), obtaining an ORAM with (amortized) logarithmic overhead in total work, which is known to be optimal. Oblivious Parallel RAM (OPRAM) is a natural extension of ORAM to the (more realistic) parallel setting where several processors make concurrent accesses to a shared memory. It is known that any OPRAM must incur logarithmic work overhead and for highly parallel RAMs a logarithmic depth blowup (in the balls and bins model). Despite the significant recent advances, there is still a large gap: all existing OPRAM schemes incur a poly-logarithmic overhead either in total work or in depth. Our main result closes the aforementioned gap and provides an essentially optimal OPRAM scheme. Specifically, assuming one-way functions, we show that any Parallel RAM with memory capacity~$N$ can be obliviously simulated in space $O(N)$, incurring only $O(\log N)$ blowup in (amortized) total work as well as in depth. Our transformation supports all PRAMs in the CRCW mode and the resulting simulation is in the CRCW mode as well.

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct the first universally composable (UC) protocol for oblivious transfer secure against active static adversaries based on the Computational Diffie-Hellman (CDH) assumption. Our protocol is proven secure in the observable Global Random Oracle model. We start by constructing a protocol that realizes an OT functionality with a selective failure issue, but shown to be sufficient to instantiate efficient OT extension protocols. In terms of complexity, this protocol only requires the computation of 6 modular exponentiations and the communication of 5 group elements, five binary strings of security parameter length, and two binary strings of message length. Finally, we lift this weak construction to obtain a protocol that realizes the standard OT functionality (without any selective failures) at an additional cost of computing 9 modular exponentiations and communicating 4 group elements, four binary strings of security parameter length and two binary strings of message length. As an intermediate step before constructing our CDH based protocols, we design generic OT protocols from any OW-CPA secure public-key encryption scheme with certain properties, which could potentially be instantiated from more assumptions other than CDH.

Selfish mining (SM) attack of Eyal and Sirer (2018) endangers permissionless Proof-of-Work blockchains by allowing a rational mining pool with a hash power (a) much less than 50% of the whole network to deviate from the honest mining algorithm and to steal from the fair shares of honest miners. Since then, the attack has been studied extensively in various settings, for understanding its interesting dynamics, optimizing it, and mitigating it. In this context, Heilman (14) ''Freshness Preferred'', we propose a timestamp based defence if timestamps are not generated by an authority. To use this proposal in a decentralized setting, we would like to remove the timestamp authority, but due to two natural and simple attacks this turns out to be a non-trivial task. These attacks are composed of Oracle mining by setting the timestamp to future and Bold mining by generating an alternative chain by starting from a previous block. Unfortunately, these attacks are hard to analyze and optimize, and the available tools, to our knowledge, fail to help us for this task. Thus, we propose generalized formulas for revenue and profitability of SM attacks to ease our job in analysis and optimization of these attacks. Our analyses show that although the use of timestamps would be promising for selfish mining mitigation, Freshness Preferred, in its current form, is quite vulnerable, as any rational miner with a>0 can directly benefit from our attacks. To cope with this problem, we propose an SM mitigation algorithm Fortis with forgeable timestamps (without the need for a trusted authority), which protects the honest miners' shares against any attacker with a<27.0% against all the known SM-type attacks. By building upon the blockchain simulator BlockSim by Alharby and Moorsel (2019), we simulate our Oracle and Bold mining attacks against the Freshness Preferred and our Fortis defenses. Similar to our theoretical results, the simulation results demonstrate the effectiveness of these attacks against the former and their ineffectiveness against the latter.

I describe a blockchain design that hides the transaction graph from Blockchain Analyzers. The design is based on the realization that today the miner creating a block needs enough information to verify the validity of transactions, which makes details about the transactions public and thus allows blockchain analysis. Some protocols, such as Mimblewimble, obscure the transaction amounts but not the source of the funds which is enough to allow for analysis. The insight in this technical note is that the block creator can be restricted to the task of ensuring no double spends. The task of actually verifying transaction balances really belongs to the receiver. The receiver is the one motivated to verify that she is receiving a valid transaction output since she has to convince the next receiver that the balances are valid, otherwise no one will accept her spending transaction. The bulk of the transaction can thus be encrypted in such a manner that only the receiver can decrypt and examine it. Opening this transaction allows the receiver to also open previous transactions to allow her to work her way backward in a chain until she arrives at the coin generation blocks and completely verify the validity of the transaction. Since transactions are encrypted on the blockchain a blockchain analyzer cannot create a transaction graph until he is the receiver of a transaction that allows backward tracing through to some target transaction.

Basic key exchange protocols built from the learning with errors (LWE) assumption are insecure if secret keys are reused in the face of active attackers. One example of this is Fluhrer’s attack on the Ding, Xie, and Lin (DXL) LWE key exchange protocol, which exploits leakage from the signal function for error correction. Protocols aiming to achieve security against active attackers generally use one of two techniques: demonstrating well-formed keyshares using re-encryption like in the Fujisaki–Okamoto transform; or directly combining multiple LWE values, similar to MQV-style Diffie–Hellman-based protocols. In this work, we demonstrate improved and new attacks exploiting key reuse in several LWE-based key exchange protocols. First, we show how to greatly reduce the number of samples required to carry out Fluhrer’s attack and reconstruct the secret period of a noisy square waveform, speeding up the attack on DXL key exchange by a factor of over 200. We show how to adapt this to attack a protocol of Ding, Branco, and Schmitt (DBS) designed to be secure with key reuse, breaking the claimed 128-bit security level in under a minute. We also apply our technique to a second authenticated key exchange protocol of DBS that uses an additive MQV design, although in this case our attack makes use of ephemeral key compromise powers of the eCK security model, which was not in scope of the claimed BR-model security proof. Our results show that building secure authenticated key exchange protocols directly from LWE remains a challenging and mostly open problem.

Cryptographic Primitives in Multivariate Public Key Cryptography are of relevant interest, specially in the quadratic case. These primitives classify the families of schemes that we encounter in this field. In this paper, the reader can find a new primitive based on the product of the roots of a polynomial over a field, where the coefficients of this polynomials are the elementary symmetric polynomials on $n$ variables, which guarantees a solution when inverting the scheme. Moreover, a cryptosystem and a digital signature scheme are built on top of this primitive, where distinct parametrizations and criteria that define the schemes are commented, along with applications of attacks available in literature.

Secure two-party computation considers the problem of two parties computing a joint function of their private inputs without revealing anything beyond the output of the computation. In this work, we take the first steps towards understanding the setting where: 1) the two parties (Alice and Bob) can communicate only via a classical channel, 2) the input of Bob is quantum, and 3) the input of Alice is classical. Our first result indicates that in this setting it is in general impossible to realize a two-party quantum functionality with black-box simulation in the case of malicious quantum adversaries. In particular, we show that the existence of a secure quantum computing protocol that relies only on classical channels would contradict the quantum no-cloning argument. We circumvent this impossibility following three different approaches. The first is by considering a weaker security notion called one-sided simulation security. This notion protects the input of one party (the quantum Bob) in the standard simulation-based sense and protects the privacy of the other party's input (the classical Alice). We show how to realize a protocol that satisfies this notion relying on the learning with errors assumption. The second way to circumvent the impossibility result, while at the same time providing standard simulation-based security also against a malicious Bob, is by assuming that the quantum input has an efficient classical representation. Finally, we focus our attention on the class of zero-knowledge functionalities and provide a compiler that takes as input a classical proof of quantum knowledge (PoQK) protocol for a QMA relation R (a classical PoQK is a PoQK that can be verified by a classical verifier) and outputs a zero-knowledge PoQK for R that can be verified by classical parties. The direct implication of our result is that Mahadev’s protocol for classical verification of quantum computations (FOCS’18) can be turned into a zero-knowledge proof of quantum knowledge with classical verifiers. To the best of our knowledge, we are the first to instantiate such a primitive.

We construct the first multi-input functional encryption \allowbreak(MIFE) scheme for quadratic functions from pairings. Our construction supports polynomial number of users, where user $i$, for $i \in [n]$, encrypts input $\bfx_i \in \mbZ^m$ to obtain ciphertext $\ct_i$, the key generator provides a key $\sk_\bfc$ for vector $\bfc \in \mbZ^{({mn})^2}$ and decryption, given $\ct_1,\ldots,\ct_n$ and $\sk_\bfc$, recovers $\ip{\bfc}{\bfx \otimes \bfx}$ and nothing else. We achieve indistinguishability-based (selective) security against unbounded collusions under the standard bilateral matrix Diffie-Hellman assumption. All previous MIFE schemes either support only inner products (linear functions) or rely on strong cryptographic assumptions such as indistinguishability obfuscation or multi-linear maps.

Physically unclonable functions (PUFs) are gaining attention as a promising cryptographic technique, with the main applications including challenge-response authentication and key generation (key storage). When a PUF is applied to these applications, min-entropy estimation is essential. Min-entropy is a measure of the lower bound of the unpredictability of PUF responses. Using the test suite of the National Institute of Standards and Technology (NIST) specification (SP) 800-90B is currently considered the best method for estimating the min-entropy of PUF responses. Several previous studies have estimated the min-entropy of PUFs as well as those of random number generators (RNGs). However, we feel doubtful about some of these estimated results; for example, an evaluator can reorder PUF responses to make the PUF performance appear much better. It is also known that the test suite of NIST SP 800-90B has no suitable estimator. In particular, it has been reported that concatenating PUF responses of two-dimensional PUFs, such as an SRAM PUF, into one-dimensional data may obfuscate spatial correlations. In this paper, we explore the inherent problems in min-entropy estimation by using our static random-access memory (SRAM) PUF and our complementary metal-oxide-semiconductor (CMOS) image sensor with a PUF (CIS PUF). We apply three orderings to the PUF responses of our SRAM PUF and CIS PUF: row-direction ordering, column-direction ordering, and random-shuffle ordering. We show how much the min-entropy estimated by NIST SP 800-90B varies and discuss the estimation results. Next, we discuss the threat of PUFs (i.e., predictability of PUF responses) when a digitizer in a PUF has an offset error. PUF sources are generally defined as circuits and transistors used to extract intrinsic physical properties and generate device-unique responses. Variation in the manufacturing of circuits and transistors other than the PUF sources, especially digitizers, may cause lower entropy. We call these circuits and transistors ``entropy-loss sources.'' We investigate the effect of entropy-loss sources on min-entropy theoretically and clarify how much the theoretical results differ from those estimated by NIST SP 800-90B. Finally, we propose an entropy prediction scheme that considers entropy-loss sources (offset error). We show through experiments that the proposed scheme more accurately estimates the min-entropy of PUFs.

We give a sieving algorithm for finding pairs of consecutive smooth numbers that utilizes solutions to the Prouhet-Tarry-Escott (PTE) problem. Any such solution induces two degree-$n$ polynomials, $a(x)$ and $b(x)$, that differ by a constant integer $C$ and completely split into linear factors in $\mathbb{Z}[x]$. It follows that for any $\ell \in \mathbb{Z}$ such that $a(\ell) \equiv b(\ell) \equiv 0 \bmod{C}$, the two integers $a(\ell)/C$ and $b(\ell)/C$ differ by 1 and necessarily contain $n$ factors of roughly the same size. For a fixed smoothness bound $B$, restricting the search to pairs of integers that are parameterized in this way increases the probability that they are $B$-smooth. Our algorithm combines a simple sieve with parametrizations given by a collection of solutions to the PTE problem. The motivation for finding large twin smooth integers lies in their application to compact isogeny-based post-quantum protocols. The recent key exchange scheme B-SIDH and the recent digital signature scheme SQISign both require large primes that lie between two smooth integers; finding such a prime can be seen as a special case of finding twin smooth integers under the additional stipulation that their sum is a prime $p$. When searching for cryptographic parameters with $2^{240} \leq p <2^{256}$, an implementation of our sieve found primes $p$ where $p+1$ and $p-1$ are $2^{15}$-smooth; the smoothest prior parameters had a similar sized prime for which $p-1$ and $p+1$ were $2^{19}$-smooth. In targeting higher security levels, our sieve found a 376-bit prime lying between two $2^{21}$-smooth integers, a 384-bit prime lying between two $2^{22}$-smooth integers, and a 512-bit prime lying between two $2^{28}$-smooth integers. Our analysis shows that using previously known methods to find high-security instances subject to these smoothness bounds is computationally infeasible.

Several quantum-resistant authenticated key exchange protocols (AKEs) have been proposed from supersingular isogeny and lattice. Most of their security analyses are conducted in the classical random oracle model, leaving their securities in the quantum random oracle model (QROM) as open problems. In this paper, we propose a generic construction of two-message AKE in QROM. It can be regarded as a QROM-secure version of X3LH [Xue et al. ASIACRYPT 2018], a generic AKE based on double-key PKE. We prove that, with some modification, the QROM security of X3LH can be reduced to the one-way security of double-key PKE. Aside from answering open problems on the QROM security of prior AKEs, such as SIAKE [Xu et al. ASIACRYPT 2019] based on supersingular isogeny, 2Kyber-AKE based on Module-LWE, and FSXY, we propose a new construction, CSIAKE, based on commutative supersingular isogeny. Our framework enjoys the following desirable features. First of all, it supports PKEs with non-perfect correctness. Secondly, the basic building block is compact and only requires one-wayness. Finally, the resulting AKE achieves the security in CK+ model as strong as X3LH, and the transformation overhead is low.

Secure group messaging protocols, providing end-to-end encryption for group communication, need to handle mobile devices frequently being offline, group members being added or removed, and the possibility of device compromises during long-lived chat sessions. Existing work targets a centralized network model in which all messages are routed through a single server, which is trusted to provide a consistent total order on updates to the group state. In this paper we adapt secure group messaging for decentralized networks that have no central authority. Servers may still optionally be used, but they are trusted less. We define decentralized continuous group key agreement (DCGKA), a new cryptographic primitive encompassing the core of a decentralized secure group messaging protocol; we give a practical construction of a DCGKA protocol and prove its security; and we describe how to construct a full messaging protocol from DCGKA. In the face of device compromise our protocol achieves forward secrecy and post-compromise security. We evaluate the performance of a prototype implementation, and demonstrate that our protocol has practical efficiency.

Efficient, leakage-free search on encrypted data has remained an unsolved problem for the last two decades; efficient schemes are vulnerable to leakage-abuse attacks, and schemes that eliminate leakage are impractical to deploy. To overcome this tradeoff, we reexamine the system model. We surveyed five companies providing end-to-end encrypted filesharing to better understand what they require from an encrypted search system. Based on our findings, we design and build DORY, an encrypted search system that addresses real-world requirements and protects search access patterns; namely, when a user searches for a keyword over the files within a folder, the server learns only that a search happens in that folder, but does not learn which documents match the search, the number of documents that match, or other information about the keyword. DORY splits trust between multiple servers to protect against a malicious attacker who controls all but one of the servers. We develop new cryptographic and systems techniques to meet the efficiency and trust model requirements outlined by the companies we surveyed. We implement DORY and show that it performs orders of magnitude better than a baseline built on ORAM. Parallelized across 8 servers, each with 16 CPUs, DORY takes 116ms to search roughly 50K documents and 862ms to search over 1M documents.

We introduce new tightly-secure authenticated key exchange (AKE) protocols that are extremely efficient, yet have only a constant security loss and can be instantiated in the random oracle model both from the standard DDH assumption and a subgroup assumption over RSA groups. These protocols can be deployed with optimal parameters, independent of the number of users or sessions, without the need to compensate a security loss with increased parameters and thus decreased computational efficiency. We use the standard “Single-Bit-Guess” AKE security (with forward secrecy and state corruption) requiring all challenge keys to be simultaneously pseudo-random. In contrast, most previous papers on tightly secure AKE protocols (Bader et al., TCC 2015; Gjøsteen and Jager, CRYPTO 2018; Liu et al., ASIACRYPT 2020) concentrated on a non-standard “Multi-Bit-Guess” AKE security which is known not to compose tightly with symmetric primitives to build a secure communication channel. Our key technical contribution is a new generic approach to construct tightly-secure AKE protocols based on non-committing key encapsulation mechanisms. The resulting DDH-based protocols are considerably more efficient than all previous constructions.

We present implementations of the lattice-based digital signature scheme Dilithium for ARM Cortex-M3 and ARM Cortex-M4. Dilithium is one of the three signature finalists of the NIST post-quantum cryptography competition. As our Cortex-M4 target, we use the popular STM32F407-DISCOVERY development board. Compared to the previous speed records on the Cortex-M4 by Ravi, Gupta, Chattopadhyay, and Bhasin we speed up the key operations $\text{NTT}$ and $\text{NTT}^{-1}$ by 20% which together with other optimizations results in speedups of 7%, 15%, and 9% for Dilithium3 key generation, signing, and verification respectively. We also present the first constant-time Dilithium implementation on the Cortex-M3 and use the Arduino Due for benchmarks. For Dilithium3, we achieve on average 2 562 kilocycles for key generation, 10 667 kilocycles for signing, and 2 321 kilocycles for verification. Additionally, we present stack consumption optimizations applying to both our CortexM3 and Cortex-M4 implementation. Due to the iterative nature of the Dilithium signing algorithm, there is no optimal way to achieve the best speed and lowest stack consumption at the same time. We present three different strategies for the signing procedure which allow trading more stack and flash memory for faster speed or vice-versa. Our implementation of Dilithium3 with the smallest memory footprint uses less than 12kB. As an additional output of this work, we present the first Cortex-M3 implementations of the key-encapsulation schemes NewHope and Kyber.

Several electromagnetic fault injection (EMFI) platforms have been developed these last years. They rely on different technical solutions and figures of merit used in the related datasheets or publications are also different. This renders difficult the comparison of the various EMFI platforms and the choice of the one adapted to its own usage. This paper suggests a characterization protocol which application is fast and requires equipment usually available in labs involved in security characterization. It also introduces an effective solution to enhance (by a factor 5) the timing resolution of EMFI platforms built around a commercial voltage pulse generator designed to drive 50 Ohm termination.

Public key cryptography is an indispensable component used in almost all of our present day digital infrastructure. However, most if not all of it is predominantly built upon hardness guarantees of number theoretic problems that can be broken by large scale quantum computers in the future. Sensing the imminent threat from continued advances in quantum computing, NIST has recently initiated a global level standardization process for quantum resistant public-key cryptographic primitives such as public key encryption, digital signatures and key encapsulation mechanisms. While the process received proposals from various categories of post-quantum cryptography, lattice-based cryptography features most prominently among all the submissions. Lattice-based cryptography offers a very attractive alternative to traditional public-key cryptography mainly due to the variety of lattice-based schemes offering varying flavors of security and efficiency guarantees. In this paper, we survey the evolution of lattice-based key sharing schemes (public key encryption and key encapsulation schemes) and cover various aspects ranging from theoretical security guarantees, general algorithmic frameworks, practical implementation aspects and physical attack security, with special focus on lattice-based key sharing schemes competing in the NIST's standardization process. Please note that our work is focussed on the results available from the second round of the NIST's standardization process while the standardization process has progressed to the third and final round at the time of publishing this document.

We introduce Xiphos and Kopis, new transparent zero-knowledge succinct non-interactive arguments of knowledge (zkSNARKs) for R1CS. They do not require a trusted setup, and their security relies on the standard SXDH problem. They achieve non-interactivity in the random oracle model using the Fiat-Shamir transform. Unlike prior transparent zkSNARKs, which support either a fast prover, short proofs, or quick verification, our work is the first to simultaneously achieve all three properties (both asymptotically and concretely) and in addition an inexpensive setup phase, thereby providing the first quadruple-efficient transparent zkSNARKs (Quarks). Under both schemes, for an R1CS instance of size n and security parameter $\lambda$, the prover incurs $O_{\lambda}(n)$ costs to produce a proof of size $O_{\lambda}(\log{n})$. In Xiphos, verification time is $O_{\lambda}(\log{n})$, and in Kopis it is $O_{\lambda}(\sqrt{n})$. In terms of concrete efficiency, compared to prior state-of-the-art transparent zkSNARKs, Xiphos offers the fastest verification; its proof sizes are competitive with those of SuperSonic [EUROCRYPT 2020], a prior transparent SNARK with the shortest proofs in the literature. Xiphos’s prover is fast: its prover is $\approx$$3.8\times$ of Spartan [CRYPTO 2020], a prior transparent zkSNARK with the fastest prover in the literature, and is $376$$\times$ faster than SuperSonic. Kopis, at the cost of increased verification time (which is still concretely faster than SuperSonic), shortens Xiphos’s proof sizes further, thereby producing proofs shorter than SuperSonic. Xiphos and Kopis incur $10$--$10,000\times$ lower preprocessing costs for the verifier in the setup phase depending on the baseline. Finally, a byproduct of Kopis is Lakonia, a NIZK for R1CS with $O_{\lambda}(\log{n})$-sized proofs, which provides an alternative to Bulletproofs [S&P 2018] with over an order of magnitude faster proving and verification times.

This paper presents Dory, a transparent setup, public-coin interactive argument for proving correctness of an inner-pairing product between committed vectors of elements of the two source groups. For an inner product of length $n$, proofs are $6 \log n$ target group elements, $1$ element of each source group and $3$ scalars. Verifier work is dominated by an $O(\log n)$ multi-exponentiation in the target group. Security is reduced to the symmetric external Diffie Hellman assumption in the standard model. We also show an argument reducing a batch of two such instances to one, requiring $O(n^{1/2})$ work on the Prover and $O(1)$ communication. We apply Dory to build a multivariate polynomial commitment scheme via the Fiat-Shamir transform. For $n$ the product of one plus the degree in each variable, Prover work to compute a commitment is dominated by a multi-exponentiation in one source group of size $n$. Prover work to show that a commitment to an evaluation is correct is $O(n^{\log 8 / \log 25})$ in general and $O(n^{1/2})$ for univariate or multilinear polynomials, whilst communication complexity and Verifier work are both $O(\log n)$. Using batching, the Verifier can validate $\ell$ polynomial evaluations for polynomials of size at most $n$ with $O(\ell + \log n)$ group operations and $O(\ell \log n)$ field operations.

In this paper, we extend the protocol of classical verification of quantum computations (CVQC) recently proposed by Mahadev to make the verification efficient. Our result is obtained in the following three steps: - We show that parallel repetition of Mahadev's protocol has negligible soundness error. This gives the first constant round CVQC protocol with negligible soundness error. In this part, we only assume the quantum hardness of the learning with error (LWE) problem similar to Mahadev's work. - We construct a two-round CVQC protocol in the quantum random oracle model (QROM) where a cryptographic hash function is idealized to be a random function. This is obtained by applying the Fiat-Shamir transform to the parallel repetition version of Mahadev's protocol. -We construct a two-round CVQC protocol with an efficient verifier in the CRS+QRO model where both prover and verifier can access a (classical) common reference string generated by a trusted third party in addition to quantum access to QRO. Specifically, the verifier can verify a $\mathsf{QTIME}(T)$ computation in time $\mathsf{poly}(\lambda,\log T)$ where $\lambda$ is the security parameter. For proving soundness, we assume that a standard model instantiation of our two-round protocol with a concrete hash function (say, SHA-3) is sound and the existence of post-quantum indistinguishability obfuscation and post-quantum fully homomorphic encryption in addition to the quantum hardness of the LWE problem.

In this work, we present a primary construction of bent functions based on cellular automata (CA). We consider the well-known characterization of bent functions in terms of Hadamard matrices and employ some recent results about mutually orthogonal Latin squares (MOLS) based on linear bipermutive CA (LBCA) to design families of Hadamard matrices of the form required for bent functions. In particular, the main question to address in this construction can be reduced to finding a large enough set of coprime polynomials over $\mathbb{F}_q$, which are used to define a set of MOLS via LBCA. This set of MOLS is, in turn, used to define a Hadamard matrix of the specific structure characterizing a bent function. We settle the existence question of such bent functions by proving that the required coprime sets exist if and only if the degree of the involved polynomials is either $1$ or $2$, and we count the resulting sets. Next, we check if the functions of $8$ variables arising from our construction are EA-equivalent to Maiorana-McFarland functions, observing that most of them are not. Finally, we show how to represent the support of these bent functions as a union of the kernels of the underlying linear CA. This allows us, in turn, to prove that the functions generated by our construction belong to the partial spread class $\mathcal{PS}^-$. In particular, we remark that for degree $1$ our construction is a particular case of the Desarguesian spread construction.

Functional Encryption (FE) allows users who hold a specific secret key (known as the functional key) to learn a specific function of encrypted data whilst learning nothing about the content of the underlying data. Considering this functionality and the fact that the field of FE is still in its infancy, we sought a route to apply this potent tool to solve the existing problem of designing decentralised additive reputation systems. To this end, we first built a symmetric FE scheme for the $\ell_1$ norm of a vector space, which allows us to compute the sum of the components of an encrypted vector (i.e. the votes). Then, we utilized our construction, along with functionalities offered by Intel SGX, to design the first FE-based decentralized additive reputation system with Multi-Party Computation. While our reputation system faces certain limitations, this work is amongst the first attempts that seek to utilize FE in the solution of a real-life problem.