Recently, Kumar and Chand proposed an anonymous authentication protocol for wireless body area network. They claimed that their scheme meets major security requirements and is able to resist known attacks. However, in this paper we demonstrate that their scheme is prone to traceability attack. Followed by this attack, an attacker can launch a man-in-the-middle attack and share a session key with the victim node, and hence the scheme does not achieve secure authentication. Also, we show that this protocol does not provide perfect forward secrecy which considered as a key security property in the design of any secure key agreement protocol.

A recent result by Dulek et al. (EUROCRYPT 2020) showed a secure protocol for computing any quantum circuit even without the presence of an honest majority. Their protocol, however, is susceptible to a ``denial of service'' attack and allows even a single corrupted party to force an abort. We propose the first quantum protocol that admits security-with-identifiable-abort, which allows the honest parties to agree on the identity of a corrupted party in case of an abort. Additionally, our protocol is the first to have the property that the number of rounds where quantum communication is required is independent of the circuit complexity. Furthermore, if there exists a post-quantum secure classical protocol whose round complexity is independent of the circuit complexity, then our protocol has this property as well. Our protocol is secure under the assumption that classical quantum-resistant fully homomorphic encryption schemes with decryption circuit of logarithmic depth exist. Interestingly, our construction also admits a reduction from quantum fair secure computation to classical fair secure computation.

In this article, we analyze and investigate two authenticated encryption algorithms: GIFT-COFB and HyENA. The two modes differ in some low levels details in both the design and security proofs. However, they share a lot of similarities. We take a look at the best-known attacks and security proofs of these designs. We show that the best-known attack is not a matching attack to the security bounds provided by the designers in the security proof. Second, we give a new attack that we characterize as an {\it "almost matching"} attack. It is significantly closer to the provable security bounds. The new attack requires $O(2^{n/4})$ encryptions and $O(2^{n/2})$ decryptions, as opposed to $O(2^{n/2})$ encryptions and $O(2^{n/2})$ decryptions shown previously. However, there is still a substantial logarithmic gap between this attack and the corresponding security bound. Next, we analyze why this gap still exists and why it is unlikely to find matching attacks. We give two arguments. The first argument is by analyzing the security proof and showing how it masks a term with non-negligible encryption complexity. The second argument looks at the attacker's point of view. A successful attack requires satisfying a non-trivial linear equation over secret random variables. Satisfying such an equation requires more decryption queries than what is bounded by the security proof. It is worth emphasizing that the analysis and attacks presented in this paper {\it do not} threaten the security claims made by the designers or the security of these designs within the parameters required by the NIST lightweight cryptography project. The results increase confidence in the security claims of GIFT-COFB and HyENA while showing their limitations by relying mostly on bounding the number of unsuccessful forgeries.

The Covid-19 pandemic created various new challenges for our societies. Quickly discovering new infections using automated contact tracing without endangering privacy of the general public is one of these. Most discussions concerning architectures for contact tracing applications revolved around centralized against decentralized approaches. In contrast, the system proposed in this work builds on the idea of message-based contact tracing to inform users of their risk. Our main contribution is the combination of a blind-signature approach to verify infections with an anonymous postbox service. In our evaluation we analyze all components in our system for performance and privacy, as well as security. We derive parameters for operating our system in a pandemic scenario.

The modular squaring operation has attracted significant attention due to its potential in constructing cryptographic time-lock puzzles and verifiable delay functions. In such applications, it is important to understand precisely how quickly a modular squaring operation can be computed, even in parallel on dedicated hardware. We use tools from circuit complexity and number theory to prove concrete numerical lower bounds for squaring on a parallel machine, yielding nontrivial results for practical input bitlengths. For example, for $n=2048$, we prove that every logic circuit (over AND, OR, NAND, NOR gates of fan-in two) computing modular squaring on all $n$-bit inputs (and any modulus that is at least $2^{n-1}$) requires depth (critical path length) at least $12$. By a careful analysis of certain exponential Gauss sums related to the low-order bit of modular squaring, we also extend our results to the average case. For example, our results imply that every logic circuit (over any fan-in two basis) computing modular squaring on at least $76\%$ of all $2048$-bit inputs (for any RSA modulus that is at least $2^{n-1}$) requires depth at least $9$.

We present MAGIC, a mode for authenticated encryption that simultaneously supports encryption, message authentication and error correction, all with the same code. In MAGIC, the same code employed for cryptographic integrity is also the parity used for error correction. To correct errors, MAGIC employs the Galois Hash transformation, which due to its bit linearity can perform corrections in a similar way as other codes do (e.g., Reed Solomon). To provide a cryptographically strong MAC, MAGIC encrypts the output of the Galois Hash using a secret key. To analyze the security of this construction we adapt the definition of the MAC adversary so that it is applicable to systems that combine message authentication with error correction. We demonstrate that MAGIC offers security in the order of O(2 to the N/2) with N being the tag size.

In this report, we analyze the hardware implementations of 10 candidates for Round 2 of the NIST lightweight cryptography standardization process. These candidates are Ascon, DryGASCON, Elephant, Gimli, PHOTON-Beetle, Pyjamask, Romulus, Subterranean, TinyJAMBU and Xoodyak. Specifically, we study the implementations of these algorithms when synthesized using the TSMC 65nm and FDSOI 28nm technologies and Synopsys Design Compiler, targeting various performance trade-offs and different use-cases. We show how different candidates stack-up against such trade-offs. We base our benchmarking parameters and metrics on real-world use-cases, such as high-speed applications, lightweight communication protocols and internet payloads.

Ascon, DryGASCON, and Shamash are submissions to NIST's lightweight cryptography standardization process and have similar designs. We analyze these algorithms against subspace trails, truncated differentials, and differential-linear distinguishers. We provide probability one 4-round subspace trails for DryGASCON-256, 3-round subspace trails for \DryGASCON-128, and 2-round subspace trails for \Shamash permutations. Moreover, we provide the first 3.5-round truncated differential and 5-round differential-linear distinguisher for DryGASCON-128. Finally, we improve the data and time complexity of the 4 and 5-round differential-linear attacks on Ascon.

This work presents a detailed study of the classical security of the post-quantum supersingular isogeny key encapsulation (SIKE) protocol using a realistic budget-based cost model that considers the actual computing and memory costs that are needed for cryptanalysis. In this effort, we design especially-tailored hardware accelerators for the time-critical multiplication and isogeny computations that we use to model an ASIC-powered instance of the van Oorschot-Wiener (vOW) parallel collision search algorithm. We then extend the analysis to AES and SHA-3 in the context of the NIST post-quantum cryptography standardization process to carry out a parameter analysis based on our cost model. This analysis, together with the state-of-the-art quantum security analysis of SIKE, indicates that the current SIKE parameters offer higher practical security than currently believed, closing an open issue on the suitability of the parameters to match NIST's security levels. In addition, we explore the possibility of using significantly smaller primes to enable more efficient and compact implementations with reduced bandwidth. Our improved cost model and analysis can be applied to other cryptographic settings and primitives, and can have implications for other post-quantum candidates in the NIST process.

Authenticated encryption (AE) is used in a wide variety of applications, potentially in settings for which it was not originally designed. Recent research tries to understand what happens when AE is not used as prescribed by its designers. A question given relatively little attention is whether an AE scheme guarantees ``key commitment'': ciphertext should only decrypt to a valid plaintext under the key used to generate the ciphertext. Generally, AE schemes do not guarantee key commitment as it is not part of AE's design goal. Nevertheless, one would not expect this seemingly obscure property to have much impact on the security of actual products. In reality, however, products do rely on key commitment. We discuss three recent applications where missing key commitment is exploitable in practice. We provide proof-of-concept attacks via a tool that constructs AES-GCM ciphertext which can be decrypted to two plaintexts valid under a wide variety of file formats, such as PDF, Windows executables, and DICOM. Finally we discuss two solutions to add key commitment to AE schemes which have not been analyzed in the literature: a generic approach that adds an explicit key commitment scheme to the AE scheme, and a simple fix which works for AE schemes like AES-GCM and ChaCha20Poly1305, but requires separate analysis for each scheme.

In the last few years a new design paradigm, the so-called ARX (modular addition, rotation, exclusive-or) ciphers, have gained popularity in part because of their non-linear operation's seemingly `inherent resilience' against Differential Power Analysis (DPA) Attacks: the non-linear modular addition is not only known to be a poor target for DPA attacks, but also the computational complexity of DPA-style attacks grows exponentially with the operand size and thus DPA-style attacks quickly become practically infeasible. We however propose a novel DPA-style attack strategy that scales linearly with respect to the operand size in the chosen-message attack setting.

Secure function evaluation (SFE) allows Alice to publish an encrypted version of her input $m$ such that Bob (holding a circuit $C$) can send a single message that reveals $C(m)$ to Alice, and nothing more. Security is required to hold against malicious parties, that may behave arbitrarily. In this work we study the notion of SFE in the quantum setting, where Alice outputs an encrypted quantum state $|\psi>$ and learns $C(|\psi>)$ after receiving Bob's message. We show that, assuming the quantum hardness of the learning with errors problem (LWE), there exists an SFE protocol for quantum computation with communication complexity $(||\psi>| + |C(|\psi>)|) · (1 + o(1))$, which is nearly optimal. This result is obtained by two main technical steps, which might be of independent interest. Specifically, we show (i) a construction of a rate-1 quantum fully-homomorphic encryption and (ii) a generic transformation to achieve malicious circuit privacy in the quantum setting.

Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, the verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize $GF(p^{6})$ security by computations in $GF(p^{2})$ without explicit constructions of $GF(p^{6})$, where $p$ is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, our schemes can achieve the same security level with shorter parameters by using trace function. What's more, our schemes are much simpler to operate than those schemes based on Elliptic Curve Cryptography (ECC). In addition, our schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes according to the actual situation when participants, secrets or the threshold needs to be changed.

The security of digital communication relies on few cryptographic protocols that are used to protect internet traffic, from web sessions to instant messaging. These protocols and the cryptographic primitives they rely on have been extensively studied and are considered secure. Yet, sophisticated attackers are often able to bypass rather than break security mechanisms. Kleptography or algorithm substitution attacks (ASA) describe techniques to place backdoors right into cryptographic primitives. While highly relevant as a building block, we show that the real danger of ASAs is their use in cryptographic protocols. In fact, we show that highly desirable security properties of these protocols - forward secrecy and post-compromise security - imply the applicability of ASAs. We then analyze the application of ASAs in three widely used protocols: TLS, WireGuard, and Signal. We show that these protocols can be easily subverted by carefully placing ASAs. Our analysis shows that careful design of ASAs makes detection unlikely while leaking long-term secrets within a few messages in the case of TLS and WireGuard, allowing impersonation attacks. In contrast,Signal's double-ratchet protocol shows higher immunity to ASAs, as the leakage requires much more messages.

Secure computation protocols enable mutually distrusting parties to compute a function of their private inputs while revealing nothing but the output. Protocols with {\em full security} (also known as {\em guaranteed output delivery}) in particular protect against denial-of-service attacks, guaranteeing that honest parties receive a correct output. This feature can be realized in the presence of an honest majority, and significant research effort has gone toward attaining full security with good asymptotic and concrete efficiency. We present an efficient protocol for {\em any constant} number of parties $n$, with {\em full security} against $t<n/2$ corrupted parties, that makes a black-box use of a pseudorandom generator. Our protocol evaluates an arithmetic circuit $C$ over a finite ring $R$ (either a finite field or $R=\Z_{2^k}$) with communication complexity of $\frac{3t}{2t+1}S + o(S)$ $R$-elements per party, where $S$ is the number of multiplication gates in $C$ (namely, $<1.5$ elements per party per gate). This matches the best known protocols for the semi-honest model up to the sublinear additive term. For a small number of parties $n$, this improves over a recent protocol of Goyal {\em et al.} (Crypto 2020) by a constant factor for circuits over large fields, and by at least an $\Omega(\log n)$ factor for Boolean circuits or circuits over rings. Our protocol provides new methods for applying the sublinear-communication distributed zero-knowledge proofs of Boneh {\em et al.}~(Crypto 2019) for compiling semi-honest protocols into fully secure ones, in the more challenging case of $t>1$ corrupted parties. Our protocol relies on {\em replicated secret sharing} to minimize communication and simplify the mechanism for achieving full security. This results in computational cost that scales exponentially with $n$. Our main fully secure protocol builds on a new intermediate honest-majority protocol for verifying the correctness of multiplication triples by making a {\em general} use of distributed zero-knowledge proofs. While this intermediate protocol only achieves the weaker notion of {\em security with abort}, it applies to any linear secret-sharing scheme and provides a conceptually simpler, more general, and more efficient alternative to previous protocols from the literature. In particular, it can be combined with the Fiat-Shamir heuristic to simultaneously achieve logarithmic communication complexity and constant round complexity.

Anonymous attestation for secure hardware platforms leverages tailored group signature schemes and assumes the hardware to be trusted. Yet, there is an ever increasing concern on the trustworthiness of hardware components and embedded systems. A subverted hardware may, for example, use its signatures to exfiltrate identifying information or even the signing key. In this paper we focus on Enhanced Privacy ID (EPID)---a popular anonymous attestation scheme used in commodity secure hardware platforms like Intel SGX. We define and instantiate a \emph{subversion resilient} EPID scheme (or SR-EPID). In a nutshell, SR-EPID provides the same functionality and security guarantees of the original EPID, despite potentially subverted hardware. In our design, a ``sanitizer'' ensures no covert channel between the hardware and the outside world both during enrollment and during attestation (i.e., when signatures are produced). We design a practical SR-EPID scheme secure against adaptive corruptions and based on a novel combination of malleable NIZKs and hash functions modeled as random oracles. Our approach has a number of advantages over alternative designs. Namely, the sanitizer bears no secret information---hence, a memory leak does not erode security. Further, the role of sanitizer may be distributed in a cascade fashion among several parties so that sanitization becomes effective as long as one of the parties has access to a good source of randomness. Also, we keep the signing protocol non-interactive, thereby minimizing latency during signature generation.

We propose a practical zero-knowledge proof system for proving knowledge of short solutions s, e to linear relations A s + e= u mod q which gives the most efficient solution for two naturally-occurring classes of problems. The first is when A is very ``tall'', which corresponds to a large number of LWE instances that use the same secret s. In this case, we show that the proof size is independent of the height of the matrix (and thus the length of the error vector e) and rather only linearly depends on the length of s. The second case is when A is of the form A' tensor I, which corresponds to proving many LWE instances (with different secrets) that use the same samples A'. The length of this second proof is square root in the length of s, which corresponds to square root of the length of all the secrets. Our constructions combine recent advances in ``purely'' lattice-based zero-knowledge proofs with the Reed-Solomon proximity testing ideas present in some generic zero-knowledge proof systems -- with the main difference is that the latter are applied directly to the lattice instances without going through intermediate problems.

There has been a lot of recent progress in constructing efficient zero-knowledge proofs for showing knowledge of an $\vec{\mathbf{s}}$ with small coefficients satisfying $\bm{A}\vec{\mathbf{s}}=\vec{\mathbf{t}}$. For typical parameters, the proof sizes have gone down from several megabytes to a bit under $50$KB (Esgin et al., Asiacrypt 2020). These are now within an order of magnitude of the sizes of lattice-based signatures, which themselves constitute proof systems which demonstrate knowledge of something weaker than the aforementioned equation. One can therefore see that this line of research is approaching optimality. In this paper, we modify a key component of these proofs, as well as apply several other tweaks, to achieve a further reduction of around $30\%$ in the proof output size. We also show that this savings propagates itself when these proofs are used in a general framework to construct more complex protocols.

Lai et al. (CCS 2019) have shown how Bulletproof’s arithmetic circuit zero-knowledge protocol (Bootle et al., EUROCRYPT 2016 and Bünz et al., S&P 2018) can be generalized to work for bilinear group arithmetic circuits directly, i.e., without requiring these circuits to be translated into arithmetic circuits. In a nutshell, a bilinear group arithmetic circuit is a standard arithmetic circuit augmented with special gates capturing group exponentiations or pairings. Such circuits are highly relevant, e.g., in the context of zero-knowledge statements over pairing-based languages. As expressing these special gates in terms of a standard arithmetic circuit results in a significant overhead in circuit size, an approach to zero-knowledge via standard arithmetic circuits may incur substantial additional costs. The approach due to Lai et al. shows how to avoid this by integrating additional zero-knowledge techniques into the Bulletproof framework so as to handle the special gates very efficiently. We take a different approach by generalizing Compressed $\Sigma$-Protocol Theory (CRYPTO 2020) from arithmetic circuit relations to bilinear group arithmetic circuit relations. Besides its conceptual simplicity, our approach has the practical advantage of reducing the communication costs of Lai et al.'s protocol by roughly a multiplicative factor 3. Finally, we show an application of our results which may be of independent interest. We construct the first k-out-of-n threshold signature scheme (TSS) that allows for transparent setup and that yields threshold signatures of size logarithmic in n. The threshold signature hides the identities of the k signers and the threshold k can be dynamically chosen at aggregation time.

We introduce and study a simple kind of proof system called line-point zero knowledge (LPZK). In an LPZK proof, the prover encodes the witness as an affine line $\mathbf{v}(t) := \mathbf{a}t + \mathbf{b}$ in a vector space $\mathbb{F}^n$, and the verifier queries the line at a single random point $t=\alpha$. LPZK is motivated by recent practical protocols for vector oblivious linear evaluation (VOLE), which can be used to compile LPZK proof systems into lightweight designated-verifier NIZK protocols. We construct LPZK systems for proving satisfiability of arithmetic circuits with attractive efficiency features. These give rise to designated-verifier NIZK protocols that require only 2-5 times the computation of evaluating the circuit in the clear (following an input-independent preprocessing phase), and where the prover communicates roughly 2 field elements per multiplication gate, or roughly 1 element in the random oracle model with a modestly higher computation cost. On the theoretical side, our LPZK systems give rise to the first linear interactive proofs (Bitansky et al., TCC 2013) that are zero knowledge against a malicious verifier. We then apply LPZK towards simplifying and improving recent constructions of reusable non-interactive secure computation (NISC) from VOLE (Chase et al., Crypto 2019). As an application, we give concretely efficient and reusable NISC protocols over VOLE for bounded inner product, where the sender's input vector should have a bounded $L_2$-norm.

This note presents two attacks against COMET, a second-round candidate in the NIST lightweight cryptography standardization process. The first attack uses a long message to detect the use of weak keys, whereas the second attack focuses on the resistance of COMET against slide attacks. These attacks do not invalidate the security claims of the designers.

This work is dedicated to APN and AB functions which are optimal against differential and linear cryptanlysis when used as S-boxes in block ciphers. They also have numerous applications in other branches of mathematics and information theory such as coding theory, sequence design, combinatorics, algebra and projective geometry. In this paper we give an overview of known constructions of APN and AB functions, in particular, those leading to infinite classes of these functions. Among them, the bivariate construction method, the idea first introduced in 2011 by the third author of the present paper, turned out to be one of the most fruitful. It has been known since 2011 that one of the families derived from the bivariate construction contains the infinite families derived by Dillon's hexanomial method. Whether the former family is larger than the ones it contains has stayed an open problem which we solve in this paper. Further we consider the general bivariate construction from 2013 by the third author and study its relation to the recently found infinite families of bivariate APN functions.

Cloud storage is becoming increasingly popular among end users that outsource their personal data to services such as Dropbox or Google Drive. For security, uploaded data should ideally be encrypted under a key that is controlled and only known by the user. Current solutions that support user-centric encryption either require the user to manage strong cryptographic keys, or derive keys from weak passwords. While the former has massive usability issues and requires secure storage by the user, the latter approach is more convenient but offers only little security since encrypted data is susceptible to offline attacks. The recent concept of password-authenticated secret-sharing (PASS) enables users to securely derive strong keys from weak passwords by leveraging a distributed server setup, and has been considered a promising step towards secure and usable encryption. However, using PASS for encryption is not as suitable as originally thought: it only considers the (re)construction of a \emph{single}, static key -- whereas practical encryption will require the management of \emph{many}, object-specific keys. Using a dedicated PASS instance for every key makes the solution vulnerable against online attacks, inherently leaks access patterns to the servers and poses the risk of permanent data loss when an incorrect password is used at encryption. We therefore propose a new protocol that directly targets the problem of boostrapping encryption from a single password: distributed password-authenticated symmetric encryption DPaSE. DPaSE offers strong security and usability, such as protecting the user's password against online and offline attacks, and ensuring message privacy and ciphertext integrity as long as at least one server is honest. We formally define the desired security properties in the UC framework and propose a provably secure instantiation. The core of our protocol is a new type of Oblivious Pseudorandom Function (OPRF) that allows to extend a previous partially-blind query with a follow-up request and will be used to blindly carry over passwords across evaluations and avoid online attacks. Our (proof-of-concept) implementation of DPaSE uses $10$ exponentiations at the user, $4$ exponentiations and $2$ pairings at each server, and has a server throughput of $76$ account creations and $37$ (user authentication followed by) encryptions per second, when run between a user and 2-10 servers.

In this paper, we study the effect of two modifications to multivariate public key encryption schemes: internal perturbation (ip), and Q_+. Focusing on the Dob encryption scheme, a construction utilising these modifications, we accurately predict the number of degree fall polynomials produced in a Gröbner basis attack, up to and including degree five. The predictions remain accurate even when fixing variables. Based on this new theory we design a novel attack on the Dob encryption scheme, which breaks Dob using the parameters suggested by its designers. While our work primarily focuses on the Dob encryption scheme, we also believe that the presented techniques will be of particular interest to the analysis of other big-field schemes.

Decentralized cryptocurrencies still suffer from three interrelated weaknesses: Low transaction rates, high transaction fees, and long confirmation times. Payment Channels promise to be a solution to these issues, and many constructions for real-life cryptocurrencies, such as Bitcoin, are known. Somewhat surprisingly, no such solution is known for Monero, the largest privacy-preserving cryptocurrency, without requiring system-wide changes like a hard-fork of its blockchain. In this work, we close this gap by presenting \textsc{PayMo}, the first payment channel protocol that is fully compatible with Monero. \textsc{PayMo} does not require any modification of Monero and can be readily used to perform off-chain payments. Notably, transactions in \textsc{PayMo} are identical to standard transactions in Monero, therefore not hampering the coins' fungibility. Using \textsc{PayMo}, we also construct the first fully compatible secure atomic-swap protocol for Monero: One can now securely swap a token of Monero with a token of several major cryptocurrencies such as Bitcoin, Ethereum, Ripple, Cardano, etc. Before our work, it was not known how to implement secure atomic swaps protocols for Monero without forcing a hard fork. Our main technical contribution is a new construction of an efficient verifiable timed linkable ring signature, where signatures can be hidden for a pre-determined amount of time, in a verifiable way. Our scheme is fully compatible with the transaction scheme of Monero and it might be of independent interest. We implemented \textsc{PayMo} and our results show that, even with high network latency and with a single CPU core, two regular users can perform up to 93500 payments over a span of 2 minutes (the block production rate of Monero). This is approximately five orders of magnitude improvement over the current payment rate of Monero.

Nowadays, virtually all products and services offered by financial institutions are backed by technology. While the frontend banking services seem to be simple, the core-banking backend systems and architecture are complex and often based on legacy technologies. Customer-facing applications and services are evolving rapidly, yet they have data dependencies on core banking systems running on ancient technology standards. While those legacy systems are preferred for their stability, reliability, availability, and security properties, in adapting the frontends and services many security and privacy issues can occur. Clearly, this issues are arising as those systems have been designed decades ago, without considering the enormous amounts of data that they are required to handle and also considering different threat scenarios. Moreover, the trend towards using new technologies such as Distributed Ledger Technologies (DLT) has also emerged in the financial sector. As the nodes in DLT systems are decentralized, additional security threats come to light. The focus of this work is the security of financial technologies in the FinTech domain. We provide relevant categorization and taxonomies for a better understanding of the main cyber-attack types, and suitable countermeasures. Our findings are supported by using security-by-design principles for some selected critical financial use-cases, and include a detailed discussion of the resulting threats, attack vectors and security recommendations.

Nextcloud provides a server side encryption feature that is implemented by the Default Encryption Module. This paper presents cryptographic vulnerabilities that existed within the Default Encryption Module as well as other shortcomings that still need to be addressed. The vulnerabilities allowed an attacker to break the provided confidentiality and integrity protection guarantees. There is a high risk that ownCloud also contains some of the issues presented in this paper as it still has cryptographic code in common with Nextcloud.

In this paper, we present a detailed study of the cost of the quantum key search attack using Grover. We consider the popular Feedback Shift Register (FSR) based ciphers Grain-128-AEAD, TinyJAMBU, LIZARD, and Grain-v1 considering the NIST's MAXDEPTH depth restriction. We design reversible quantum circuits for these ciphers and also provide the QISKIT implementations for estimating gate counts. Our results show that cryptanalysis is possible with gate count less than $2^{170}$. In this direction, we also study the scenario where initial keystreams may be discarded before using it for encryption so that the Grovers attack on key search becomes costly in terms of circuit repetition. Finally, we connect Grover with BSW sampling for stream ciphers with low sampling resistance. We implement this attack on LIZARD (secret key size of 120 bits, state 121 bits, and security equivalent to 80 bits) and successfully recover the internal states with $2^{40.5}$ queries to the cryptographic oracle and $ 2^{40} $ amount of data. Our results provide a clear view of the exact status of quantum cryptanalysis against FSR based symmetric ciphers.

Typical approaches for minimizing the round complexity of multiparty computation (MPC) come at the cost of increased communication complexity (CC) or the reliance on setup assumptions. A notable exception is the recent work of Ananth et al. [TCC 2019], which used Functional Encryption (FE) combiners to obtain a round optimal (two-round) semi-honest MPC in the plain model with a CC proportional to the depth and input-output length of the circuit being computed—we refer to such protocols as circuit scalable. This leaves open the question of obtaining communication efficient protocols that are secure against malicious adversaries in the plain model, which we present in this work. Concretely, our two main contributions are: 1) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-scalable maliciously secure MPC protocols in the plain model, assuming (succinct) FE combiners. 2) We provide a round-preserving black-box compiler that compiles a wide class of MPC protocols into circuit-independent— i.e., with a CC that depends only on the input-output length of the circuit—maliciously secure MPC protocols in the plain model, assuming Multi-Key Fully-Homomorphic Encryption (MFHE). Our constructions are based on a new compiler that turns a wide class of MPC protocols into k-delayed-input function MPC protocols (a notion we introduce), where the function that is being computed is specified only in the k-th round of the protocol. As immediate corollaries of our two compilers, we derive (1) the first round-optimal and circuit-scalable maliciously secure MPC protocol, and (2) the first round-optimal and circuit-independent maliciously secure MPC protocol in the plain model. The latter achieves the best to-date CC for a round-optimal maliciously secure MPC protocol. In fact, it is even communication-optimal when the output size of the function being evaluated is smaller than its input size (e.g., for boolean functions). All of our results are based on standard polynomial time assumptions.

We describe a novel type of weak cryptographic private key that can exist in any discrete logarithm based public-key cryptosystem set in a group of prime order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on numerical size (such as smaller private keys, or private keys lying in an interval) that will always exist in any DLP cryptosystems, our type of weak private keys occurs purely due to parameter choice of $p$, and hence, can be removed with appropriate value of $p$. Using the theory of implicit group representations, we present algorithms that can determine whether a key is weak, and if so, recover the private key from the corresponding public key. We analyze several elliptic curves proposed in the literature and in various standards, giving counts of the number of keys that can be broken with relatively small amounts of computation. Our results show that many of these curves, including some from standards, have a considerable number of such weak private keys. We also use our methods to show that none of the 14 outstanding Certicom Challenge problem instances are weak in our sense, up to a certain weakness bound.

Publicly Verifiable Zero-Knowledge proofs are known to exist only from setup assumptions such as a trusted Common Reference String (CRS) or a Random Oracle. Unfortunately, the former requires a trusted party while the latter does not exist. Blockchains are distributed systems that already exist and provide certain security properties (under some honest majority assumption), hence, a natural recent research direction has been to use a blockchain as an alternative setup assumption. In TCC 2017 Goyal and Goyal proposed a construction of a publicly verifiable zero-knowledge (pvZK) proof system for some proof-of-stake blockchains. The zero-knowledge property of their construction however relies on some additional and not fully specified assumptions about the current and future behavior of honest blockchain players. In this paper, we provide several contributions. First, we show that when using a blockchain to design a provably secure protocol, it is dangerous to rely on demanding additional requirements on behaviors of the blockchain players. We do so by showing an “attack of the clones” whereby a malicious verifier can use a smart contract to slyly (not through bribing) clone capabilities of honest stakeholders and use those to invalidate the zero-knowledge property of the proof system by Goyal and Goyal. Second, we propose a new publicly verifiable zero-knowledge proof system that relies on non-interactive commitments and on an assumption on the min-entropy of some blocks appearing on the blockchain. Third, motivated by the fact that blockchains are a recent innovation and their resilience in the long run is still controversial, we introduce the concept of collapsing blockchain, and we prove that the zero-knowledge property of our scheme holds even if the blockchain eventually becomes insecure and all blockchain players eventually become dishonest.

Incoercible multi-party computation (Canetti-Gennaro ’96) allows parties to engage in secure computation with the additional guarantee that the public transcript of the computation cannot be used by a coercive outsider to verify representations made by the parties regarding their inputs, outputs, and local random choices. That is, it is guaranteed that the only deductions regarding the truthfulness of such representations, made by an outsider who has witnessed the communication among the parties, are the ones that can be drawn just from the represented inputs and outputs alone. To date, all incoercible secure computation protocols withstand coercion of only a fraction of the parties, or else assume that all parties use an execution environment that makes some crucial parts of their local states physically inaccessible even to themselves. We consider, for the first time, the setting where all parties are coerced, and the coercer expects to see the entire history of the computation. We allow both protocol participants and external attackers to access a common reference string which is generated once and for all by an uncorruptable trusted party. In this setting we construct: - A general multi-party function evaluation protocol, for any number of parties, that withstands coercion of all parties, as long as all parties use the prescribed ``faking algorithm'' upon coercion. This holds even if the inputs and outputs represented by coerced parties are globally inconsistent with the evaluated function. - A general two-party function evaluation protocol that withstands even the %``mixed'' case where some of the coerced parties do follow the prescribed faking algorithm. (For instance, these parties might collude with the coercer and disclose their true local states.) This protocol is limited to functions where the input of at least one of the parties is taken from a small (poly-size) domain. It uses fully deniable encryption with public deniability for one of the parties; when instantiated using the fully deniable encryption of Canetti, Park, and Poburinnaya (Crypto'20), it takes 3 rounds of communication. Both protocols operate in the common reference string model, and use fully bideniable encryption (Canetti Park and Poburinnaya, Crypto'20) and sub-exponential indistinguishability obfuscation. Finally, we show that protocols with certain communication pattern cannot be incoercible, even in a weaker setting where only some parties are coerced.

We consider interactive proofs for social graphs, where the verifier has only oracle access to the graph and can query for the $i^{th}$ neighbor of a vertex $v$, given $i$ and $v$. In this model, we construct a doubly-efficient public-coin two-message interactive protocol for estimating the size of the graph to within a multiplicative factor $\epsilon>0$. The verifier performs $\tilde{O}(1/\epsilon^2 \cdot \tau_{mix} \cdot \Delta)$ queries to the graph, where $\tau_{mix}$ is the mixing time of the graph and $\Delta$ is the average degree of the graph. The prover runs in quasi-linear time in the number of nodes in the graph. Furthermore, we develop a framework for computing the quantiles of essentially any (reasonable) function $f$ of vertices/edges of the graph. Using this framework, we can estimate many health measures of social graphs such as the clustering coefficients and the average degree, where the verifier performs only a small number of queries to the graph. Using the Fiat-Shamir paradigm, we are able to transform the above protocols to a non-interactive argument in the random oracle model. The result is that social media companies (e.g., Facebook, Twitter, etc.) can publish, once and for all, a short proof for the size or health of their social network. This proof can be publicly verified by any single user using a small number of queries to the graph.

The celebrated work of Gorbunov, Vaikuntanathan and Wee provided the first key policy attribute based encryption scheme (ABE) for circuits from the Learning With Errors (LWE) assumption. However, the arguably more natural ciphertext policy variant has remained elusive, and is a central primitive not yet known from LWE. In this work, we construct the first symmetric key ciphertext policy attribute based encryption scheme (CP-ABE) for all polynomial sized circuits from the learning with errors (LWE) assumption. In more detail, the ciphertext for a message $m$ is labelled with an access control policy $f$, secret keys are labelled with public attributes $x$ from the domain of $f$ and decryption succeeds to yield the hidden message $m$ if and only if $f(x)=1$. The size of our public and secret key do not depend on the size of the circuits supported by the scheme -- this enables our construction to support circuits of unbounded size (but bounded depth). Our construction is secure against collusions of unbounded size. We note that current best CP-ABE schemes [BSW07,Wat11,LOSTW10,OT10,LW12,RW13,Att14,Wee14,AHY15,CGW15,AC17,KW19] rely on pairings and only support circuits in the class NC1 (albeit in the public key setting). We adapt our construction to the public key setting for the case of bounded size circuits. The size of the ciphertext and secret key as well as running time of encryption, key generation and decryption satisfy the efficiency properties desired from CP-ABE, assuming that all algorithms have RAM access to the public key. However, the running time of the setup algorithm and size of the public key depends on the circuit size bound, restricting the construction to support circuits of a-priori bounded size. We remark that the inefficiency of setup is somewhat mitigated by the fact that setup must only be run once. We generalize our construction to consider attribute and function hiding. The compiler of lockable obfuscation upgrades any attribute based encryption scheme to predicate encryption, i.e. with attribute hiding [GKW17,WZ17]. Since lockable obfuscation can be constructed from LWE, we achieve ciphertext policy predicate encryption immediately. For function privacy, we show that the most natural notion of function hiding ABE for circuits, even in the symmetric key setting, is sufficient to imply indistinguishability obfuscation. We define a suitable weakening of function hiding to sidestep the implication and provide a construction to achieve this notion for both the key policy and ciphertext policy case. Previously, the largest function class for which function private predicate encryption (supporting unbounded keys) could be achieved was inner product zero testing, by Shen, Shi and Waters [SSW09].

We present simpler and improved constructions of 2-round protocols for secure multi-party computation (MPC) in the semi-honest setting. Our main results are new information-theoretically secure protocols for arithmetic NC1 in two settings: (i) the plain model tolerating up to $t < n/2$ corruptions; and (ii) in the OLE-correlation model tolerating any number of corruptions. Our protocols achieve adaptive security and require only black-box access to the underlying field, whereas previous results only achieve static security and require non-black-box field access. Moreover, both results extend to polynomial-size circuits with computational and adaptive security, while relying on black-box access to a pseudorandom generator. In the OLE correlation model, the extended protocols for circuits tolerate up to $n-1$ corruptions. Along the way, we introduce a conceptually novel framework for 2-round MPC that does not rely on the round collapsing framework underlying all of the recent advances in 2-round MPC.

We investigate fairness in secure multiparty computation when the number of parties $n = poly(\lambda)$ grows polynomially in the security parameter, $\lambda$. Prior to this work, efficient protocols achieving fairness with no honest majority and polynomial number of parties were known only for the AND and OR functionalities (Gordon and Katz, TCC'09). We show the following: --We first consider symmetric Boolean functions $F : \{0,1\}^n \to \{0,1\}$, where the underlying function $f_{n/2,n/2}: \{0, \ldots, n/2\} \times \{0, \ldots, n/2\} \to \{0,1\}$ can be computed fairly and efficiently in the $2$-party setting. We present an efficient protocol for any such $F$ tolerating $n/2$ or fewer corruptions, for $n = poly(\lambda)$ number of parties. --We present an efficient protocol for $n$-party majority tolerating $n/2+1$ or fewer corruptions, for $n = poly(\lambda)$ number of parties. The construction extends to $n/2+c$ or fewer corruptions, for constant $c$. --We extend both of the above results to more general types of adversarial structures and present instantiations of non-threshold adversarial structures of these types. These instantiations are obtained via constructions of projective planes and combinatorial designs.

Information-theoretic private information retrieval (PIR) schemes have attractive concrete efficiency features. However, in the standard PIR model, the computational complexity of the servers must scale linearly with the database size. We study the possibility of bypassing this limitation in the case where the database is a truth table of a "simple" function, such as a union of (multi-dimensional) intervals or convex shapes, a decision tree, or a DNF formula. This question is motivated by the goal of obtaining lightweight homomorphic secret sharing (HSS) schemes and secure multiparty computation (MPC) protocols for the corresponding families. We obtain both positive and negative results. For "first-generation" PIR schemes based on Reed-Muller codes, we obtain computational shortcuts for the above function families, with the exception of DNF formulas for which we show a (conditional) hardness result. For "third-generation" PIR schemes based on matching vectors, we obtain stronger hardness results that apply to all of the above families. Our positive results yield new information-theoretic HSS schemes and MPC protocols with attractive efficiency features for simple but useful function families. Our negative results establish new connections between information-theoretic cryptography and fine-grained complexity.

There has been a large body of work characterizing the round complexity of general-purpose maliciously secure two-party computation (2PC) against probabilistic polynomial time adversaries. This is particularly true for zero-knowledge, which is a special case of 2PC. In fact, in the special case of zero knowledge, optimal protocols with unconditional security against one of the two players have also been meticulously studied and constructed. On the other hand, general-purpose maliciously secure 2PC with statistical or unconditional security against one of the two participants has remained largely unexplored so far. In this work, we initiate the study of such protocols, which we refer to as 2PC with one-sided statistical security. We settle the round complexity of 2PC with one-sided statistical security with respect to black-box simulation by obtaining the following tight results: In a setting where only one party obtains an output, we design 2PC in $4$ rounds with statistical security against receivers and computational security against senders. In a setting where both parties obtain outputs, we design 2PC in $5$ rounds with computational security against the party that obtains output first and statistical security against the party that obtains output last. Katz and Ostrovsky (CRYPTO 2004) showed that 2PC with black-box simulation requires at least $4$ rounds when one party obtains an output and $5$ rounds when both parties obtain outputs, even when only computational security is desired against both parties. Thus in these settings, not only are our results tight, but they also show that statistical security is achievable at no extra cost to round complexity. This still leaves open the question of whether 2PC can be achieved with black-box simulation in $4$ rounds with statistical security against senders and computational security against receivers. Based on a lower bound on computational zero-knowledge proofs due to Katz (TCC 2008), we observe that the answer is negative unless the polynomial hierarchy collapses.

We establish barriers on the efficiency of succinct arguments in the random oracle model. We give evidence that, under standard complexity assumptions, there do not exist succinct arguments where the argument verifier makes a small number of queries to the random oracle. The new barriers follow from new insights into how probabilistic proofs play a fundamental role in constructing succinct arguments in the random oracle model. *IOPs are necessary for succinctness.* We prove that any succinct argument in the random oracle model can be transformed into a corresponding interactive oracle proof (IOP). The query complexity of the IOP is related to the succinctness of the argument. *Algorithms for IOPs.* We prove that if a language has an IOP with good soundness relative to query complexity, then it can be decided via a fast algorithm with small space complexity. By combining these results we obtain barriers for a large class of deterministic and non-deterministic languages. For example, a succinct argument for 3SAT with few verifier queries implies an IOP with good parameters, which in turn implies a fast algorithm for 3SAT that contradicts the Exponential-Time Hypothesis. We additionally present results that shed light on the necessity of several features of probabilistic proofs that are typically used to construct succinct arguments, such as holography and state restoration soundness. Our results collectively provide an explanation for "why" known constructions of succinct arguments have a certain structure.

Minimizing the computational cost of the prover is a central goal in the area of succinct arguments. In particular, it remains a challenging open problem to construct a succinct argument where the prover runs in linear time and the verifier runs in polylogarithmic time. We make progress towards this goal by presenting a new linear-time probabilistic proof. For any fixed $\epsilon > 0$, we construct an interactive oracle proof (IOP) that, when used for the satisfiability of an $N$-gate arithmetic circuit, has a prover that uses $O(N)$ field operations and a verifier that uses $O(N^{\epsilon})$ field operations. The sublinear verifier time is achieved in the holographic setting for every circuit (the verifier has oracle access to a linear-size encoding of the circuit that is computable in linear time). When combined with a linear-time collision-resistant hash function, our IOP immediately leads to an argument system where the prover performs $O(N)$ field operations and hash computations, and the verifier performs $O(N^{\epsilon})$ field operations and hash computations (given a short digest of the $N$-gate circuit).

Zero-knowledge protocols enable the truth of a mathematical statement to be certified by a verifier without revealing any other information. Such protocols are a cornerstone of modern cryptography and recently are becoming more and more practical. However, a major bottleneck in deployment is the efficiency of the prover and, in particular, the space-efficiency of the protocol. For every $\mathsf{NP}$ relation that can be verified in time $T$ and space $S$, we construct a public-coin zero-knowledge argument in which the prover runs in time $T \cdot \mathrm{polylog}(T)$ and space $S \cdot \mathrm{polylog}(T)$. Our proofs have length $\mathrm{polylog}(T)$ and the verifier runs in time $T \cdot \mathrm{polylog}(T)$ (and space $\mathrm{polylog}(T)$). Our scheme is in the random oracle model and relies on the hardness of discrete log in prime-order groups. Our main technical contribution is a new space efficient polynomial commitment scheme for multi-linear polynomials. Recall that in such a scheme, a sender commits to a given multi-linear polynomial $P \colon \mathbb{F}^n \rightarrow \mathbb{F}$ so that later on it can prove to a receiver statements of the form "$P(x) = y$". In our scheme, which builds on the commitment schemes of Bootle et al. (Eurocrypt 2016) and Bünz et al. (S&P 2018), we assume that the sender is given multi-pass streaming access to the evaluations of $P$ on the Boolean hypercube and w show how to implement both the sender and receiver in roughly time $2^n$ and space $n$ and with communication complexity roughly $n$.

The HFEv- signature scheme is a twenty year old multivariate public key signature scheme. It uses the Minus and the Vinegar modifier on the original HFE scheme. An instance of the HFEv- signature scheme called GeMSS is one of the alternative candidates for signature schemes in the third round of the NIST Post Quantum Crypto (PQC) Standardization Project. In this paper, we propose a new key recovery attack on the HFEv- signature scheme. We show that the Minus modification does not enhance the security of cryptosystems of the HFE family, while the Vinegar modification increases the complexity of our attack only by a polynomial factor. By doing so, we show that the proposed parameters of the GeMSS scheme are not as secure as claimed. Our attack shows that it is very difficult to build a secure and efficient signature scheme on the basis of HFEv-.

Given a ciphertext, is it possible to prove the deletion of the underlying plaintext? Since classical ciphertexts can be copied, clearly such a feat is impossible using classical information alone. In stark contrast to this, we show that quantum encodings enable certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext should the decryption key be revealed. Our scheme is feasible with current quantum technology: the honest parties only require quantum devices for single-qubit preparation and measurements; the scheme is also robust against noise in these devices. Furthermore, we provide an analysis that is suitable in the finite-key regime.

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. We show that this same task can in fact be performed non-interactively (with setup) and in zero-knowledge. Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP. We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

A family of one-way functions is extractable if given a random function in the family, an efficient adversary can only output an element in the image of the function if it knows a corresponding preimage. This knowledge extraction guarantee is particularly powerful since it does not require interaction. However, extractable one-way functions (EFs) are subject to a strong barrier: assuming indistinguishability obfuscation, no EF can have a knowledge extractor that works against all polynomial-size non-uniform adversaries. This holds even for non-black-box extractors that use the adversary’s code. Accordingly, the literature considers either EFs based on non-falsifiable knowledge assumptions, where the extractor is not explicitly given, but it is only assumed to exist, or EFs against a restricted class of adversaries with a bounded non-uniform advice. This falls short of cryptography’s gold standard of security that requires an explicit reduction against non-uniform adversaries of arbitrary polynomial size. Motivated by this gap, we put forward a new notion of weakly extractable one-way functions (WEFs) that circumvents the known barrier. We then prove that WEFs are inextricably connected to the long standing question of three-message zero knowledge protocols. We show that different flavors of WEFs are sufficient and necessary for three-message zero knowledge to exist. The exact flavor depends on whether the protocol is computational or statistical zero knowledge and whether it is publicly or privately verifiable. Combined with recent progress on constructing three message zero-knowledge, we derive a new connection between keyless multi-collision resistance and the notion of incompressibility and the feasibility of non-interactive knowledge extraction. Another interesting corollary of our result is that in order to construct three-message zero knowledge arguments, it suffices to construct such arguments where the honest prover strategy is unbounded.

We present simple and improved constructions of public-key functional encryption (FE) schemes for quadratic functions. Our main results are: - an FE scheme for quadratic functions with constant-size keys as well as shorter ciphertexts than all prior schemes based on static assumptions; – a public-key partially-hiding FE that supports NC1 computation on public attributes and quadratic computation on the private message, with ciphertext size independent of the length of the public attribute. Both constructions achieve selective, simulation-based security against unbounded collusions, and rely on the (bi-lateral) k-linear assumption in prime-order bilinear groups. At the core of these constructions is a new reduction from FE for quadratic functions to FE for linear functions.

We study information-theoretic secure multiparty protocols that achieve full security, including guaranteed output delivery, at the presence of an active adversary that corrupts a constant fraction of the parties. It is known that 2 rounds are insufficient for such protocols even when the adversary corrupts only two parties (Gennaro, Ishai, Kushilevitz, and Rabin; Crypto 2002), and that perfect protocols can be implemented in $3$ rounds as long as the adversary corrupts less than a quarter of the parties (Applebaum , Brakerski, and Tsabary; Eurocrypt, 2019). Furthermore, it was recently shown that the quarter threshold is tight for any 3-round \emph{perfectly-secure} protocol (Applebaum, Kachlon, and Patra; FOCS 2020). Nevertheless, one may still hope to achieve a better-than-quarter threshold at the expense of allowing some negligible correctness errors and/or statistical deviations in the security. Our main results show that this is indeed the case. Every function can be computed by 3-round protocols with \emph{statistical} security as long as the adversary corrupts less than a third of the parties. Moreover, we show that any better resiliency threshold requires $4$ rounds. Our protocol is computationally inefficient and has an exponential dependency in the circuit's depth $d$ and in the number of parties $n$. We show that this overhead can be avoided by relaxing security to computational, assuming the existence of a non-interactive commitment (NICOM). Previous 3-round computational protocols were based on stronger public-key assumptions. When instantiated with statistically-hiding NICOM, our protocol provides \emph{everlasting statistical} security, i.e., it is secure against adversaries that are computationally unlimited \emph{after} the protocol execution. To prove these results, we introduce a new hybrid model that allows for 2-round protocols with a linear resiliency threshold. Here too we prove that, for perfect protocols, the best achievable resiliency is $n/4$, whereas statistical protocols can achieve a threshold of $n/3$. In the plain model, we also construct the first 2-round $n/3$-statistical verifiable secret sharing that supports second-level sharing and prove a matching lower-bound, extending the results of Patra, Choudhary, Rabin, and Rangan (Crypto 2009). Overall, our results refine the differences between statistical and perfect models of security and show that there are efficiency gaps even for thresholds that are realizable in both models.

We present the first complete implementation of the offline Simon's algorithm, and estimate its cost to attack the MAC Chaskey, the block cipher PRINCE and the NIST lightweight candidate AEAD scheme Elephant. These attacks require a reasonable amount of qubits, comparable to the number of qubits required to break RSA-2048. They are faster than other collision algorithms, and the attacks against PRINCE and Chaskey are the most efficient known to date. As Elephant has a key smaller than its state size, the algorithm is less efficient and ends up more expensive than exhaustive search. We also propose an optimized quantum circuit for boolean linear algebra as well as complete reversible implementations of PRINCE, Chaskey, spongent and Keccak which are of independent interest for quantum cryptanalysis. We stress that our attacks could be applied in the future against today's communications, and recommend caution when choosing symmetric constructions for cases where long-term security is expected.

Correlated secret randomness is a useful resource for many cryptographic applications. We initiate the study of pseudorandom correlation functions (PCFs) that offer the ability to securely generate virtually unbounded sources of correlated randomness using only local computation. Concretely, a PCF is a keyed function $F_k$ such that for a suitable joint key distribution $(k_0,k_1)$, the outputs $(f_{k_0}(x),f_{k_1}(x))$ are indistinguishable from instances of a given target correlation. An essential security requirement is that indistinguishability hold not only for outsiders, who observe the pairs of outputs, but also for insiders who know one of the two keys. We present efficient constructions of PCFs for a broad class of useful correlations, including oblivious transfer and multiplication triple correlations, from a variable-density variant of the Learning Parity with Noise assumption (VDLPN). We also present several cryptographic applications that motivate our efficient PCF constructions. The VDLPN assumption is independently motivated by two additional applications. First, different flavors of this assumption give rise to weak pseudorandom function candidates in depth-2 $\mathsf{AC}^0[\oplus]$ that can be conjectured to have subexponential security, matching the best known learning algorithms for this class. This is contrasted with the quasipolynomial security of previous (higher-depth) $\mathsf{AC}^0[\oplus]$ candidates. We support our conjectures by proving resilience to several classes of attacks. Second, VDLPN implies simple constructions of pseudorandom generators and weak pseudorandom functions with security against XOR related-key attacks.

In this paper, we present the more accurate definition of strong linear complexity of feedback shift registers based on Boolean algebraic than before, and analyze the bound of strong linear complexity by the fixed feedback function. Furthermore, the feedback shift registers with maximum strong linear complexity are constructed, whose feedback functions require the least number of monomials. We also show that the conclusions provide particular ideas and criteria for the design of feedback shift registers.

With the emerging popularity of cloud computing, the problem of how to query over cryptographically-protected data has been widely studied. However, most existing works focus on querying protected relational databases, few work has shown interests in graph databases. In this paper, we first investigate and summarize two single-instruction queries, namely Graph Pattern Matching (GPM) and Graph Navigation (GN). Then we follow their design intuitions and leverage secure Multi-Party Computation (MPC) to implement their functionalities in a privacy-preserving manner. Moreover, we propose a general framework for processing multi-instruction query on secret-shared graph databases and present a novel cryptographic primitive Oblivious Filter (OF) as a core building block. Nevertheless, we formalize the problem of OF and present its constructions using homomorphic encryption. Finally, we conduct an empirical study to evaluate the efficiency of our proposed OF protocol.

Mixed Integer Linear Programming (MILP) is a very common method of modelling differential and linear bounds for ciphers, as it automates the process of finding the best differential trail or linear approximation. The Convex Hull (CH) modelling, introduced by Sun et al. (Eprint 2013/Asiacrypt 2014), is a popular method in this regard, which can convert the conditions corresponding to a small (4-bit) SBox to MILP constraints efficiently. In our work, we study this modelling with CH in more depth and observe a previously unreported problem associated with it. Our analysis shows, there are SBoxes for which the CH modelling can yield incorrect modelling. As such, using the CH modelling may lead to incorrect differential or linear bounds. This arises from the observation that although the CH is generated for a certain set of points, there can be points outside this set which also satisfy all the inequalities of the CH. As apparently no variant of the CH modelling can circumvent this problem, we propose a new modelling for differential and linear bounds. Our modelling makes use of every points of interest individually. This modelling works for an arbitrary SBox, and is able to find the exact bound. Additionally, we also explore the possibility of using redundant constraints, such that the run time for an MILP solver can be reduced while keeping the optimal result unchanged. For this purpose, we revisit the CH modelling and use the CH constraints as redundant constraints (on top of our usual constraints, which ensure the aforementioned problem does not occur). In fact, we choose two heuristics from the convex hull modelling. The first uses all the inequalities of a convex hull, while second uses a reduced number of inequalities. Apart from that, we also propose to use the solutions for the smaller rounds as another heuristic to find the optimal bound for a higher round. With our experiments on round-reduced GIFT-128, we show it is possible to reduce the run time a few folds using a suitable choice of redundant constraints. Further, we observe the necessity to consider separate heuristics for the differential and linear cases. We also present the optimal linear bounds for 11- and 12-rounds of GIFT-128, extending from the best-known result of 10-rounds.

We present a two-message oblivious transfer protocol achieving statistical sender privacy and computational receiver privacy based on the RLWE assumption for cyclotomic number fields. This work improves upon prior lattice-based statistically sender-private oblivious transfer protocols by reducing the total communication between parties by a factor $O(n\log q)$ for transfer of length $O(n)$ messages. Prior work of Brakerski and Döttling uses transference theorems to show that either a lattice or its dual must have short vectors, the existence of which guarantees lossy encryption for encodings with respect to that lattice, and therefore statistical sender privacy. In the case of ideal lattices from embeddings of cyclotomic integers, the existence of one short vector implies the existence of many, and therefore encryption with respect to either a lattice or its dual is guaranteed to ``lose" more information about the message than can be ensured in the case of general lattices. This additional structure of ideals of cyclotomic integers allows for efficiency improvements beyond those that are typical when moving from the generic to ideal lattice setting, resulting in smaller message sizes for sender and receiver, as well as a protocol that is simpler to describe and analyze.

We study the communication complexity of unconditionally secure multiparty computation (MPC) protocols in the honest majority setting. Despite tremendous efforts in achieving efficient protocols for binary fields under computational assumptions, there are no efficient unconditional MPC protocols in this setting. In particular, there are no $n$-party protocols with constant overhead admitting communication complexity of $O(n)$ bits per gate. Cascudo, Cramer, Xing and Yuan (CRYPTO 2018) were the first ones to achieve such an overhead in the amortized setting by evaluating $O(\log n)$ copies of the same circuit in the binary field in parallel. In this work, we construct the first unconditional MPC protocol secure against a malicious adversary in the honest majority setting evaluating just a single boolean circuit with amortized communication complexity of $O(n)$ bits per gate.

We construct uniquely decodable codes against channels which are computationally bounded. Our construction requires only a public-coin (transparent) setup. All prior work for such channels either required a setup with secret keys and states, could not achieve unique decoding, or got worse rates (for a given bound on codeword corruptions). On the other hand, our construction relies on a strong cryptographic hash function with security properties that we only instantiate in the random oracle model.

Zero knowledge proofs are an important building block in many cryptographic applications. Unfortunately, when the proof statements become very large, existing zero-knowledge proof systems easily reach their limits: either the computational overhead, the memory footprint, or the required bandwidth exceed levels that would be tolerable in practice. We present an interactive zero-knowledge proof system for boolean and arithmetic circuits, called Mac'n'Cheese, with a focus on supporting large circuits. Our work follows the commit-and-prove paradigm instantiated using information-theoretic MACs based on vector oblivious linear evaluation to achieve high efficiency. We additionally show how to optimize disjunctions, with a general OR transformation for proving the disjunction of $m$ statements that has communication complexity proportional to the longest statement (plus an additive term logarithmic in $m$). These disjunctions can further be nested, allowing efficient proofs about complex statements with many levels of disjunctions. We also show how to make Mac'n'Cheese non-interactive (after a preprocessing phase) using the Fiat-Shamir transform, and with only a small degradation in soundness. We have implemented the online phase of Mac'n'Cheese and achieve a runtime of 144 ns per AND gate and 1.5 $\mu$s per multiplication gate in $\mathbb{F}_{2^{61}-1}$ when run over a network with a 95 ms latency and a bandwidth of 31.5 Mbps. In addition, we show that the disjunction optimization improves communication as expected: when proving a boolean circuit with eight branches and each branch containing roughly 1 billion multiplications, Mac'n'Cheese requires only 75 more bytes to communicate than in the single branch case.

In this work we apply the dynamical systems analysis of Hanrot et al. (CRYPTO'11) to a class of lattice block reduction algorithms that includes (natural variants of) slide reduction and block-Rankin reduction. This implies sharper bounds on the polynomial running times (in the query model) for these algorithms and opens the door to faster practical variants of slide reduction. We give heuristic arguments showing that such variants can indeed speed up slide reduction significantly in practice. This is confirmed by experimental evidence, which also shows that our variants are competitive with state-of-the-art reduction algorithms.

Broadcast is a primitive which allows a specific party to distribute a message consistently among $n$ parties, even if up to $t$ parties exhibit malicious behaviour. In the classical model with a complete network of bilateral authenticated channels, the seminal result of Pease et al. [PSL80] shows that broadcast is achievable if and only if $t < n/3$. There are two generalizations suggested for the broadcast problem -- with respect to the adversarial model and the communication model. Fitzi and Maurer [FM98] consider a (non-threshold) 'general adversary' that is characterized by the subsets of parties that could be corrupted, and show that broadcast can be realized from bilateral channels if and only if the union of no three possible corrupted sets equals the entire set of $n$ parties. On the other hand, Considine et al. [CFF+05] extend the standard model of bilateral channels with the existence of $b$-minicast channels that allow to locally broadcast among any subset of $b$ parties; the authors show that in this enhanced model of communication, secure broadcast tolerating up to $t$ corrupted parties is possible if and only if $t < \frac{b-1}{b+1}n$. These generalizations are unified in the work by Raykov [Ray15], where a tight condition on the possible corrupted sets is presented such that broadcast is achievable from a complete set of $b$-minicasts. This paper investigates the achievability of broadcast in 'general networks', i.e., networks where only some subsets of minicast channels may be available, thereby addressing open problems posed in [JMS12,Ray15]. To that end, we propose a hierarchy over all possible general adversaries, and identify for each class of general adversaries 1) a set of minicast channels that are necessary to achieve broadcast and 2) a set of minicast channels that are sufficient to achieve broadcast. In particular, this allows us to derive bounds on the amount of $b$-minicasts that are necessary and that suffice towards constructing broadcast in general $b$-minicast networks.

Let $p$ be a prime such that $p=1+2^nm$, where $n\geq 1$ and $m$ is odd. Given a square $u$ in $\mathbb{Z}_p$ and a non-square $z$ in $\mathbb{Z}_p$, we describe an algorithm to compute a square root of $u$ which requires $\mathfrak{T}+O(n^{3/2})$ operations (i.e., squarings and multiplications), where $\mathfrak{T}$ is the number of operations required to exponentiate an element of $\mathbb{Z}_p$ to the power $(m-1)/2$. This improves upon the Tonelli-Shanks (TS) algorithm which requires $\mathfrak{T}+O(n^{2})$ operations. Bernstein had proposed a table look-up based variant of the TS algorithm which requires $\mathfrak{T}+O((n/w)^{2})$ operations and $O(2^wn/w)$ storage, where $w$ is a parameter. A table look-up variant of the new algorithm requires $\mathfrak{T}+O((n/w)^{3/2})$ operations and the same storage. In concrete terms, the new algorithm is shown to require significantly fewer operations for particular values of $n$.

Secure electronic voting is a relatively trivial exercise if a single authority can be completely trusted. In contrast, the construction of efficient and usable schemes which provide strong security without strong trust assumptions is still an open problem, particularly in the remote setting. Coercion-resistance is one of, if not the hardest property to add to a verifiable e-voting system. Numerous secure e-voting systems have been designed to provide coercion-resistance. One of these systems is VoteAgain (Usenix Security 2020) whose security we revisit in this work. We discovered several pitfalls that break the security properties of VoteAgain in threat scenarios for which it was claimed secure. The most critical consequence of our findings is that there exists a voting authority in VoteAgain which needs to be trusted for all security properties. This means that VoteAgain is as (in)secure as a trivial voting system with a single and completely trusted voting authority. We argue that this problem is intrinsic to VoteAgain's design and could thus only be resolved, if possible, by fundamental modifications. We hope that our work will ensure that VoteAgain is not employed for real elections in its current form. Further, we highlight subtle security pitfalls to avoid on the path towards more efficient, usable, and reasonably secure coercion-resistant e-voting. To this end, we conclude the paper by describing the open problems which need to be solved to make VoteAgain's approach secure.

Grover search algorithm can be used to find the $n$-bit secret key at the speed of $\sqrt{n}$, which is the most effective quantum attack method for block ciphers. In order to apply the Grover search algorithm, the target block cipher should be implemented in quantum circuits. Many recent research works optimized the expensive substitute layer to evaluate the need for quantum resources of AES block ciphers. Research on the implementation of quantum circuits for lightweight block ciphers such as SIMON, SPECK, HIGHT, CHAM, LEA, and Gimli, an active research field, is also gradually taking place. In this paper, we present optimized implementations of GIFT block ciphers for quantum computers. To the best of our knowledge, this is the first implementation of GIFT in quantum circuits. Finally, we estimate quantum resources for applying the Grover algorithm to the our optimized GIFT quantum circuit.

The cube attack is one of the most important cryptanalytic techniques against Trivium. Many improvements have been proposed and lots of key-recovery attacks based on cube attacks have been established. However, among these key-recovery attacks, few attacks can recover the 80-bit full key practically. In particular, the previous best practical key-recovery attack was on 784-round Trivium proposed by Fouque and Vannet at FSE 2013 with on-line complexity about $2^{39}$. To mount a practical key-recovery attack against Trivium on a PC, a sufficient number of low-degree superpolies should be recovered, which is around 40. This is a difficult task both for experimental cube attacks and division property based cube attacks with randomly selected cubes due to lack of efficiency. In this paper, we give a new algorithm to construct candidate cubes targeting at linear superpolies in cube attacks. It is shown by our experiments that the new algorithm is very effective. In our experiments, the success probability is $ 100\% $ for finding linear superpolies using the constructed cubes. As a result, we mount a practical key-recovery attack on 805-round Trivium, which increases the number of attacked initialisation rounds by 21. We obtain over 1000 cubes with linear superpolies for 805-round Trivium, where 42 linearly independent ones could be selected. With these superpolies, for 805-round Trivium, the 80-bit key could be recovered within on-line complexity $ 2^{41.40} $, which could be carried out on a single PC equipped with a GTX-1080 GPU in several hours. Furthermore, the new algorithm is applied to 810-round Trivium, a cube of size 43 is constructed and two subcubes of size 42 with linear superpolies for 810-round Trivium are found.

A graph signature scheme is a digital signature scheme that allows a recipient to obtain a signature on a graph and subsequently prove properties thereof in zero-knowledge proofs of knowledge. While known to be expressive enough to encode statements from NP languages, one main use of graph signatures is in topology certification and confidentiality-preserving security assurance. In this paper, we present an efficient and provably secure graph signature scheme in the standard model with tight reduction. Based on the MoniPoly attribute-based credential system, this new graph signature scheme offers zero-knowledge proofs of possession of the signature itself as well as confidentiality-preserving show proofs on logical statements such as the existence of vertices, graph connectivity or isolation.

Evaluating resistance of ciphers against differential cryptanalysis is essential to define the number of rounds of new designs and to mount attacks derived from differential cryptanalysis. In this paper, we compare existing automatic tools to find the best differential characteristic on the SKINNY block cipher. As usually done in the literature, we split this search in two stages denoted by Step 1 and Step 2. In Step 1, each difference variable is abstracted with a Boolean variable and we search for the value that minimizes the trail weight, whereas Step 2 tries to instantiate each difference value while maximizing the overall differential characteristic probability. We model Step 1 using a MILP tool, a SAT tool, an ad-hoc method and a CP tool based on the Choco-solver library and provide performance results. Step 2 is modeled using the Choco-solver as it seems to outperform all previous methods on this stage. Notably, for SKINNY-128 in the SK model and for 13 rounds, we retrieve the results of Abdelkhalek et al. within a few seconds (to compare with 16 days) and we provide, for the first time, the best differential related-tweakey characteristic up to respectively 14 and 12 rounds for the TK1 and TK2 models.

We present a garbling scheme for quantum circuits, thus achieving a decomposable randomized encoding scheme for quantum computation. Specifically, we show how to compute an encoding of a given quantum circuit and quantum input, from which it is possible to derive the output of the computation and nothing else. In the classical setting, garbled circuits (and randomized encodings in general) are a versatile cryptographic tool with many applications such as secure multiparty computation, delegated computation, depth-reduction of cryptographic primitives, complexity lower-bounds, and more. However, a quantum analogue for garbling general circuits was not known prior to this work. We hope that our quantum randomized encoding scheme can similarly be useful for applications in quantum computing and cryptography. To illustrate the usefulness of quantum randomized encoding, we use it to design a conceptually-simple zero-knowledge (ZK) $\Sigma$-protocol for the complexity class QMA. Our protocol has a single-bit challenge, and allows the inputs to be delayed to the last round. The only previously-known ZK $\Sigma$-protocol for QMA is due to Broadbent and Grilo (FOCS 2020), which does not have the aforementioned properties.

Transferable e-cash is the most faithful digital analog of physical cash, as it allows users to transfer coins between them in isolation, that is, without interacting with a bank or a “ledger”. Appropriate protection of user privacy and, at the same time, providing means to trace fraudulent behavior (double-spending of coins) have made instantiating the concept notoriously hard. Baldimtsi et al. (PKC'15) gave a first instantiation, but, as it relies on a powerful cryptographic primitive, the scheme is not practical. We also point out a flaw in their scheme. In this paper we revisit the model for transferable e-cash and propose simpler yet stronger security definitions. We then provide the first concrete construction, based on bilinear groups, give rigorous proofs that it satisfies our model, and analyze its efficiency in detail.

We present a novel public key encryption scheme that enables users to exchange many bits messages by means of \emph{at least} two large prime numbers in a Goldwasser-Micali manner. Our cryptosystem is in fact a generalization of the Joye-Libert scheme (being itself an abstraction of the first probabilistic encryption scheme). We prove the security of the proposed cryptosystem in the standard model (based on the gap $2^k$-residuosity assumption) and report complexity related facts. We also describe an application of our scheme to biometric authentication and discuss the security of our suggested protocol. Last but not least, we indicate several promising research directions.

Minimal codes are characterized by the property that none of the codewords is covered by some other linearly independent codeword. We first show that the use of a bent function $g$ in the so-called direct sum of Boolean functions $h(x,y)=f(x)+g(y)$, where $f$ is arbitrary, induces minimal codes. This approach gives an infinite class of minimal codes of length $2^n$ and dimension $n+1$ (assuming that $h: \F_2^n \rightarrow \F_2$), whose weight distribution is exactly specified for certain choices of $f$. To increase the dimension of these codes with respect to their length, we introduce the concept of \textit{non-covering permutations} (referring to the property of minimality) used to construct a bent function $g$ in $s$ variables, which allows us to employ a suitable subspace of derivatives of $g$ and generate minimal codes of dimension $s+s/2+1$ instead. Their exact weight distribution is also determined. In the second part of this article, we first provide an efficient method (with easily satisfied initial conditions) of generating minimal $[2^n,n+1]$ linear codes that cross the so-called Ashikhmin-Barg bound. This method is further extended for the purpose of generating minimal codes of larger dimension $n+s/2+2$, through the use of suitable derivatives along with the employment of non-covering permutations. To the best of our knowledge, the latter method is the most general framework for designing binary minimal linear codes that violate the Ashikhmin-Barg bound. More precisely, for a suitable choice of derivatives of $h(x,y)=f(x) + g(y)$, where $g$ is a bent function and $f$ satisfies certain minimality requirements, for any fixed $f$, one can derive a huge class of non-equivalent wide binary linear codes of the same length by varying the permutation $\phi$ when specifying the bent function $g(y_1,y_2)=\phi(y_2)\cdot y_1$ in the Maiorana-McFarland class. The weight distribution is given explicitly for any (suitable) $f$ when $\phi$ is an almost bent permutation.

In this paper, we show how multiplication for polynomial rings used in the NIST PQC finalists Saber and NTRU can be efficiently implemented using the Number-theoretic transform (NTT). We obtain superior performance compared to the previous state of the art implementations using Toom–Cook multiplication on both NIST’s primary software optimization targets AVX2 and Cortex-M4. Interestingly, these two platforms require different approaches: On the Cortex-M4, we use 32-bit NTT-based polynomial multiplication, while on Intel we use two 16-bit NTT-based polynomial multiplications and combine the products using the Chinese Remainder Theorem (CRT). For Saber, the performance gain is particularly pronounced. On Cortex-M4, the Saber NTT-based matrix-vector multiplication is 61% faster than the Toom-Cook multiplication resulting in 22% fewer cycles for Saber encapsulation. For NTRU, the speed-up is less impressive, but still NTT-based multiplication performs better than Toom–Cook for all parameter sets on Cortex-M4. The NTT-based polynomial multiplication for NTRU-HRSS is 10% faster than Toom–Cook which results in a 6% cost reduction for encapsulation. On AVX2, we obtain speed-ups for three out of four NTRU parameter sets. As a further illustration, we also include code for AVX2 and Cortex-M4 for the Chinese Association for Cryptologic Research competition award winner LAC (also a NIST round 2 candidate) which outperforms existing code.

Recently, privacy-preserving logistic regression techniques on distributed data among several data owners drew attention in terms of their applicability in federated learning environment. Many of them have been built upon cryptographic primitives such as secure multiparty computations(MPC) and homomorphic encryptions(HE) to protect the privacy of data. The secure multiparty computation provides fast and secure unit operations for arithmetic and bit operations but they often does not scale with large data well enough due to large computation cost and communication overhead. From recent works, many HE primitives provide their operations in a batch sense so that the technique can be an appropriate choice in a big data environment. However computationally expensive operations such as ciphertext slot rotation or refreshment(so called bootstrapping) and large public key size are hurdles that hamper widespread of the technique in the industry-level environment. In this paper, we provide a new hybrid approach of a privacy-preserving logistic regression training and a inference, which utilizes both MPC and HE techniques to provide efficient and scalable solution while minimizing needs of key management and complexity of computation in encrypted state. Utilizing batch sense properties of HE, we present a method to securely compute multiplications of vectors and matrices using one HE multiplication, compared to the naive approach which requires linear number of multiplications regarding to the size of input data. We also show how we used a 2-party additive secret sharing scheme to control noises of expensive HE operations such as bootstrapping efficiently.

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of constant-round post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and polynomial quantum hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest: - A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of an LWE-based circular security assumption. This yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys. - Constant-round zero-knowledge secure against multiple parallel quantum verifiers from spooky encryption for relations computable by quantum circuits. To enable this, we develop a new straight-line non-black-box simulation technique against parallel verifiers that does not clone the adversary's state. This forms the heart of our technical contribution and may also be relevant to the classical setting. - A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.

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

Digital contact tracing apps allow to alert people who have been in contact with people who may be contagious. The Google/Apple Exposure Notification (GAEN) system is based on Bluetooth proximity estimation. It has been adopted by many countries around the world. However, many possible attacks are known. The goal of some of them is to inject a false alert on someone else's phone. This way, an adversary can eliminate a competitor in a sport event or a business in general. Political parties can also prevent people from voting. In this report, we review several methods to inject false alerts. One of them requires to corrupt the clock of the smartphone of the victim. For that, we build a time-traveling machine to be able to remotely set up the clock on a smartphone and experiment our attack. We show how easy this can be done. We successfully tested several smartphones with either the Swiss or the Italian app (SwissCovid or Immuni). We confirms is also works on other GAEN-based apps: NHS COVID-19 (in England and Wales), Corona-Warn-App (in Germany), and Coronalert (Belgium). The time-machine can also be used in active attack to identify smartphones. We can recognize smartphones that we have passively seen in the past. We can passively recognize in the future smartphones that we can see in present. We can also make smartphones identify themselves with a unique number. Finally, we report a simpler attack which needs no time machine but relies on the existence of still-valid keys reported on the server. We observed the case in several countries. The attack is made trivial in Austria, Denmark, Spain, Italy, the Netherlands, Alabama, Delaware, Wyoming, Canada, and England & Whales. Other regions are affected by interoperability too.

Boyle et al. (TCC 2019) proposed a new approach for secure computation in the preprocessing model building on function secret sharing (FSS), where a gate $g$ is evaluated using an FSS scheme for the related offset family $g_r(x)=g(x+r)$. They further presented efficient FSS schemes based on any pseudorandom generator (PRG) for the offset families of several useful gates $g$ that arise in "mixed-mode'' secure computation. These include gates for zero test, integer comparison, ReLU, and spline functions. The FSS-based approach offers significant savings in online communication and round complexity compared to alternative techniques based on garbled circuits or secret sharing. In this work, we improve and extend the previous results of Boyle et al. by making the following three kinds of contributions: - Improved Key Size: The preprocessing and storage costs of the FSS-based approach directly depend on the FSS key size. We improve the key size of previous constructions through two steps. First, we obtain roughly 4x reduction in key size for Distributed Comparison Function (DCF), i.e., FSS for the family of functions $f^<_a_,_b(x)$ that output $b$ if $x < a$ and $0$ otherwise. DCF serves as a central building block in the constructions of Boyle et al. Second, we improve the number of DCF instances required for realizing useful gates $g$. For example, whereas previous FSS schemes for ReLU and $m$-piece spline required 2 and $2m$ DCF instances, respectively, ours require only a single instance of DCF in both cases. This improves the FSS key size by 6-22x for commonly used gates such as ReLU and sigmoid. - New Gates: We present the first PRG-based FSS schemes for arithmetic and logical shift gates, as well as for bit-decomposition where both the input and outputs are shared over $Z_N$ for $N = 2^n$. These gates are crucial for many applications related to fixed-point arithmetic and machine learning. - A Barrier: The above results enable a 2-round PRG-based secure evaluation of "multiply-then-truncate,'' a central operation in fixed-point arithmetic, by sequentially invoking FSS schemes for multiplication and shift. We identify a barrier to obtaining a 1-round implementation via a single FSS scheme, showing that this would require settling a major open problem in the area of FSS: namely, a PRG-based FSS for the class of bit-conjunction functions.

In this paper, we initiate the study of interactive proofs for the promise problem $\mathsf{QBBC}$ (i.e., quantum black-box computations), which consists of a quantum device $\mathcal{D}(|x\rangle |y\rangle) =|x\rangle D_x(|y\rangle)$ acting on $(n+m)$ qubits for some self-joint unitary $D_x$ (i.e., $D_x(D_x(|y\rangle)) = |y\rangle$), a classical device $\mathcal{R}_F$ deciding the input-output relation of some unknown function $F:\{0,1\}^n \rightarrow \{0,1\}^m$, and two reals $0< b < a \leq 1$. Let $p(\mathcal{D},x) = \| |x,F(x)\rangle \langle x,F(x)| \mathcal{D}(|x\rangle |0^m\rangle)\|^2$ be the probability of obtaining $(x,F(x))$ as a result of a standard measurement of the $(n+m)$-qubit state returned by $\mathcal{D}$ on input $|x\rangle |0^m\rangle$. The task of the problem $\mathsf{QBBC}(\mathcal{D},\mathcal{R}_F,a,b)$ is to distinguish between two cases for all $x\in \{0,1\}^n$: \\ $\bullet$ YES Instance: $p(\mathcal{D},x) \geq a$; $\bullet$ NO Instance: $p(\mathcal{D},x) \leq b$. First, we show that for any constant $15/16< a \leq 1$, the problem $\mathsf{QBBC}(\mathcal{D},\mathcal{R}_F,a,b)$ has an efficient two-round interactive proof $(\mathcal{P}^{\mathcal{D}},\mathcal{V}^{\mathcal{R}_F})$ which basically allows a verifier $\mathcal{V}$, given a classical black-box device $\mathcal{R}_F$, to efficiently verify if the prover $\mathcal{P}$ has a quantum black-box device $\mathcal{D}$ (correctly) computing $F$. This proof system achieves completeness $\frac{1 + a}{2}$ and soundness error $\frac{31}{32} + \frac{\epsilon}{2} + \mathsf{negl}(n)$ for any constant $\max(0,b-\frac{15}{16})<\epsilon<a - \frac{15}{16}$, given that the verifier $\mathcal{V}$ has some (limited) quantum capabilities. In terms of query complexities, the prover $\mathcal{P}^\mathcal{D}$ will make at most two quantum queries to $\mathcal{D}$, while the verifier $\mathcal{V}^{\mathcal{R}_F}$ only makes a single classical query to $\mathcal{R}_F$. This result is based on an information versus disturbance lemma, which may be of independent interest. Second, under the learning with errors (LWE) assumption in (Regev 2005), we show that the problem $\mathsf{QBBC}(\mathcal{D},\mathcal{R}_F,a,b)$ can even have an efficient interactive proof $(\mathcal{P}^{\mathcal{D}},\mathcal{V}^{\mathcal{R}_F})$ with a fully classical verifier $\mathcal{V}$ that does not have any quantum capability. This proof system achieves completeness $\frac{1 + a}{2}-\mathsf{negl}(n)$ and soundness error $\frac{1+b}{2} + \mathsf{negl}(n)$, and thus applies to any $\mathsf{QBBC}(\mathcal{D},\mathcal{R}_F,a,b)$ with constants $0< b<a \leq 1$. Moreover, this proof system has the same query complexities as above. This result is based on the techniques introduced in (Brakerski et al. 2018) and (Mahadev 2018). As an application, we show that the problem of distinguishing the random oracle model (ROM) and the quantum random oracle model (QROM) in cryptography can be naturally seen as a $\mathsf{QBBC}$ problem. By applying the above result, we immediately obtain a separation between ROM and QROM under the standard LWE assumption.

Threshold signing research progressed a lot in the last three years, especially for ECDSA, which is less MPC-friendly than Schnorr-based signatures such as EdDSA. This progress was mainly driven by blockchain applications, and boosted by breakthrough results concurrently published by Lindell and by Gennaro & Goldfeder. Since then, several research teams published threshold signature schemes with different features, design trade-offs, building blocks, and proof techniques. Furthermore, threshold signing is now deployed within major organizations to protect large amounts of digital assets. Researchers and practitioners therefore need a clear view of the research state, of the relative merits of the protocols available, and of the open problems, in particular those that would address "real-world" challenges. This survey therefore proposes to (1) describe threshold signing and its building blocks in a general, unified way, based on the extended arithmetic black-box formalism (ABB+); (2) review the state-of-the-art threshold signing protocols, highlighting their unique properties and comparing them in terms of security assurance and performance, based on criteria relevant in practice; (3) review the main open-source implementations available.

One of the NIST Post-Quantum Cryptography Standardization Process Round 2 candidates is the NewHope cryptosystem, which is a suite of two RLWE based key encapsulation mechanisms. Recently, four key reuse attacks were proposed against NewHope by Bauer et al., Qin et al., Bhasin et al. and Okada et al. In these attacks, the adversary has access to the key mismatch oracle which tells her if a given ciphertext decrypts to a given message under the targeted secret key. Previous attacks either require more than 26 000 queries to the oracle or they never recover the whole secret key. In this paper, we present a new attack against the NewHope cryptosystem in these key reuse situations. Our attack recovers the whole secret key with the probability of 100% and requires less than 3 200 queries on average. Our work improves state-of-the-art results for NewHope and makes the comparison with other candidates more relevant.

This work studies signcryption of classical data in the quantum setting. Essentially, we investigate the quantum security of generic constructions of signcryption schemes based on three paradigms, viz., encrypt-then-sign (EtS), sign-then-encrypt (StE) and commit-then-encrypt-and-sign (CtE&S). For doing that we define the confidentiality and authenticity of signcryption for classical data both in insider and outsider models against quantum adversaries. In the insider model, we show that the quantum variants of the classical results hold in the quantum setting. However, for arguing authenticity in outsider model of StE and CtE&S paradigms, we need to consider an intermediate setting in which the adversary is given quantum access to unsigncryption oracle but classical access to signcryption oracle. In two-user outsider model, as in the classical setting, we show that post-quantum CPA security of the base encryption scheme is amplified in the EtS paradigm if the base signature scheme satisfies a stronger definition. We prove an analogous result in the StE paradigm. Interestingly, in the multi-user setting, our results strengthen the known classical results. Furthermore, our results for the EtS and StE paradigms in the two-user outsider model also extend to the setting of authenticated encryption. Finally, we briefly discuss concrete instantiations in various paradigms utilizing some available candidates of quantum secure encryption and signature schemes.

To expand capacity, many resource-constrained industrial devices encrypt and outsource their private data to public clouds, employing a searchable encryption (SE) scheme that provides efficient search service directly to encrypted data. Current tree-based SE schemes can do this and support sublinear encrypted Boolean queries. However, they all suffer from log n overhead in a search procedure. To resolve the challenge, in this paper, we propose a new tree structure called the four-branch tree (FB-tree). Our key design is to build a tree node with four branches, which helps a search reach the destination nodes with fast jumps. Based on the index tree, we setup two systems for different requirements. The first system for efficiency-first settings achieves nearly optimal search complexity and adaptive security. The second, constructed via an oblivious RAM for security-first environments, still achieves worst-case sublinear search complexity. FB-tree performance is extensively evaluated with several real datasets. The Experimental data demonstrate that the FB-tree-based systems outperform the state-of-the-art solutions in terms of efficiency and scalability when Boolean queries are issued.

We construct the first decentralized multi-authority attribute-based encryption (MA-ABE) scheme for a non-trivial class of access policies whose security is based (in the random oracle model) solely on the Learning With Errors (LWE) assumption. The supported access policies are ones described by DNF formulas. All previous constructions of MA-ABE schemes supporting any non-trivial class of access policies were proven secure (in the random oracle model) assuming various assumptions on bilinear maps. In our system, any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. A party can simply act as a standard ABE authority by creating a public key and issuing private keys to different users that reflect their attributes. A user can encrypt data in terms of any DNF formulas over attributes issued from any chosen set of authorities. Finally, our system does not require any central authority. In terms of efficiency, when instantiating the scheme with a global bound $s$ on the size of access policies, the sizes of public keys, secret keys, and ciphertexts, all grow with $s$. Technically, we develop new tools for building ciphertext-policy ABE (CP-ABE) schemes using LWE. Along the way, we construct the first provably secure CP-ABE scheme supporting access policies in $\mathsf{NC}^1$ that avoids the generic universal-circuit-based key-policy to ciphertext-policy transformation. In particular, our construction relies on linear secret sharing schemes with new properties and in some sense is more similar to CP-ABE schemes that rely on bilinear maps. While our CP-ABE construction is not more efficient than existing ones, it is conceptually intriguing and further we show how to extend it to get the MA-ABE scheme described above.

In this paper, we present new algorithms for the field arithmetic of supersingular isogeny Diffie-Hellman; one of the fifteen remaining candidates in the NIST post-quantum standardization process. Our approach uses a polynomial representation of the field elements together with mechanisms to keep the coefficients within bounds during the arithmetic operations. We present timings and comparisons for SIKEp503 and suggest a novel 736-bit prime that offers a $1.17\times$ speedup compared to SIKEp751 for a similar level of security.

In a recent seminal work, Bitansky and Shmueli (STOC '20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counterparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called $\epsilon$-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box $\epsilon$-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC '96) though the proof of $\epsilon$-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box $\epsilon$-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifier's internal state in an appropriate sense.

Dilithium is a lattice-based digital signature, one of the finalist candidates in the NIST's standardization process for post-quantum cryptography. In this paper, we propose a first side-channel attack on the process of signature generation of Dilithium. During the Dilithium signature generation process, we used NTT encryption single-trace for machine learning-based profiling attacks. In addition, it is possible to attack masked Dilithium using sparse multiplication. The proposed method is shown through experiments that all key values can be exposed 100% through a single-trace regardless of the optimization level.

A multi-identity pure fully homomorphic encryption (MIFHE) enables a server to perform arbitrary computation on the ciphertexts that are encrypted under different identities. In case of multi-attribute pure FHE (MAFHE), the ciphertexts are associated with different attributes. Clear and McGoldrick (CANS 2014) gave the first chosen-plaintext attack secure MIFHE and MAFHE based on indistinguishability obfuscation. In this study, we focus on building MIFHE and MAFHE which are se- cure under type 1 of chosen-ciphertext attack (CCA1) security model. In particular, using witness pseudorandom functions (Zhandry, TCC 2016) and multi-key pure FHE or MFHE (Mukherjee and Wichs, EUROCRYPT 2016) we propose the following constructions: – CCA secure identity-based encryption (IBE) that enjoys an optimal size ciphertexts, which we extend to a CCA1 secure MIFHE scheme. – CCA secure attribute-based encryption (ABE) having an optimal size ciphertexts, which we transform into a CCA1 secure MAFHE scheme. By optimal size, we mean that the bit-length of a ciphertext is the bit-length of the message plus a security parameter multiplied with a constant. Known constructions of multi-identity(attribute) FHEs are either leveled, that is, support only bounded depth circuit evaluations or secure in a weaker CPA security model. With our new approach, we achieve both CCA1 security and evaluation on arbitrary depth circuits for multi-identity(attribute) FHE schemes.

Prior works in privacy-preserving biometric authentication mostly focus on the following setting. An organization collects users' biometric data during registration and later authorized access to the organization services after successful authentication. Each organization has to maintain its own biometric database. Similarly each user has to release her biometric information to multiple organizations; Independently, government authorities are making their extensive, nation-wide biometric database available to agencies and organizations, for countries that allow such access. This will enable organizations to provide authentication without maintaining biometric databases, while users only need to register once. However privacy remains a concern. We propose a privacy-preserving system, PBio, for this new setting. The core component of PBio is a new protocol comprising distance recoverable encryption and secure distance computation. We introduce an encrypt-then-split mechanism such that each of the organizations holds only an encrypted partial biometric database. This minimizes the risk of template reconstruction in the event that the encrypted partial database is recovered due to leak of the encryption key. PBio is also secure even when the organizations collude. A by-product benefit is that the use of encrypted partial templates allows quicker rejection for non-matching instances. We implemented a cloud-based prototype with desktop and Android applications. Our experiment results based on real remote users show that PBio is highly efficient. A round-trip authentication takes approximately 74ms (desktop) and 626ms (Android). The computation and communication overhead introduced by our new cryptographic protocol is only about 10ms (desktop) and 54ms (Android).

In this paper the author introduces methods that represent elements of a Finite Field $F_q$ as matrices that linearize certain operations like the product of elements in $F_q$. Since the Central Polynomial Map $\mathcal{F}(X)$ coming from the HFE scheme involves multiplication of elements in a Finite Field $F_q$, using a \textit{novel method} based in Linear Algebra the Quadratic Forms resulting from the polynomial map of the Public Key can be computed in few steps and these are bounded by the matrix $R$ that represents the linear action of the polynomial remainder modulo $f(t)$, which is the irreducible polynomial that identifies $F_q$. When the irreducible polynomial $f(t)$ is of the form $t^a+t^b+1$ \textit{modulo $2$}, the matrix $R$ is computed deterministically in few steps and all the Quadratic Forms are derived from this matrix. The research done tells that the central Polynomial Map $\mathcal{F}(X)$ is computed extremely fast, for example, in the CAS \textit{Mathematica}, taking an HFE Polynomial, Quadratic Forms are computed in $\textcolor{red}{\approx 1.4}$ seconds for the case $n=128$. This raises the more general lemma that Quadratic Forms obtained from BigField schemes are entirely dependent on the selected irreducible polynomial $f(t)$ as the matrix $R$ is conditioned by the structure of this polynomial.

Access Control or authorization is referred to as the confinement of specific actions of an entity to perform an action. Blockchain driven access control mechanisms have gained considerable attention since applications for blockchain were found beyond the premises of cryptocurrencies. However, there are no systematic efforts to analyze existing empirical evidence. To this end, we aim to synthesize literature to understand the state-of-the-art in blockchain driven access control mechanisms with respect to underlying platforms, utilized blockchain properties, nature of the models and associated testbeds & tools. We conducted the review in a systematic way. Meta Analysis and thematic synthesis was performed on the findings and results from the relevant primary studies in order to answer the research questions in perspective. We identified 76 relevant primary studies passing the quality assessment. A number of problems like single point of failure, security, privacy etc were targeted by the relevant primary studies. The meta analysis suggests the use of different blockchain platforms, several application domains and different utilized blockchain properties. In this paper, we present a systematic literature review of blockchain driven access control systems. In hindsight, we present a taxonomy of blockchain driven access control systems to better under the immense implications this field has over various application domains.

A hash function family $\mathcal{H}$ is correlation intractable for a $t$-input relation $\mathcal{R}$ if, given a random function $h$ chosen from $\mathcal{H}$, it is hard to find $x_1,\ldots,x_t$ such that $\mathcal{R}(x_1,\ldots,x_t,h(x_1),\ldots,h(x_t))$ is true. Among other applications, such hash functions are a crucial tool for instantiating the Fiat-Shamir heuristic in the plain model, including the only known NIZK for NP based on the learning with errors (LWE) problem (Peikert and Shiehian, CRYPTO 2019). We give a conceptually simple and generic construction of single-input CI hash functions from shift-hiding shiftable functions (Peikert and Shiehian, PKC 2018) satisfying an additional one-wayness property. This results in a clean abstract framework for instantiating CI, and also shows that a previously existing function family (PKC 2018) was already CI under the LWE assumption. In addition, our framework transparently generalizes to other settings, yielding new results: - We show how to instantiate certain forms of multi-input CI under the LWE assumption. Prior constructions either relied on a very strong ``brute-force-is-best'' type of hardness assumption (Holmgren and Lombardi, FOCS 2018) or were restricted to ``output-only'' relations (Zhandry, CRYPTO 2016). - We construct single-input CI hash functions from indistinguishability obfuscation (iO) and one-way permutations. Prior constructions relied essentially on variants of fully homomorphic encryption that are impossible to construct from such primitives. This result also generalizes to more expressive variants of multi-input CI under iO and additional standard assumptions.

We show that lazily Barrett reducing when computing the inverse number theoretic transform (NTT) is optimal.

We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new results on the connection between the solving degree and the last fall degree and prove that, in some cases, the solving degree is independent of coordinate changes.

The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus algorithms to solve the elliptic and hyperelliptic curve discrete logarithm problem. The complexity of solving a system of polynomial equations is closely related to the cost of computing Gröbner bases, since computing the solutions of a polynomial system can be reduced to finding a lexicographic Gröbner basis for the ideal generated by the equations. Several algorithms for computing such bases exist: We consider those based on repeated Gaussian elimination of Macaulay matrices. In this paper, we analyze the case of random systems, where random systems means either semi-regular systems, or quadratic systems in $n$ variables which contain a regular sequence of $n$ polynomials. We provide explicit formulae for bounds on the solving degree of semi-regular systems with $m>n$ equations in $n$ variables, for equations of arbitrary degrees for $m=n+1$, and for any $m$ for systems of quadratic or cubic polynomials. In the appendix, we provide a table of bounds for the solving degree of semi-regular systems of $m=n+k$ quadratic equations in $n$ variables for $2\leq k,n\leq 100$ and online we provide the values of the bounds for $2\leq k,n\leq 500$. For quadratic systems which contain a regular sequence of $n$ polynomials, we argue that the Eisenbud-Green-Harris conjecture, if true, provides a sharp bound for their solving degree, which we compute explicitly.

Memory encryption with an authentication tree has received significant attentions due to the increasing threats of active attacks and the widespread use of non-volatile memories. It is also gradually deployed to real-world systems, as shown by SGX available in Intel processors. The topic of memory encryption has been recently extensively studied, most actively from the viewpoint of system architecture. In this paper, we study the topic from the viewpoint of provable secure symmetric-key designs, with a primal focus on latency which is an important criterion for memory. A progress in such a direction can be observed in the memory encryption scheme inside SGX (SGX integrity tree or SIT). It uses dedicated, low-latency symmetric-key components, i.e., a message authentication code (MAC) and an authenticated encryption (AE) scheme based on AES-GCM. SIT has an excellent latency, however, it has a scalability issue for its on-chip memory size. By carefully examining the required behavior of MAC and AE schemes and their interactions in the tree operations, we develop a new memory encryption scheme called ELM. It consists of fully-parallelizable, low-latency MAC and AE schemes and utilizes an incremental property of the MAC. Our AE scheme is similar to OCB, however it improves OCB in terms of decryption latency. To showcase the effectiveness, we consider instantiations of ELM using the same cryptographic cores as SIT, and show that ELM has significantly lower latency than SIT for large memories. We also conducted preliminary hardware implementations to show that the total implementation size is comparable to SIT.

Improved filter permutators are designed to build stream ciphers that can be efficiently evaluated homomorphically. So far the transciphering with such ciphers has been implemented with homomorphic schemes from the second generation. In theory the third generation is more adapted for the particular design of these ciphers. In this article we study how suitable it is in practice. We implement the transciphering of different instances of the stream cipher family FiLIP with homomorphic encryption schemes of the third generation using the TFHE library. We focus on two kinds of filter for FiLIP. First we consider the direct sum of monomials, already evaluated using HElib and we show the improvements on these results. Then we focus on the XOR-threshold filter, we develop strategies to efficiently evaluate any symmetric Boolean function in an homomorphic way, allowing us to give the first timings for such filters. We investigate different approaches for the homomorphic evaluation: using the leveled homomorphic scheme TGSW, an hybrid approach combining TGSW and TLWE schemes, and the gate boostrapping approach. We discuss the costs in time and memory and the impact on delegation of computation of these different approaches, and we perform a comparison with others transciphering schemes.

Searchable Symmetric Encryption(SSE) remains to be one of the hot topics in the field of cloud storage technology. However, malicious servers may return incorrect search results intentionally, which will bring significant security risks to users. Therefore, verifiable searchable encryption emerged. In the meantime, single-keyword query limits the applications of searchable encryption. Accordingly, more expressive searchable encryption schemes are desirable. In this paper, we propose a verifiable conjunctive keyword search scheme based on Cuckoo filter (VCKSCF), which significantly reduces verification and storage overhead. Security analysis indicates that the proposed scheme achieves security in the face of indistinguishability under chosen keyword attack and the unforgeability of proofs and search tokens. Meanwhile, the experimental evaluation demonstrates that it achieves preferable performance in real-world settings.

We extend the classical problem of privacy amplification to a setting where the active adversary, Eve, is also allowed to fully corrupt the internal memory (which includes the shared randomness, and local randomness tape) of one of the honest parties, Alice and Bob, before the execution of the protocol. We require that either one of Alice or Bob detects tampering, or they agree on a shared key that is indistinguishable from the uniform distribution to Eve. We obtain the following results: (1) We give a privacy amplification protocol via low-error non-malleable two-source extractors with one source having low min-entropy. In particular, this implies the existence of such (non-efficient) protocols; (2) We show that even slight improvements to the state-of-the-art explicit non-malleable two-source extractors would lead to explicit low-error, low min-entropy two-source extractors, thereby resolving a long-standing open question. This suggests that obtaining (information-theoretically secure) explicit non-malleable two-source extractors for (1) might be hard; (3) We present explicit constructions of low-error, low min-entropy non-malleable two-source extractors in the CRS model of (Garg, Kalai, Khurana, Eurocrypt 2020), assuming either the quasi-polynomial hardness of DDH or the existence of nearly-optimal collision-resistant hash functions; (4) We instantiate our privacy amplification protocol with the above mentioned non-malleable two-source extractors in the CRS model, leading to explicit, computationally-secure protocols. This is not immediate from (1) because in the computational setting we need to make sure that, in particular, all randomness sources remain samplable throughout the proof. This requires upgrading the assumption of quasi-polynomial hardness of DDH to sub-exponential hardness of DDH. We emphasize that each of the first three results can be read independently.

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.