Cryptanalysis of the LowMC block cipher when the attacker has access to a single known plaintext/ciphertext pair is a mathematically challenging problem. This is because the attacker is unable to employ most of the standard techniques in symmetric cryptography like linear and differential cryptanalysis. This scenario is particularly relevant while arguing the security of the \picnic digital signature scheme in which the plaintext/ciphertext pair generated by the LowMC block cipher serves as the public (verification) key and the corresponding LowMC encryption key also serves as the secret (signing) key of the signature scheme. In the paper by Banik et al. (IACR ToSC 2020:4), the authors used a linearization technique of the LowMC S-box to mount attacks on some instances of the block cipher. In this paper, we first make a more precise complexity analysis of the linearization attack. Then, we show how to perform a 2-stage MITM attack on LowMC. The first stage reduces the key candidates corresponding to a fraction of key bits of the master key. The second MITM stage between this reduced candidate set and the remaining fraction of key bits successfully recovers the master key. We show that the combined computational complexity of both these stages is significantly lower than those reported in the ToSC paper by Banik et al.

BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round. This paper presents FPGA implementations of BIKE with the best area-time performance reported in literature. We optimize two key arithmetic operations, which are the sparse polynomial multiplication and the polynomial inversion. Our sparse multiplier achieves time-constancy for sparse polynomials of indefinite Hamming weight used in BIKE’s encapsulation. The polynomial inversion is based on the extended Euclidean algorithm, which is unprecedented in current BIKE implementations. Our optimized design results in a 5.5 times faster key generation compared to previous implementations based on Fermat’s little theorem. Besides the arithmetic optimizations, we present a united hardware design of BIKE with shared resources and shared sub-modules among KEM functionalities. On Xilinx Artix-7 FPGAs, our light-weight implementation consumes only 3 777 slices and performs a key generation, encapsulation, and decapsulation in 3 797 µs, 443 µs, and 6 896 µs, respectively. Our high-speed design requires 7 332 slices and performs the three KEM operations in 1 672 µs, 132 µs, and 1 892 µs, respectively.

Blum, Kalai and Wasserman (JACM 2003) gave the first sub-exponential algorithm to solve the Learning Parity with Noise (LPN) problem. In particular, consider the LPN problem with constant noise $\mu=(1-\gamma)/2$. The BKW solves it with space complexity $2^{\frac{(1+\epsilon)n}{\log n}}$ and time/sample complexity $2^{\frac{(1+\epsilon)n}{\log n}}\cdot 2^{O(n^{\frac{1}{1+\epsilon}})}$ for small constant $\epsilon\to 0^+$. We propose a variant of the BKW by tweaking Wagner's generalized birthday problem (Crypto 2002) and adapting the technique to a $c$-ary tree structure. In summary, our algorithm achieves the following: (Time-space tradeoff). We obtain the same time-space tradeoffs for LPN and LWE as those given by Esser et al. (Crypto 2018), but without resorting to any heuristics. For any $2\leq c\in\mathbb{N}$, our algorithm solves the LPN problem with time/sample complexity $2^{\frac{\log c(1+\epsilon)n}{\log n}}\cdot 2^{O(n^{\frac{1}{1+\epsilon}})}$ and space complexity $2^{\frac{\log c(1+\epsilon)n}{(c-1)\log n}}$, where one can use Grover's quantum algorithm or Dinur et al.'s dissection technique (Crypto 2012) to further accelerate/optimize the time complexity. (Time/sample optimization). A further adjusted variant of our algorithm solves the LPN problem with sample, time and space complexities all kept at $2^{\frac{(1+\epsilon)n}{\log n}}$ for $\epsilon\to 0^+$, saving factor $2^{\Omega(n^{\frac{1}{1+\epsilon}})}$ in time/sample compared to the original BKW, and the variant of Devadas et al. (TCC 2017). This benefits from a careful analysis of the error distribution among the correlated candidates, and therefore avoids repeating the same process $2^{\Omega(n^{\frac{1}{1+\epsilon}})}$ times on fresh new samples. (Sample reduction) Our algorithm provides an alternative to Lyubashevsky's BKW variant (RANDOM 2005) for LPN with a restricted amount of samples. In particular, given $Q=n^{1+\epsilon}$ (resp., $Q=2^{n^{\epsilon}}$) samples, our algorithm saves a factor of $2^{\Omega(n)/(\log n)^{1-\kappa}}$ (resp., $2^{\Omega(n^{\kappa})}$) for constant $\kappa \to 1^-$ in running time while consuming roughly the same space, compared with Lyubashevsky's algorithm. We seek to bridge the gaps between theoretical and heuristic LPN solvers, but take a different approach from Devadas et al. (TCC 2017). We exploit weak yet sufficient conditions (e.g., pairwise independence), and the analysis uses only elementary tools (e.g., Chebyshev's inequality).

We construct efficient (function hiding) functional commitments for arithmetic circuits of polynomial size. A (function hiding) functional commitment scheme enables a \textit{committer} to commit to a secret function $f$ and later prove that $y = f(x)$ for public $x$ and $y$ without revealing any other information about $f$. As such, functional commitments allow the operator of a secret process to prove that the process is being applied uniformly to everyone. For example, one can commit to the secret function that computes credit scores and then prove that it is applied uniformly to all. To build a functional commitment scheme, we introduce a new primitive called a proof of function relation (PFR) to show that a committed relation is a function. We show that combining a suitable preprocessing zk-SNARK (or more precisely, an Algebraic Holographic Proof) with a PFR yields a secure functional commitment scheme. We then construct efficient PFRs for two popular preprocessing zk-SNARKs, and obtain two functional commitment schemes for arithmetic circuits. Along the way we develop new techniques for proving interesting properties of committed polynomials, which may be of independent interest.

The goal of anonymous whistleblowing is to publicly disclose a message while at the same time hiding the identity of the sender in a way that even if suspected of being the sender, this cannot be proven. While many solutions to this problem have been proposed over the years, they all require some form of interaction with trusted or non-colluding parties. In this work, we ask whether this is fundamentally inherent. We put forth the notion of anonymous transfer as a primitive allowing to solve this problem without relying on any participating trusted parties. We initiate the theoretical study of this question, and derive negative and positive results on the existence of such a protocol. We refute the feasibility of asymptotically secure anonymous transfer, where the message will be received with overwhelming probability while at the same time the identity of the sender remains hidden with overwhelming probability. On the other hand, resorting to fine-grained cryptography, we provide a heuristic instantiation (assuming ideal obfuscation) which guarantees that the message will be correctly received with overwhelming probability and the identity of the sender leaks with vanishing probability. Our results provide strong foundations for the study of the possibility of anonymous communications through authenticated channels, an intriguing goal which we believe to be of fundamental interest.

Leakage-resilient authenticated encryption (AE) schemes received considerable attention during the previous decade. Two core security models of bounded and unbounded leakage have evolved, where the latter has been motivated in a very detailed and practice-oriented manner. In that setting, designers often build schemes based on (tweakable) block ciphers due to the small state size, such as the recent two-pass AE scheme TEDT from TCHES 1/2020. TEDT is interesting due to its high security guarantees of O(n - log(n^2))-bit integrity under leakage and similar AE security in the black-box setting. Though, a detail limited it to provide only n/2-bit privacy under leakage. In this work, we extend TEDT to TEDT2 in three aspects with the help of a tweakable block cipher with a 3n-bit tweakey: we (1) adopt the idea from the design team of Romulus of replacing TEDT's previous internal hash function with Naito's MDPH, (2) move the nonce from the hash to the tag-generation function both for more efficiency, and (3) strengthen the security of the encryption to obtain beyond-birthday-bound security also under leakage.

The NIST selection process for standardizing Post-Quantum Cryptography Mechanisms is currently running. Many papers already studied their theoretical security, but the resistance in deployed device has not been much investigated so far. In particular, fault attack is a serious threat for algorithms implemented in embedded devices. One particularly powerful technique is to use safe-error attacks. Such attacks exploit the fact that a specific fault may or may not lead to a faulty output depending on a secret value. In this paper, we investigate the resistance of various Post-Quantum candidates algorithms against such attacks.

We propose a new hard problem, called the Embedded Multilayer Equations (eMLE) problem in this paper. An example of eMLE, with one secret variable x and three layers, is given below. 6268 = 57240 * x + (1248 * x + (9 * x mod 16) mod 2053) mod 65699 In this example, the eMLE problem is to find x from the above equation. eMLE in this paper has the same number of variables and equations. The hardness of eMLE problem lies in its layered structure. Without knowing the eMLE value of lower layer (i.e., the layer with modulus 2053), the top layer (i.e., the layer with modulus 65699) has many candidate solutions; the adversary has to search the solution space for a few valid ones. A lower-bound for the number of searches has been proven in the paper, together with the expected number of valid solutions. The hardness of eMLE can be increased by adding more layers, without changing the number of variables and equations; no existing NP-complete problems have this feature. Over the hardness of eMLE, a post-quantum signature scheme, eMLE-Sig, is constructed. Compared with all existing signature schemes (conventional and post-quantum), eMLE-Sig might be the simplest to understand, analyze, instantiate, and implement. At the security level above 128 bits, five configurations are provided; all of them have keys and signatures smaller than RSA keys and signatures (above 380 bytes) at the 128-bit security level. The smallest configuration is with two variables and three layers, having 84.1/52.2 bytes for private/public key and 168.4 bytes for signatures.

A comparison of two encrypted numbers is an important operation needed in many machine learning applications, for example, decision tree or neural network inference/training. An efficient instantiation of this operation in the context of fully homomorphic encryption (FHE) can be challenging, especially when a relatively high precision is sought. The conventional FHE way of evaluating the comparison operation, which is based on the sign function evaluation using FHEW/TFHE bootstrapping (often referred in literature as programmable bootstrapping), can only support very small precision (practically limited to 4-5 bits or so). For higher precision, the runtime complexity scales linearly with the ciphertext (plaintext) modulus (i.e., exponentially with the modulus bit size). We propose sign function evaluation algorithms that scale logarithmically with the ciphertext (plaintext) modulus, enabling the support of large-precision comparison in practice. Our sign evaluation algorithms are based on an iterative use of homomorphic floor function algorithms, which are also derived in our work. Further, we generalize our procedures for floor function evaluation to arbitrary function evaluation, which can be used to support both small plaintext moduli (directly) and larger plaintext moduli (by using a homomorphic digit decomposition algorithm, also suggested in our work). We implement all these algorithms using the PALISADE lattice cryptography library, introducing several implementation-specific optimizations along the way, and discuss our experimental results.

Recent exciting breakthroughs, starting with the work of Chattopadhyay and Zuckerman (STOC 2016) have achieved the first two-source extractors that operate in the low min-entropy regime. Unfortunately, these constructions suffer from non-negligible error, and reducing the error to negligible remains an important open problem. In recent work, Garg, Kalai, and Khurana (GKK, Eurocrypt 2020) investigated a meaningful relaxation of this problem to the computational setting, in the presence of a common random string (CRS). In this relaxed model, their work built explicit two-source extractors for a restricted class of unbalanced sources with min-entropy $n^{\gamma}$ (for some constant $\gamma$) and negligible error, under the sub-exponential DDH assumption. In this work, we investigate whether computational extractors in the CRS model be applied to more challenging environments. Specifically, we study network extractor protocols (Kalai et al., FOCS 2008) and extractors for adversarial sources (Chattopadhyay et al., STOC 2020) in the CRS model. We observe that these settings require extractors that work well for balanced sources, making the GKK results inapplicable. We remedy this situation by obtaining the following results, all of which are in the CRS model and assume the sub-exponential hardness of DDH. - We obtain ``optimal'' computational two-source and non-malleable extractors for balanced sources: requiring both sources to have only poly-logarithmic min-entropy, and achieving negligible error. To obtain this result, we perform a tighter and arguably simpler analysis of the GKK extractor. - We obtain a single-round network extractor protocol for poly-logarithmic min-entropy sources that tolerates an optimal number of adversarial corruptions. Prior work in the information-theoretic setting required sources with high min-entropy rates, and in the computational setting had round complexity that grew with the number of parties, required sources with linear min-entropy, and relied on exponential hardness (albeit without a CRS). - We obtain an ``optimal'' {\em adversarial source extractor} for poly-logarithmic min-entropy sources, where the number of honest sources is only 2 and each corrupted source can depend on either one of the honest sources. Prior work in the information-theoretic setting had to assume a large number of honest sources.

Fully Homomorphic Encryption (FHE) gives the ability to evaluate any function over encrypted data. However, despite numerous improvements during the last decade, the computational overhead caused by homomorphic computations is still very important. As a consequence, optimizing the way of performing the computations homomorphically remains fundamental. Several popular FHE schemes such as BGV and BFV encode their data, and thus perform their computations, in finite fields. In this work, we study and exploit algebraic relations occurring in prime characteristic allowing to speed-up the homomorphic evaluation of several functions over prime fields. More specifically we give several examples of unary functions: "modulo", "is power of $b$", "Hamming weight" and "Mod2'" whose homomorphic evaluation complexity over $\mathbb{F}_p$ can be reduced from the generic bound $\sqrt{2p} + \mathcal{O}(\log(p))$ homomorphic multiplications, to $\sqrt{p} + \mathcal{O}(\log(p))$, $\mathcal{O}(\log (p))$, $\mathcal{O}(\sqrt{p/\log (p)})$ and $\mathcal{O}(\sqrt{p/\log (p)})$ respectively. Additionally we provide a proof of a recent claim regarding the structure of the polynomial interpolation of the "less-than" bivariate function which confirms that this function can be evaluated in $2p-6$ homomorphic multiplications instead of $3p-5$ over $\mathbb{F}_p$ for $p\geq 5$.

In this work, we study what minimal sets of assumptions suffice for constructing indistinguishability obfuscation ($i\mathcal{O}$). We prove: {\bf Theorem}(Informal): Assume sub-exponential security of the following assumptions: - the Learning Parity with Noise ($\mathsf{LPN}$) assumption over general prime fields $\mathbb{F}_p$ with polynomially many $\mathsf{LPN}$ samples and error rate $1/k^\delta$, where $k$ is the dimension of the $\mathsf{LPN}$ secret, and $\delta>0$ is any constant; - the existence of a Boolean Pseudo-Random Generator ($\mathsf{PRG}$) in $\mathsf{NC}^0$ with stretch $n^{1+\tau}$, where $n$ is the length of the $\mathsf{PRG}$ seed, and $\tau>0$ is any constant; - the Decision Linear ($\mathsf{DLIN}$) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists. Further, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.} This removes the reliance on the Learning With Errors (LWE) assumption from the recent work of [Jain, Lin, Sahai STOC'21]. As a consequence, we obtain the first fully homomorphic encryption scheme that does not rely on any lattice-based hardness assumption. Our techniques feature a new notion of randomized encoding called Preprocessing Randomized Encoding (PRE) that, essentially, can be computed in the exponent of pairing groups. When combined with other new techniques, PRE gives a much more streamlined construction of $\iO$ while still maintaining reliance only on well-studied assumptions.

Lossless compression algorithms such as DEFLATE strive to reliably process arbitrary inputs, while achieving compressed sizes as low as possible for commonly encountered data inputs. It is well-known that it is mathematically impossible for a compression algorithm to simultaneously achieve non-trivial compression on some inputs (i.e. compress these inputs into strictly shorter outputs) and to never expand any other input (i.e. guaranteeing that all inputs will be compressed into an output which is no longer than the input); this is a direct application of the "pigeonhole principle". Despite their mathematical impossibility, we show in this paper how to build such paradoxical compression and decompression algorithms, with the aid of some tools from cryptography, notably verifiable delay functions, and, of course, by slightly cheating.

A natural and recurring idea in the knapsack/lattice cryptography literature is to start from a lattice with remarkable decoding capability as your private key, and hide it somehow to make a public key. This is also how the code-based encryption scheme of McEliece (1978) proceeds. This idea has never worked out very well for lattices: ad-hoc approaches have been proposed, but they have been subject to ad-hoc attacks, using tricks beyond lattice reduction algorithms. On the other hand the framework offered by the Short Integer Solution (SIS) and Learning With Errors (LWE) problems, while convenient and well founded, remains frustrating from a coding perspective: the underlying decoding algorithms are rather trivial, with poor decoding performance. In this work, we provide generic realizations of this natural idea (independently of the chosen remarkable lattice) by basing cryptography on the lattice isomorphism problem (LIP). More specifically, we provide: - a worst-case to average-case reduction for search-LIP and distinguish-LIP within an isomorphism class, by extending techniques of Haviv and Regev (SODA 2014). - a zero-knowledge proof of knowledge (ZKPoK) of an isomorphism. This implies an identification scheme based on search-LIP. - a key encapsulation mechanism (KEM) scheme and a hash-then-sign signature scheme, both based on distinguish-LIP. The purpose of this approach is for remarkable lattices to improve the security and performance of lattice-based cryptography. For example, decoding within poly-logarithmic factor from Minkowski's bound in a remarkable lattice would lead to a KEM resisting lattice attacks down to poly-logarithmic approximation factor, provided that the dual lattice is also close to Minkowski's bound. Recent works have indeed reached such decoders for certain lattices (Chor-Rivest, Barnes-Sloan), but these do not perfectly fit our need as their duals have poor minimal distance.

By exploiting the inherent randomness used by certain digital signature protocols, subliminal channels can subvert these protocols without degrading their security. Due to their nature, these channels cannot be easily detected by an outside observer. Therefore, they pose a severe challenge for protocol designers. More precisely, designers consider certain assumptions implicitly, but in reality these assumptions turn out to be false or cannot be enforced or verified. In this paper we exemplify exactly such a situation by presenting several subliminal channels with a small capacity in Zhang et al. and Dong et al.'s subliminal-free signature protocols.

Two common variations of ECDSA signatures are additive key derivation and presignatures. Additive key derivation is a simple mechanism for deriving many subkeys from a single master key, and is already widely used in cryptocurrency applications with the Hierarchical Deterministic Wallet mechanism standardized in Bitcoin Improvement Proposal 32 (BIP32). Because of its linear nature, additive key derivation is also amenable to efficient implementation in the threshold setting. With presignatures, the secret and public nonces used in the ECDSA signing algorithm are precomputed. In the threshold setting, using presignatures along with other precomputed data allows for an extremely efficient "online phase" of the protocol. Recent works have advocated for both of these variations, sometimes combined together. However, somewhat surprisingly, we are aware of no prior security proof for additive key derivation, let alone for additive key derivation in combination with presignatures. In this paper, we provide a thorough analysis of these variations, both in isolation and in combination. Our analysis is in the generic group model (GGM). Importantly, we do not modify ECDSA or weaken the standard notion of security in any way. Of independent interest, we also present a version of the GGM that is specific to elliptic curves. This EC-GGM better models some of the idiosyncrasies (such as the conversion function and malleability) of ECDSA. In addition to this analysis, we report security weaknesses in these variations that apparently have not been previously reported. For example, we show that when both variations are combined, there is a cube-root attack on ECDSA, which is much faster than the best known, square-root attack on plain ECDSA. We also present two mitigations against these weaknesses: re-randomized presignatures and homogeneous key derivation. Each of these mitigations is very lightweight, and when used in combination, the security is essentially the same as that of plain ECDSA (in the EC-GGM).

Evaluating a block cipher’s strength against differential or linear cryptanalysis can be a difficult task. Several approaches for finding the best differential or linear trails in a cipher have been proposed, such as using mixed integer linear programming or SAT solvers. Recently a different approach was suggested, modelling the problem as a staged, acyclic graph and exploiting the large number of paths the graph contains. This paper follows up on the graph-based approach and models the prob- lem via compressed right-hand side equations. The graph we build contains paths which represent differential or linear trails in a cipher with few active S-boxes. Our method incorporates control over the memory usage, and the time complexity scales linearly with the number of rounds of the cipher being analysed. The proposed method is made available as a tool, and using it we are able to find differential trails for the Klein and Prince ciphers with higher probabilities than previously published.

The majority of recently demonstrated Deep-Learning Side-Channel Analysis (DLSCA) use neural networks trained on a segment of traces containing operations only related to the target subkey. However, when the size of the training set is limited, as in this paper with only 5K power traces, the deep learning (DL) model cannot effectively learn the internal features of the data due to insufficient training data. In this paper, we propose a cross-subkey training approach that acts as a trace augmentation. We train deep-learning models not only on a segment of traces containing the SBox operation of the target subkey of AES-128 but also on segments for other 15 subkeys. Experimental results show that the accuracy of the subkey combination training model is 28.20% higher than that of the individual subkey training model on traces captured in the microcontroller implementation of the STM32F3 with AES-128. And validation is performed on two additional publicly available datasets. At the same time, the number of traces that need to be captured when the model is trained is greatly reduced, demonstrating the effectiveness and practicality of the method.

Most cryptography is based on assumptions such as factoring and discrete log, which assume an adversary has bounded computational power. With the recent development in quantum computing as well as concern with everlasting security, there is an interest in coming up with information-theoretic constructions in the bounded storage model. In this model, an adversary is computationally unbounded but has lim- ited space. Past works have constructed schemes such as key exchange and bit commitment in this model. In this work, we expand the function- alities further by building a semi-honest MPC protocol in the bounded storage model. We use the hardness of the parity learning problem (recently shown by Ran Raz (FOCS 16) without any cryptographic assump- tions) to prove the security of our construction, following the work by Guan and Zhandry (EUROCRYPT 19).

Implantable medical devices, sensors and wearables are widely deployed today. However, establishing a secure wireless communication channel to these devices is a major challenge, amongst others due to the constraints on energy consumption and the need to obtain immediate access in emergencies. To address this issue, researchers have proposed various key agreement protocols based on the measurement of physiological signals such as a person's heart signal. At the core of such protocols are fuzzy cryptographic primitives that allow to agree on a shared secret based on several simultaneous, noisy measurements of the same signal. So far, although many fuzzy primitives have been proposed, there is no comprehensive evaluation and comparison yet of the overhead that such methods incur on resource-constrained embedded devices. In this paper, we study the feasibility of six types of fuzzy cryptographic primitives on embedded devices for 128-bit key agreement. We configure several variants for each fuzzy primitive under different parameter selections and mismatch rates of the physiological signal measurements on an MSP430 microcontroller, and then measure and compare their energy consumption and communication overhead. The most efficient constructions consume between 0.021 mJ and 0.198 mJ for the transmitter and between 0.029 mJ and 0.380 mJ for the receiver under different mismatch rates. Subsequently, we modify the best performing methods so that they run in constant time to protect against timing side-channel attacks, and observe that these changes only minimally affect resource consumption. Finally, we provide open-source implementations and energy consumption data of each fuzzy primitive as a reference for real-world designs.

Decentralized multi-authority attribute-based encryption (𝖬𝖠-𝖠𝖡𝖤) is a strengthening of standard ciphertext-policy attribute-based encryption so that there is no trusted central authority: 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. Essentially, any party can act as an authority for some attribute by creating a public key of its own and issuing private keys to different users that reflect their attributes. This paper presents the first 𝖬𝖠-𝖠𝖡𝖤 proven secure under the standard search variant of bilinear Diffie-Hellman (CBDH) and in the random oracle model. Our scheme supports all access policies captured by 𝖭𝖢1 circuits. All previous constructions were proven secure in the random oracle model and additionally were based on decision assumptions such as the DLIN assumption, non-standard 𝑞-type assumptions, or subspace decision assumptions over composite-order bilinear groups.

In a lockable obfuscation scheme, a party called the obfuscator takes as input a circuit C, a lock value y and, a message m, and outputs an obfuscated circuit. Given the obfuscated circuit, an evaluator can run it on an input x and learn the message if C(x) = y. For security, we require that the obfuscation reveals no information on the circuit as long as the lock y has high entropy even given the circuit C. The only known constructions of lockable obfuscation schemes require indistinguishability obfuscation (iO) or the learning with errors (LWE) assumption. Furthermore, in terms of technique, all known constructions, excluding iO-based, are build from provably secure variations of graph-induced multilinear maps. We show a generic construction of a lockable obfuscation scheme build from a (leveled) fully homomorphic encryption scheme that is circularly insecure. Specifically, we need a fully homomorphic encryption scheme that is secure under chosen-plaintext attack (IND-CPA) but for which there is an efficient cycle tester that can detect encrypted key cycles. Our finding sheds new light on how to construct lockable obfuscation schemes and shows why cycle tester constructions were helpful in the design of lockable obfuscation schemes. One of the many use cases for lockable obfuscation schemes are constructions for IND-CPA secure but circularly insecure encryption schemes. Our work shows that there is a connection in both ways between circular insecure encryption and lockable obfuscation.

This paper investigates __anonymity__ of all NIST PQC Round 3 KEMs: Classic McEliece, Kyber, NTRU, Saber, BIKE, FrodoKEM, HQC, NTRU Prime (Streamlined NTRU Prime and NTRU LPRime), and SIKE. We show the following results: * NTRU is anonymous in the quantum random oracle model (QROM) if the underlying deterministic PKE is strongly disjoint-simulatable. NTRU is collision-free in the QROM. A hybrid PKE scheme constructed from NTRU as KEM and appropriate DEM is anonymous and robust. (Similar results for BIKE, FrodoKEM, HQC, NTRU LPRime, and SIKE hold except for two of three parameter sets of HQC.) * Classic McEliece is anonymous in the QROM if the underlying PKE is strongly disjoint-simulatable and a hybrid PKE scheme constructed from it as KEM and appropriate DEM is anonymous. * Grubbs, Maram, and Paterson pointed out that Kyber and Saber have a gap in the current IND-CCA security proof in the QROM (EUROCRYPT 2022). We found that Streamlined NTRU Prime has another technical obstacle for the IND-CCA security proof in the QROM. Those answer the open problem to investigate the anonymity and robustness of NIST PQC Round~3 KEMs posed by Grubbs, Maram, and Paterson (EUROCRYPT 2022). We use strong disjoint-simulatability of the underlying PKE of KEM and strong pseudorandomness and smoothness/sparseness of KEM as the main tools, which will be of independent interest.

The SIDH key exchange is the main building block of SIKE, the only isogeny based scheme involved in the NIST standardization process. In 2016, Galbraith et al. presented an adaptive attack on SIDH. In this attack, a malicious party manipulates the torsion points in his public key in order to recover an honest party's static secret key, when having access to a key exchange oracle. In 2017, Petit designed a passive attack (which was improved by de Quehen et al. in 2020) that exploits the torsion point information available in SIDH public key to recover the secret isogeny when the endomorphism ring of the starting curve is known. In this paper, firstly, we generalize the torsion point attacks by de Quehen et al. Secondly, we introduce a new adaptive attack vector on SIDH-type schemes. Our attack uses the access to a key exchange oracle to recover the action of the secret isogeny on larger subgroups. This leads to an unbalanced SIDH instance for which the secret isogeny can be recovered in polynomial time using the generalized torsion point attacks. Our attack is different from the GPST adaptive attack and constitutes a new cryptanalytic tool for isogeny based cryptography. This result proves that the torsion point attacks are relevant to SIDH parameters in an adaptive attack setting. We suggest attack parameters for some SIDH primes and discuss some countermeasures.

Fair data trading online is a challenging task when there is mistrust between data providers and data collectors. The trust issue leads to an unsolvable situation where the data collector is unwilling to pay until she receives the data while the data provider will not send the data unless she receives the payment. The traditional solutions toward fair data trading rely on the trust-third party. After the emergence of the blockchain, many researchers use a smart contract on blockchain as a trust-less third party to address the mistrust deadlock. However, involving a smart contract in the protocol inevitably exposes some information to the public if the smart contract is on public blockchain cryptocurrency systems. We observe that the existing fair data trading protocols do not take privacy into account, which, for instance, is critical when trading the sensitive data or the players simply do not want to leak any information about the tradings on the public blockchain. In this paper, we construct a fair trading protocol based on a smart contract that provides better privacy to the participants. We introduce new security notions for privacy-preserving blockchain-based fair data trading protocol and prove our protocol is secure under our new notions. Furthermore, we give a prototype implementation on Ethereum smart contract.

Supersingular isogeny Diffe-Hellman (SIDH) is attractive for its relatively small public key size, but it is still unsatisfactory due to its effciency, compared to other post-quantum proposals. In this paper, we focus on the performance of SIDH when the starting curve is $E_6 : y^2 = x^3 + 6x^2 + x$, which is fixed in Round-3 SIKE implementation. Inspired by the previous work, we present several tricks to accelerate key generation of SIDH and each process of SIKE. Our experimental results show that the performance of this work is at least $6.09\%$ faster than that of the current SIKE implementation, and we can further improve the performance when large storage is available.

A recent work of Benhamouda and Lin (TCC~'20) identified a dream version of secure multiparty computation (MPC), termed **Multiparty reusable Non-Interactive Secure Computation** (MrNISC), that combines at the same time several fundamental aspects of secure computation with standard simulation security into one primitive: round-optimality, succinctness, concurrency, and adaptivity. In more detail, MrNISC is essentially a two-round MPC protocol where the first round of messages serves as a reusable commitment to the private inputs of participating parties. Using these commitments, any subset of parties can later compute any function of their choice on their respective inputs by broadcasting one message each. Anyone who sees these parties' commitments and evaluation messages (even an outside observer) can learn the function output and nothing else. Importantly, the input commitments can be computed without knowing anything about other participating parties (neither their identities nor their number) and they are reusable across any number of computations. By now, there are several known MrNISC protocols from either (bilinear) group-based assumptions or from LWE. They all satisfy semi-malicious security (in the plain model) and require trusted setup assumptions in order to get malicious security. We are interested in maliciously secure MrNISC protocols **in the plain model, without trusted setup**. Since the standard notion of polynomial simulation is un-achievable in less than four rounds, we focus on MrNISC with **super-polynomial**-time simulation (SPS). Our main result is the first maliciously secure SPS MrNISC in the plain model. The result is obtained by generically compiling any semi-malicious MrNISC and the security of our compiler relies on several well-founded assumptions, including an indistinguishability obfuscator and a time-lock puzzle (all of which need to be sub-exponentially hard). As a special case we also obtain the first 2-round maliciously secure SPS MPC based on well-founded assumptions. This MPC is also concurrently self-composable and its first message is short (i.e., its size is independent of the number of the participating parties) and reusable throughout any number of computations.

A ring signature is a digital signature scheme that allows identifying a group of possible signers without revealing the identity of the actual signer. In this paper, we first present a post-quantum sigma protocol for a ring that relies on the supersingular isogeny-based interactive zero-knowledge identification scheme proposed by De Feo, Jao, and Plût in 2014. Then, we construct a ring signature from the proposed sigma protocol for a ring by applying the Fiat-Shamir transform. In order to reduce the size of exchanges, we use Merkle trees and show that the signature size increases logarithmically in the size of the ring. The security proofs and complexity analyses of the proposed protocols are also provided.

Use of game theory and mechanism design in cloud security is a well-studied topic. When applicable, it has the advantages of being efficient and simple compared to cryptography alone. Most analyses consider two-party settings, or multi-party settings where coalitions are not allowed. However, many cloud security problems that we face are in the multi-party setting and the involved parties can almost freely collaborate with each other. To formalize the study of disincentivizing coalitions from deviating strategies, a well-known definition named k-resiliency has been proposed by Abraham et al. (ACM PODC '06). Since its proposal, k-resiliency and related definitions are used extensively for mechanism design. However, in this work we observe the shortcoming of k-resiliency. That is, although this definition is secure, it is too strict to use for many cases and rule out secure mechanisms as insecure. To overcome this issue, we propose a new definition named l-repellence against the presence of a single coalition to replace k-resiliency. Our definition incorporates transferable utility in game theory as it is realistic in many distributed and multi-party computing settings. We also propose m-stability definition against the presence of multiple coalitions, which is inspired by threshold security in cryptography. We then show the advantages of our novel definitions on three mechanisms, none of which were previously analyzed against coalitions: incentivized cloud computation, forwarding data packages in ad hoc networks, and connectivity in ad hoc networks. Regarding the former, our concepts improve the proposal by Küpçü (IEEE TDSC '17), by ensuring a coalition-proof mechanism.

Evaluating the side-channel resistance of a device in practice is a problematic and arduous process. Current certification schemes require to attack the device under test with an ever-growing number of techniques to validate its security. In addition, the success or failure of these techniques strongly depends on the individual implementing them, due to the fallible and human intrinsic nature of several steps of this path. To alleviate this problem, we propose a battery of automated attacks as a side-channel analysis robustness assessment of an embedded device. To prove our approach, we conduct realistic experiments on two different devices, creating a new dataset (AES_RA) as a part of our contribution. Furthermore, we propose a novel way of performing these attacks using Principal Component Analysis, which also serves as an alternative way of selecting optimal principal components automatically. In addition, we perform a detailed analysis of automated attacks against masked AES implementations, comparing our method with the state-of-the-art approaches and proposing two novel initialization techniques to overcome its limitations in this scenario. We support our claims with experiments on AES_RA and a public dataset (ASCAD), showing how our, although fully automated, approach can straightforwardly provide state-of-the-art results.

In known constructions of classical zero-knowledge protocols for NP, either of zero-knowledge or soundness holds only against computationally bounded adversaries. Indeed, achieving both statistical zero-knowledge and statistical soundness at the same time with classical verifier is impossible for NP unless the polynomial-time hierarchy collapses, and it is also believed to be impossible even with a quantum verifier. In this work, we introduce a novel compromise, which we call the certified everlasting zero-knowledge proof for QMA. It is a computational zero-knowledge proof for QMA, but the verifier issues a classical certificate that shows that the verifier has deleted its quantum information. If the certificate is valid, even unbounded malicious verifier can no longer learn anything beyond the validity of the statement. We construct a certified everlasting zero-knowledge proof for QMA. For the construction, we introduce a new quantum cryptographic primitive, which we call commitment with statistical binding and certified everlasting hiding, where the hiding property becomes statistical once the receiver has issued a valid certificate that shows that the receiver has deleted the committed information. We construct commitment with statistical binding and certified everlasting hiding from quantum encryption with certified deletion by Broadbent and Islam [TCC 2020] (in a black box way), and then combine it with the quantum sigma-protocol for QMA by Broadbent and Grilo [FOCS 2020] to construct the certified everlasting zero-knowledge proof for QMA. Our constructions are secure in the quantum random oracle model. Commitment with statistical binding and certified everlasting hiding itself is of independent interest, and there will be many other useful applications beyond zero-knowledge.

Masking is the main countermeasure against side-channel attacks on embedded devices. For cryptographic algorithms that combine Boolean and arithmetic masking, one must therefore convert between the two types of masking, without leaking additional information to the attacker. In this paper we describe a new high-order conversion algorithm between Boolean and arithmetic masking, based on table recomputation, and provably secure in the ISW probing model. We show that our technique is particularly efficient for masking structured LWE encryption schemes such as Kyber and Saber. In particular, for Kyber IND-CPA decryption, we obtain an order of magnitude improvement compared to existing techniques.

The high cost of IC design has made chip protection one of the first priorities of the semiconductor industry. In addition, with the growing number of untrusted foundries, the possibility of inside foundry attack is escalating. However, by taking advantage of polymorphic gates, the layouts of the circuits with different functionalities look exactly identical, making it impossible even for an inside foundry attacker to distinguish the defined functionality of an IC by looking at its layout. Moreover, since memristor is compatible with CMOS structure, it is possible to efficiently design hybrid memristor- CMOS circuits. In this paper, we propose a hardware obfuscation method based on polymorphic hybrid memristor-CMOS technology. Overhead of the polymorphic designs and the time complexity of possible attacks are discussed.

Group signatures allow group members to sign on behalf of the group anonymously. They are therefore well suited to storing data in a way that preserves the users’ privacy, while guaranteeing its authenticity. Garms and Lehmann (PKC’19) introduced a new type of group signatures that balance privacy with utility by allowing to selectively link subsets of the group signatures via an oblivious entity, the converter. The conversion takes a batch of group signatures and blindly transforms signatures originating from the same user into a consistent representation. Their scheme essentially targets a setting where the entity receiving fully unlinkable signatures and the converted ones is the same: only pseudonyms but not full signatures are converted, and the input to the converter is assumed to be well-formed. Thus, the converted outputs are merely linkable pseudonyms but no longer signatures. In this work we extend and strengthen such convertibly linkable group signatures. Conversion can now be triggered by malicious entities too, and the converted outputs can be publicly verified. This preserves the authentication of data during the conversion process. We define the security of this scheme and give a provably secure instantiation. Our scheme makes use of controlled-malleable NIZKs, which allow proofs to be mauled in a controlled manner. This allows signatures to be blinded, while still ensuring they can be verified during conversions.

This paper describes a practical side-channel power analysis on CRYSTALS-Kyber key-encapsulation mechanism. In particular, we analyse the polynomial multiplication in the decapsulation phase to recover the secret key in a semi-static setting. The power analysis attack was performed against the KYBER512 implementation from pqm4 running on STM32F3 M4-cortex CPU.

We consider the related-tweak impossible differential cryptanalysis of \texttt{TweAES}. It is one of the underlying primitives of Authenticated Encryption with Associated Data (AEAD) scheme \texttt{ESTATE} which was accepted as one of second-round candidates in the NIST Lightweight Cryptography Standardization project. Firstly, we reveal several properties of \texttt{TweAES}, which show what kinds of distinguishers are more effective in recovering keys. With the help of automatic solver Simple Theorem Prover (STP), we achieve many 5.5-round related-tweak impossible differentials with fixed input differences and output differences that just have one active byte. Then, we implement 8-round key recovery attacks against \texttt{TweAES} based on one of these 5.5-round distinguishes. Moreover, another 5.5-round distinguisher that has four active bytes at the end is utilized to mount a 7-round key recovery attack against \texttt{TweAES}, which needs much lower attack complexities than the 6-round related-tweak impossible differential attack of \texttt{TweAES} in the design document. Our 8-round key recovery attack is the best one against \texttt{TweAES} in terms of the number of rounds and complexities so far.

The final exponentiation affects the efficiency of pairing computations especially on pairing-friendly curves with high embedding degree. We propose an efficient method for computing the hard part of the final exponentiation on the KSS18 curve at 192-bit security level. Implementations indicate that the computation of the final exponentiation can be 8.74% faster than the previously fastest result.

This paper presents the design and evaluation of Wendy, the first Byzantine consensus protocol that achieves optimal latency (two phases), linear authenticator complexity, and optimistic responsiveness. Wendy's core technical contribution is a novel aggregate signature scheme that allows leaders to prove, with constant pairing cost, that an operation did not commit. This No-commit proof addresses prior liveness concerns in protocols with linear authenticator complexity (including view change), allowing Wendy to commit operations in two-phases only.

A variety of post-quantum cryptographic schemes are currently undergoing standardization in the National Institute of Standards and Technology's post-quantum cryptography standardization process. It is well known from classical cryptography that actual implementations of cryptographic schemes can be attacked by exploiting side-channels, e.g. timing behavior, power consumption or emanation in the electromagnetic field. Although several of the reference implementations currently in the third and final standardization round are - to some extent - implemented in a timing-constant fashion, resistance against other side-channels is not taken into account yet. Implementing sufficient countermeasures, however, is challenging. We therefore exemplarily examine CRYSTALS-Kyber, which is a lattice-based key encapsulation mechanism currently considered as a candidate for standardization. By analyzing the power consumption side-channel during message encoding we develop four more and compare six different implementations with an increasing degree of countermeasures. We show that introducing randomization countermeasures is crucial as all examined implementations aiming at reducing the leakage by minimizing the Hamming distance of the processed intermediate values only are vulnerable against single-trace attacks when implemented on an ARM Cortex-M4.

Micropayments are one of the challenges in cryptocurrencies. The problems in realizing micropayments in the blockchain are the low throughput and the high blockchain transaction fee. As a solution, decentralized probabilistic micropayment has been proposed. The winning amount is registered in the blockchain, and the tickets are issued to be won with probability $p$, which allows us to aggregate approximately $\frac{1}{p}$ transactions into one. Unfortunately, existing solutions do not allow for ticket transferability, and the smaller $p$, the more difficult it is to use them in the real world. We propose a novel decentralized probabilistic micropayment Transferable Scheme. It allows tickets to be transferable among users. By allowing tickets to be transferable, we can make $p$ smaller. We also propose a novel Proportional Fee Scheme. This is a scheme where each time a ticket is transferred, a portion of the blockchain transaction fee will be charged. With the proportional fee scheme, users will have the advantage of sending money with a smaller fee than they would generally send through the blockchain. For example, sending one dollar requires only ten cents.

This paper presents the first adaptively simulation secure functional encryption (FE) schemes for attribute-weighted sums. In such an FE scheme, encryption takes as input N pairs of attribute {(x_i, z_i )}_{i \in [N]} for some N \in \mathbb{N} where the attributes {x_i}_{i \in [N]} are public while the attributes {z_i}_{i \in [N]} are private. The indices i \in [N] are referred to as the slots. A secret key corresponds to some weight function f, and decryption recovers the weighted sum \sum_{i \in [N]} f(x_i)z_i. This is an important functionality with a wide range of potential real life applications. In the proposed FE schemes attributes are viewed as vectors and weight functions are arithmetic branching programs (ABP). We present two schemes with varying parameters and levels of adaptive security. (a) We first present a one-slot scheme that achieves adaptive security in the simulation-based security model against a bounded number of ciphertext queries and an arbitrary polynomial number of secret key queries both before and after the ciphertext queries. This is the best possible level of security one can achieve in the adaptive simulation-based framework. From the relations between the simulation-based and indistinguishability-based security frameworks for FE, it follows that the proposed FE scheme also achieves indistinguishability- based adaptive security against an a-priori unbounded number of ciphertext queries and an arbitrary polynomial number of secret key queries both before and after the ciphertext queries. Moreover, the scheme enjoys compact ciphertexts that do not grow with the number of appearances of the attributes within the weight functions. (b) Next, bootstrapping from the one-slot scheme, we present an unbounded-slot scheme that achieves simulation-based adaptive security against a bounded number of ciphertext and pre-ciphertext secret key queries while supporting an a-priori unbounded number of post-ciphertext secret key queries. The scheme achieves public parameters and secret key sizes independent of the number of slots N and a secret key can decrypt a ciphertext for any a-priori unbounded N. Further, just like the one-slot scheme, this scheme also has the ciphertext size independent of the number of appearances of the attributes within the weight functions. However, all the parameters of the scheme, namely, the master public key, ciphertexts, and secret keys scale linearly with the bound on the number of pre-ciphertext secret key queries. Our schemes are built upon asymmetric bilinear groups of prime order and the security is derived under the standard (bilateral) k-Linear (k-Lin) assumption. Our work resolves an open problem posed by Abdalla, Gong, and Wee in CRYPTO 2020, where they presented an unbounded-slot FE scheme for attribute-weighted sum achieving only semi-adaptive simulation security. At a technical level, our work extends the recent adaptive security framework of Lin and Luo [EUROCRYPT 2020], devised to achieve compact ciphertexts in the context of indistinguishability-based payload-hiding security, into the setting of simulation-based adaptive attribute-hiding security.

Let $n=2m$. In the present paper, we study the binomial Boolean functions of the form $$f_{a,b}(x) = \mathrm{Tr}_1^{n}(a x^{2^m-1 }) +\mathrm{Tr}_1^{2}(bx^{\frac{2^n-1}{3} }), $$ where $m$ is an even positive integer, $a\in \mathbb{F}_{2^n}^*$ and $b\in \mathbb{F}_4^*$. We show that $ f_{a,b}$ is a bent function if the Kloosterman sum $$K_{m}\left(a^{2^m+1}\right)=1+ \sum_{x\in \mathbb{F}_{2^m}^*} (-1)^{\mathrm{Tr}_1^{m}(a^{2^m+1} x+ \frac{1}{x})}$$ equals $4$, thus settling an open problem of Mesnager. The proof employs tools including computing Walsh coefficients of Boolean functions via multiplicative characters, divisibility properties of Gauss sums, and graph theory.

Black-box accumulation (BBA) is a cryptographic protocol that allows users to accumulate and redeem points, e.g. in payment systems, and offers provable security and privacy guarantees. Loosely speaking, the transactions of users remain unlinkable, while adversaries cannot claim a false amount of points or use points from other users. Attempts to spend the same points multiple times (double spending) reveal the identity of the misbehaving user and an undeniable proof of guilt. Known instantiations of BBA rely on classical number-theoretic assumptions, which are not post-quantum secure. In this work, we propose the first lattice-based instantiation of BBA, which is plausibly post- quantum secure. It relies on the hardness of the Learning with Errors (LWE) and Short Integer Solution (SIS) assumptions and is secure in the Random Oracle Model (ROM). Our work shows that a lattice-based instantiation of BBA can be realized with a communication cost per transaction of about 199 MB if built on the zero-knowledge protocol by Yang et al. (CRYPTO 2019) and the CL-type signature of Libert et al. (ASIACRYPT 2017). Without any zero-knowledge overhead, our protocol requires 1.8 MB communication.

With the advent of the Internet of Things (IoT), e-health has become one of the main topics of research. Due to the sensitivity of patient information, patient privacy seems challenging. Nowadays, patient data is usually stored in the cloud in healthcare programs, making it difficult for users to have enough control over their data. The recent increment in announced cases of security and surveillance breaches compromising patients' privacy call into question the conventional model, in which third-parties gather and control immense amounts of patients' Healthcare data. In this work, we try to resolve the issues mentioned above by using blockchain technology. We propose a blockchain-based protocol suitable for e-health applications that does not require trust in a third party and provides an efficient privacy-preserving access control mechanism. Transactions in our proposed system, unlike Bitcoin, are not entirely financial, and we do not use conventional methods for consensus operations in blockchain like Proof of Work (PoW). It is not suitable for IoT applications because IoT devices have resources-constraints. Usage of appropriate consensus method helps us to increase network security and efficiency, as well as reducing network cost, i.e., bandwidth and processor usage. Finally, we provide security and privacy analysis of our proposed protocol.

Isogeny-based cryptography is known as one of the promising approaches to the emerging post-quantum public key cryptography. In cryptography, an IDentification (ID) protocol is a primitive that allows someone's identity to be confirmed. We present an efficient variation of the isogeny-based interactive ID scheme used in the base form of the CSI-FiSh signature [BKV19], which was initially proposed by Couveignes-Rostovtsev-Stolbunov [Cou06, RS06], to support a larger challenge space, and consequently achieve a better soundness error rate in each execution. To this end, we prolong the public key of the basic ID protocol with some $\it{well-formed}$ elements that are generated by particular factors of the secret key. Due to the need for a well-formed (or structured) public key, the (secret and public) keys are generated by a trusted authority. Our analysis shows that, for a particular security parameter, by extending a public key of size 64 B to 2.1 MB, the prover and verifier of our ID protocol can be more than 14$\times$ faster than the basic ID protocol which has a binary challenge space, and moreover, the proof in our case will be about 13.5$\times$ shorter. Using standard techniques, we also turn the presented ID protocol into a signature scheme that is as efficient as the state-of-the-art CSI-FiSh signature, and is existentially unforgeable under chosen message attacks in the (quantum) random oracle model. However, in our signature scheme, a verifier should get the public key of a signer from a trusted authority, which is standard in a wide range of current uses of signatures. Finally, we show how to eliminate the need for a trusted authority in our proposed ID protocol.

We introduce report and trace ring signature schemes, balancing the desire for signer anonymity with the ability to report malicious behaviour and subsequently revoke anonymity. We contribute a formal security model for report and trace ring signatures that incorporates established properties of anonymity, unforgeability and traceability, and captures a new notion of reporter anonymity. We present a construction of a report and trace ring signature scheme, proving its security and analysing its efficiency, comparing with the state of the art in the accountable ring signatures literature. Our analysis demonstrates that our report and trace scheme is efficient, particularly for the choice of cryptographic primitives that we use to instantiate our construction. We contextualise our new primitive with respect to related work, and highlight, in particular, that report and trace ring signature schemes protect the identity of the reporter even after tracing is complete.

Password-based authentication is a central tool for end-user security. As part of this, password hashing is used to ensure the security of passwords at rest. If quantum computers become available at sufficient size, they are able to significantly speed up the computation of preimages of hash functions. Using Grover's algorithm, at most, a square-root speedup can be achieved, and thus it is expected that quantum password guessing also admits a square-root speedup. However, password inputs are not uniformly distributed but highly biased. Moreover, typical password attacks do not only compromise a random user's password but address a large fraction of all users' passwords within a database of millions of users. In this work, we study those quantum large-scale password guessing attacks for the first time. In comparison to classical attacks, we still gain a square-root speedup in the quantum setting when attacking a constant fraction of all passwords, even considering strongly biased password distributions as they appear in real-world password breaches. We verify the accuracy of our theoretical predictions using the LinkedIn leak and derive specific recommendations for password hashing and password security for a quantum computer era.

We propose to adapt ”low-algebra” digital signature schemes SPHINCS+ and PICNIC, present in the NIST-PQC contest, to the limitations of resource-bounded low-end devices. For this, we replaced the cryptographic primitives (hash functions and symmetric ciphers) of these schemes with lightweight alternatives presented in the NIST-LWC contest. With these specifically conceived primitives, we improve the performance of the signature schemes and still preserve the NIST’s security levels. Regarding SPHINCS+, besides replacing the hash function, we also take into consideration relaxing some parameters and introduce a new notion: security as life expectancy. Furthermore, we also introduce an attack to the SPHINCS+ scheme that takes advantage of the usage of FORS on this scheme and the way its leaves are calculated. Also, we give some solutions on how to avoid this attack. Additionally, a modification of PICNIC is introduced as PICNIC+WOTS where PICNIC is used to generate the secret keys for several WOTS+ signatures significantly reducing the size and signature time of each signature.

Modern implantable cardiologic devices communicate via radio frequency techniques and nearby gateways to a backend server on the internet. Those implanted devices, gateways, and servers form an ecosystem of proprietary hardware and protocols that process sensitive medical data and is often vital for patients’ health. This paper analyzes the security of this Ecosystem, from technical gateway aspects, via the programmer, to configure the implanted device, up to the processing of personal medical data from large cardiological device producers. Based on a real-world attacker model, we evaluated different devices and found several severe vulnerabilities. Furthermore, we could purchase a fully functional programmer for implantable cardiological devices, allowing us to re-program such devices or even induce electric shocks on untampered implanted devices. Additionally, we sent several Art. 15 and Art. 20 GDPR inquiries to manufacturers of implantable cardiologic devices, revealing non-conforming processes and a lack of awareness about patients’ rights and companies’ obligations. This, and the fact that many vulnerabilities are still to be found after many vulnerability disclosures in recent years, present a worrying security state of the whole ecosystem.

In this work, we show how weak key forgeries against polynomial hash based Authenticated Encryption (AE) schemes, such as AES-GCM, can be leveraged to launch partitioning oracle attacks. Partitioning oracle attacks were recently introduced by Len et al. (Usenix'21) as a new class of decryption error oracle which, conceptually, takes a ciphertext as input and outputs whether or not the decryption key belongs to some known subset of keys. Partitioning oracle attacks allow an adversary to query multiple keys simultaneously, leading to practical attacks against low entropy keys (e.g. those derived from passwords). Weak key forgeries were given a systematic treatment in the work of Procter and Cid (FSE'13), who showed how to construct MAC forgeries that effectively test whether the decryption key is in some (arbitrary) set of target keys. Consequently, it would appear that weak key forgeries naturally lend themselves to constructing partition oracles; we show that this is indeed the case, and discuss some practical applications of such an attack. Our attack applies in settings where AE schemes are used with static session keys, and has the particular advantage that an attacker has full control over the underlying plaintexts, allowing any format checks on underlying plaintexts to be met -- including those designed to mitigate against partitioning oracle attacks. Prior work demonstrated that key commitment is an important security property of AE schemes, in particular settings. Our results suggest that resistance to weak key forgeries should be considered a related design goal. Lastly, our results reinforce the message that weak passwords should never be used to derive encryption keys.

The asymptotically fastest known method for solving SVP is via lattice sieving, an algorithm whose computational bottleneck is solving the Nearest Neighbor Search problem. The best known algorithm for solving this problem is Hypercone Locality Sensitive Filtering (LSF). The classical time complexity of a sieve using Hypercone LSF is \(2^{0.2925d+o(d)}\). The quantum time complexity is \(2^{0.2653d+o(d)}\), which is acquired by using Grover's algorithm to speed up part of the enumeration. We present an improvement to the quantum algorithm, which improves the time complexity to \(2^{0.2571d+o(d)}\). Essentially, we provide a way to use Grover's algorithm to speed up another part of the process, providing a better tradeoff. This improvement affects the security of lattice-based encryption schemes, including NIST PQC Round 3 finalists.

We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform some basic analysis of this black box system and show that it is resistant to black box attacks. In order to instantiate this protocol, one needs to find a cryptographically complicated system of computable, commuting, unitary operators. To fill this need, we propose using Brandt operators acting on the Brandt modules associated to certain quaternion algebras. We explain why we believe this instantiation is likely to be secure.

In ESORICS 2021, Chvojka et al. introduced the idea of taking a time-lock puzzle and using its solution to generate the keys of a public key encryption (PKE) scheme [13]. They use this to define a timed- release encryption (TRE) scheme, in which the secret key is encrypted ‘to the future’ using a time-lock puzzle, whilst the public key is published. This allows multiple parties to encrypt a message to the public key of the PKE scheme. Then, once a solver has spent a prescribed length of time evaluating the time-lock puzzle, they obtain the secret key and hence can decrypt all of the messages. In this work we introduce TIDE (TIme Delayed Encryption), a novel approach to constructing timed-release encryption based upon the RSA cryptosystem, where instead of directly encrypting the secret key to the future, we utilise number-theoretic techniques to allow the solver to factor the RSA modulus, and hence derive the decryption key. We implement TIDE on a desktop PC and on Raspberry Pi devices validating that TIDE is both efficient and practically implementable. We provide evidence of practicality with an extensive implementation study detailing the source code and practical performance of TIDE.

The extended GCD (XGCD) calculation, which computes Bézout coefficients b_a, b_b such that b_a ∗ a_0 + b_b ∗ b_0 = GCD(a_0, b_0), is a critical operation in many cryptographic applications. In particular, large-integer XGCD is computationally dominant for two applications of increasing interest: verifiable delay functions that square binary quadratic forms within a class group and constant-time modular inversion for elliptic curve cryptography. Most prior work has focused on fast software implementations. The few works investigating hardware acceleration build on variants of Euclid’s division-based algorithm, following the approach used in optimized software. We show that adopting variants of Stein’s subtraction-based algorithm instead leads to significantly faster hardware. We quantify this advantage by performing a large-integer XGCD accelerator design space exploration comparing Euclid- and Stein-based algorithms for various application requirements. This exploration leads us to an XGCD hardware accelerator that is flexible and efficient, supports fast average and constant-time evaluation, and is easily extensible for polynomial GCD. Our 16nm ASIC design calculates 1024-bit XGCD in 294ns (8x faster than the state-of-the-art ASIC) and constant-time 255-bit XGCD for inverses in the field of integers modulo the prime 2^255−19 in 85ns (31× faster than state-of-the-art software). We believe our design is the first high-performance ASIC for the XGCD computation that is also capable of constant-time evaluation. Our work is publicly available at https://github.com/kavyasreedhar/sreedhar-xgcd-hardware-ches2022.

Oblivious Polynomial Evaluation (OPE) schemes are interactive protocols between a sender with a private polynomial and a receiver with a private evaluation point where the receiver learns the evaluation of the polynomial in their point and no additional information. In this work, we introduce MyOPE, a ``short-sighted'' non-interactive polynomial evaluation scheme with a poly-logarithmic communication complexity in the presence of malicious senders. In addition to strong privacy guarantees, MyOPE enforces honest sender behavior and consistency by adding verifiability to the calculations. The main building block for this new verifiable OPE is an inner product argument (IPA) over rings that guarantees an inner product relation holds between committed vectors. Our IPA works for vectors with elements from generic rings of polynomials and has constant-size proofs that consist in one commitment only while the verification, once the validity of the vector-commitments has been checked, consists is one quadratic equation only. We further demonstrate the applications of our IPA for verifiable OPE using Fully Homomorphic Encryption (FHE) over rings of polynomials: we prove the correctness of an inner product between the vector of powers of the evaluation point and the vector of polynomial coefficients, along with other inner-products necessary in this application's proof. MyOPE builds on generic secure encoding techniques for succinct commitments, that allow real-world FHE parameters and Residue Number System (RNS) optimizations, suitable for high-degree polynomials.

A $(t,n)$-public key threshold cryptosystem allows distributing the execution of a cryptographic task among a set of $n$ parties by splitting the secret key required for the computation into $n$ shares. A subset of at least $t+1$ honest parties is required to execute the task of the cryptosystem correctly, while security is guaranteed as long as at most $t < \frac{n}{2}$ parties are corrupted. Unfortunately, traditional threshold cryptosystems do not scale well, when executed at large-scale (e.g., in the Internet-environment). In such settings, a possible approach is to select a subset of $n$ players (called a committee) out of the entire universe of $N\gg n$ parties to run the protocol. If done naively, however, this means that the adversary's corruption power does not scale with $N$ as otherwise, the adversary would be able to corrupt the entire committee. A beautiful solution for this problem is given by Benhamouda et al. (TCC 2020) who present a novel form of secret sharing, where the efficiency of the protocol is \emph{independent} of $N$, but the adversarial corruption power \emph{scales} with $N$ (a.k.a. fully mobile adversary). They achieve this through a novel mechanism that guarantees parties in a committee to stay anonymous -- also referred to as the YOSO (You Only Speak Once) model -- until they start to interact within the protocol. In this work, we initiate the study of large-scale threshold cryptography in the YOSO model of communication. We formalize and present novel protocols for distributed key generation, threshold encryption, and signature schemes that guarantee security in large-scale environments. A key challenge in our analysis is that we cannot use the secret sharing protocol of Benhamouda et al. as a black-box to construct our schemes, and instead we require a more generalized version, which may be of independent interest. Finally, we show how our protocols can be concretely instantiated in the YOSO model, and discuss interesting applications of our schemes.

In this paper, we investigate the problem of constructing postquantum-secure verifiable delay functions (VDFs), particularly based on supersingular isogenies. Isogeny-based VDF constructions have been proposed before, but since verification relies on pairings, they are broken by quantum computers. We propose an entirely different approach using succinct non-interactive arguments (SNARGs), but specifically tailored to the arithmetic structure of the isogeny setting to achieve good asymptotic efficiency. We obtain an isogeny-based VDF construction with postquantum security, quasi-logarithmic verification, and requiring no trusted setup. As a building block, we also construct non-interactive arguments for isogeny walks in the supersingular graph over Fp2 , which may be of independent interest.

Combining several primitives together to offer greater security is an old idea in cryptography. Recently, this concept has resurfaced as it could be used to improve trust in new Post-Quantum (PQ) schemes and smooth the transition to PQ cryptography. In particular, several ways to combine key exchange mechanisms (KEMs) into a secure hybrid KEM have been proposed. In this work, we observe that most PQ KEMs are built using a variant of the Fujisaki-Okamoto (FO) transform. Thus, we propose several efficient combiners that take OW-CPA public-key encryption schemes (PKEs) and directly build hybrid IND-CCA KEMs. Our constructions are secure in the ROM and QROM and can be seen as generalizations of the FO transform. We also study how the hash functions (ROs) used in our transforms can be combined in order to improve efficiency and security. In a second part, we implement a hybrid KEM using one of our combiners as a proof-of-concept and benchmark it. More precisely, we build a hybrid IND-CCA KEM from the CPA-secure versions of HQC and LAC, two NIST Round 2 PQ proposals. We show that the resulting KEM offers comparable performances to HQC, thus improving security at a small cost. Finally, we discuss which PQ schemes should be combined in order to offer the best efficiency/security trade-off.

In many cryptocurrencies, the problem of key management has become one of the most fundamental security challenges. Typically, keys are kept in designated schemes called 'Wallets', whose main purpose is to store these keys securely. One such system is the BIP32 wallet (Bitcoin Improvement Proposal 32), which since its introduction in 2012 has been adopted by countless Bitcoin users and is one of the most frequently used wallet system today. Surprisingly, very little is known about the concrete security properties offered by this system. In this work, we propose the first formal analysis of the BIP32 system in its entirety and without any modification. Building on the recent work of Das et al. (CCS `19), we put forth a formal model for hierarchical deterministic wallet systems (such as BIP32) and give a security reduction in this model from the existential unforgeability of the ECDSA signature algorithm that is used in BIP32. We conclude by giving concrete security parameter estimates achieved by the BIP32 standard, and show that by moving to an alternative key derivation method we can achieve a tighter reduction offering an additional 20 bits of security (111 vs. 91 bits of security) at no additional costs.

In this paper, we construct an efficient interactive proof system for the graph 3-coloring problem and shows that it is computationally zero-knowledge against a quantum malicious verifier. Our protocol is inline with the sketch of an efficient protocol by Brassard and Crepéau (FOCS 1986) that later has been elaborated by Kilian (STOC 1992). Their protocol is not post-quantum secure since its soundness property holds based on the intractability of the factoring problem. Putting aside the post-quantum security, we argue that Kilian's interactive protocol for the graph 3-coloring problem does not fulfill the soundness property even in the classical setting. In this paper, we propose an XOR-homomorphic commitment scheme based on the Learning Parity with Noise (LPN) problem and use it to construct an efficient quantum computationally zero-knowledge interactive proof system for the graph 3-coloring problem.

Integral cryptanalysis is a powerful tool for attacking symmetric primitives, and division property is a state-of-the-art framework for finding integral distinguishers. This work describes new theoretical and practical insights into traditional bit-based division property. We focus on analyzing and exploiting monotonicity/convexity of division property and its relation to the graph indicator. In particular, our investigation leads to a new compact representation of propagation, which allows CNF/MILP modeling for larger S-Boxes, such as 16-bit Super-Sboxes of lightweight block ciphers or even 32-bit random S-boxes. This solves the challenge posed by Derbez and Fouque (ToSC 2020), who questioned the possibility of SAT/SMT/MILP modeling of 16-bit Super-Sboxes. As a proof-of-concept, we model the Super-Sboxes of the 8-round LED by CNF formulas, which was not feasible by any previous approach. Our analysis is further supported by an elegant algorithmic framework. We describe simple algorithms for computing division property of a set of $n$-bit vectors in time $O(n2^n)$, reducing such sets to minimal/maximal elements in time $O(n2^n)$, computing division property propagation table of an $n\times m$-bit S-box and its compact representation in time $O((n+m)2^{n+m})$. In addition, we develop an advanced algorithm tailored to "heavy" bijections, allowing to model, for example, a randomly generated 32-bit S-box.

Recently, the application of multi-party secure computing schemes based on homomorphic encryption in the field of machine learning attracts attentions across the research fields. Previous studies have demonstrated that secure protocols adopting packed additive homomorphic encryption (PAHE) schemes based on the ring learning with errors (RLWE) problem exhibit significant practical merits, and are particularly promising in enabling efficient secure inference in machine-learning-as-a-service applications. In this work, we introduce a new technique for performing homomorphic linear transformation (HLT) over PAHE ciphertexts. Using the proposed HLT technique, homomorphic convolutions and inner products can be executed without the use of number theoretic transform and the rotate-and-add algorithms that were proposed in existing works. To maximize the efficiency of the HLT technique, we propose APAS, a hardware-software co-design framework consisting of approximate arithmetic units for the hardware acceleration of HLT. In the experiments, we use actual neural network architectures as benchmarks to show that APAS can improve the computational and communicational efficiency of homomorphic convolution by 8x and 3x, respectively, with an energy reduction of up to 26x as compared to the ASIC implementations of existing methods.

A large number of the symmetric-key mode of operations, such as classical CBC-MAC, have serial structures. While a serial mode gives an implementation advantage in terms of required memory or footprint compared to the parallel counterparts, it wastes the capability of parallel process even when it is available. The problem is becoming more relevant as lightweight cryptography is going to be deployed in the real world. In this article, we propose an alternative implementation strategy for serial MAC modes and serial authenticated encryption (AE) modes that allows 2-block parallel operation for verification/decryption. Our proposal maintains the original functionality and security. It is simple yet novel, and generally applicable to a wide range of existing modes including two NIST recommendations, CMAC and CCM. We demonstrate the effectiveness of our proposal by showing several case studies with software implementations.

Recent Bitcoin attacks [CCS'21, CCS'21, ICDCS'19] commonly exploit the phenomenon of so-called weak block synchronization in Bitcoin. The attacks use two independently-operated Bitcoin monitors — i.e., Bitnodes and a system of customized supernodes — to confirm that block propagation in Bitcoin is surprisingly slow. In particular, Bitnodes constantly reports that around 30% of nodes are 3 blocks (or more) behind the blockchain tip and the supernodes show that on average more than 60% of nodes do not receive the latest block even after waiting for 10 minutes. In this paper, we carefully re-evaluate these controversial claims with our own experiments in the live Bitcoin network and show that block propagation in Bitcoin is, in fact, fast enough (e.g., most peers we monitor receive new blocks in about 4 seconds) for its safety property. We identify several limitations and bugs of the two monitors, which have led to these inaccurate claims about the Bitcoin block synchronization. We finally ask several open-ended questions regarding the technical and ethical issues around monitoring blockchain networks.

We propose the use of Hensel codes (a mathematical tool lifted from the theory of $p$-adic numbers) as an alternative way to construct homomorphic encryption (HE) schemes that rely on the hardness of some instance of the approximate common divisor (AGCD) problem. We provide a self-contained introduction to Hensel codes which covers all the properties of interest for this work. Two constructions are presented: a private-key leveled HE scheme and a public-key leveled HE scheme. The public-key scheme is obtained via minor modifications to the private-key scheme in which we explore asymmetric properties of Hensel codes. The efficiency and security (under an AGCD variant) of the public-key scheme are discussed in detail. Our constructions take messages from large specialized subsets of the rational numbers that admit fractional numerical inputs and associated computations for virtually any real-world application. Further, our results can be seen as a natural unification of error-free computation (computation free of rounding errors over rational numbers) and homomorphic encryption. Experimental results indicate the scheme is practical for a large variety of applications.

Existing oblivious storage systems provide strong security by hiding access patterns, but do not scale to sustain high throughput as they rely on a central point of coordination. To overcome this scalability bottleneck, we present Snoopy, an object store that is both oblivious and scalable such that adding more machines increases system throughput. Snoopy contributes techniques tailored to the high-throughput regime to securely distribute and efficiently parallelize every system component without prohibitive coordination costs. These techniques enable Snoopy to scale similarly to a plaintext storage system. Snoopy achieves 13.7x higher throughput than Obladi, a state-of-the-art oblivious storage system. Specifically, Obladi reaches a throughput of 6.7K requests/s for two million 160-byte objects and cannot scale beyond a proxy and server machine. For the same data size, Snoopy uses 18 machines to scale to 92K requests/s with average latency under 500ms.

In 2014, the author conceived of a quantal version of the classical cryptographic Diffie-Hellman key exchange protocol. However, the paper was declined to be published (by a not disclosed journal). No further publication attempts were made by the author. In the time afterwards, the aforementioned idea was conceived by others as well, resulting in a number of publications regarding this topic and even slight improvements. Thereby underlining the significance of the author's original idea, despite of being rejected by peer reviewed journals. The paper at hand therefore serves two purposes: First, it might serve others (especially young researchers) as an example to not feel discouraged by publication refusals, if they truly deem them as important novelties. Second, it provides an easy to understand introduction to grasp the concept of a quantum Diffie-Hellman key exchange. All of the following paragraphs, including the remainder of this abstract, are taken from the original 2014 publication attempt and are unchanged in comparison to the 2014 original: In this work, a quantal version of the classical cryptographic Diffie-Hellman key exchange protocol is introduced. It is called Quantum Diffie-Hellman key exchange. Unlike for the existing quantum key distribution protocols, actual quantum states, and not their measurement outcomes, are regarded as finally exchanged keys/information. By implementation of that quantal Diffie-Hellman version, both communication parties in the end are in possession of identically prepared, and secret quantum states. Thus the cryptographically important principle of forward secrecy is now available in a quantum physical framework. As a merit of the quantum setting, an improvement of the classical Diffie-Hellman protocol is also achieved, as neither of the two parties exactly know the final, exchanged states.

The discipline of reverse engineering integrated circuits (ICs) is as old as the technology itself. It grew out of the need to analyze competitor’s products and detect possible IP infringements. In recent years, the growing hardware Trojan threat motivated a fresh research interest in the topic. The process of IC reverse engineering comprises two steps: netlist extraction and specification discovery. While the process of netlist extraction is rather well understood and established techniques exist throughout the industry, specification discovery still presents researchers with a plurality of open questions. It therefore remains of particular interest to the scientific community. In this paper, we present a survey of the state of the art in IC reverse engineering while focusing on the specification discovery phase. Furthermore, we list noteworthy existing works on methods and algorithms in the area and discuss open challenges as well as unanswered questions. Therefore, we observe that the state of research on algorithmic methods for specification discovery suffers from the lack of a uniform evaluation approach. We point out the urgent need to develop common research infrastructure, benchmarks, and evaluation metrics.

Over the last decade attacks have repetitively demonstrated that bitstream protection for SRAM-based FPGAs is a persistent problem without a satisfying solution in practice. Hence, real-world hardware designs are prone to intellectual property infringement and malicious manipulation as they are not adequately protected against reverse-engineering. In this work, we first review state-of-the-art solutions from industry and academia and demonstrate their ineffectiveness with respect to reverse-engineering and design manipulation. We then describe the design and implementation of novel hardware obfuscation primitives based on the intrinsic structure of FPGAs. Based on our primitives, we design and implement LifeLine, a hardware design protection mechanism for FPGAs using hardware/software co-obfuscated cryptography. We show that LifeLine offers effective protection for a real-world adversary model, requires minimal integration effort for hardware designers, and retrofits to already deployed (and so far vulnerable) systems.

In this paper, we perform a comprehensive evaluation on blockchain sharding protocols. We deconstruct the blockchain sharding protocol into four foundational layers with orthogonal functionalities, securing some properties. We evaluate each layer of seven state-of-the-art blockchain sharding protocols, and identify a considerable number of new attacks, questionable design trade-offs and some open challenges. The layered evaluation allows us to unveil security and performance problems arising from a fundamental design choice, namely the coherence of system settings across layers. In particular, most sharded blockchains use different trust and synchrony assumptions across layers, without corresponding architectural guarantees. Unless a hybrid architecture were used, assuming differentiated system settings across layers can introduce subtle but severe failure syndromes or reduce the system’s performance.

We study the effects of the XOR transformation, that is, $f^{\oplus 2}(x_1,x_2):= f(x_1)\oplus f(x_2)$, on one-wayness. More specifically, we present an example showing that if one-way functions exist, there also exists a one-way function $f$ such that $f^{\oplus 2}$ is not even a distributional one-way function, demonstrating that one-wayness may severely deteriorate.

Assume that distributions $X_0,X_1$ (respectively $Y_0,Y_1$) are $d_X$ (respectively $d_Y$) indistinguishable for circuits of a given size. It is well known that the product distributions $X_0Y_0,\,X_1Y_1$ are $d_X+d_Y$ indistinguishable for slightly smaller circuits. However, in probability theory where unbounded adversaries are considered through statistical distance, it is folklore knowledge that in fact $X_0Y_0$ and $X_1Y_1$ are $d_X+d_Y-d_X\cdot d_Y$ indistinguishable, and also that this bound is tight. We formulate and prove the computational analog of this tight bound. Our proof is entirely different from the proof in the statistical case, which is non-constructive. As a corollary, we show that if $X$ and $Y$ are $d$ indistinguishable, then $k$ independent copies of $X$ and $k$ independent copies of $Y$ are almost $1-(1-d)^k$ indistinguishable for smaller circuits, as against $d\cdot k$ using the looser bound. Our bounds are useful in settings where only weak (i.e. non-negligible) indistinguishability is guaranteed. We demonstrate this in the context of cryptography, showing that our bounds yield simple analysis for amplification of weak oblivious transfer protocols.

Repeated Modular Squaring is a versatile computational operation that has led to practical constructions of timed-cryptographic primitives like time-lock puzzles (TLP) and verifiable delay functions (VDF) that have a fast growing list of applications. While there is a huge interest for timed-cryptographic primitives in the blockchains area, we find two real-world concerns that need immediate attention towards their large-scale practical adoption: Firstly, the requirement to constantly perform computations seems unrealistic for most of the users. Secondly, choosing the parameters for the bound $T$ seems complicated due to the lack of heuristics and experience. We present Opensquare, a decentralized repeated modular squaring service, that overcomes the above concerns. Opensquare lets clients outsource their repeated modular squaring computation via smart contracts to any computationally powerful servers that offer computational services for rewards in an unlinkable manner. Opensquare naturally gives us publicly computable heuristics about a pre-specified number ($T$) and the corresponding reward amounts of repeated squarings necessary for a time period. Moreover, Opensquare rewards multiple servers for a single request, in a sybil resistant manner to incentivise maximum server participation and is therefore resistant to censorship and single-points-of failures. We give game-theoretic analysis to support the mechanism design of Opensquare: (1) incentivises servers to stay available with their services, (2) minimizes the cost of outsourcing for the client, and (3) ensures the client receives the valid computational result with high probability. To demonstrate practicality, we also implement Opensquare's smart contract in Solidity and report the gas costs for all of its functions. Our results show that the on-chain computational costs for both the clients and the servers are quite low, and therefore feasible for practical deployments and usage.

Timed commitments [Boneh and Naor, CRYPTO 2000] are the timed analogue of standard commitments, where the commitment can be non-interactively opened after a pre-specified amount of time passes. Timed commitments have a large spectrum of applications, such as sealed bid auctions, fair contract signing, fair multi-party computation, and cryptocurrency payments. Unfortunately, all practical constructions rely on a (private-coin) trusted setup and do not scale well with the number of participants. These are two severe limiting factors that have hindered the widespread adoption of this primitive. In this work, we set out to resolve these two issues and propose an efficient timed commitment scheme that also satisfies the strong notion of CCA-security. Specifically, our scheme has a transparent (i.e. public-coin) one-time setup and the amount of sequential computation is essentially independent of the number of participants. As a key technical ingredient, we propose the first (linearly) homomorphic time-lock puzzle with a transparent setup, from class groups of imaginary quadratic order. To demonstrate the applicability of our scheme, we use it to construct a new distributed randomness generation protocol, where $n$ parties jointly sample a random string. Our protocol is the first to simultaneously achieve (1) high scalability in the number of participants, (2) transparent one-time setup, (3) lightning speed in the optimistic case where all parties are honest, and (4) ensure that the output random string is unpredictable and unbiased, even when the adversary corrupts $n-1$ parties. To substantiate the practicality of our approach, we implemented our protocol and our experimental evaluation shows that it is fast enough to be used in practice. We also evaluated a heuristic version of the protocol that is at least 3 orders of magnitude more efficient both in terms of communication size and computation time. This makes the protocol suitable for supporting hundreds of participants.

Number-theoretic algorithms often need to calculate one or both of two related quantities: modular inversion and Jacobi symbol. These two functions seem unrelated at first glance, but in fact the algorithms for calculating them are closely related: they can both be calculated either by variants of Euclid's GCD algorithm, or when the modulus is prime, by exponentiation. As a result, an implementation of one algorithm can often be adapted to compute the other instead, or they can even be calculated together in a batch. The Bernstein-Yang right-to-left modular inversion algorithm is notable for taking constant, asymptotically subquadratic time. Right-to-left algorithms are tricky to adapt for the Jacobi symbol, because they do not consider the signs of the values being operated on. But the Jacobi symbol is defined only on positive integers, and the rules for computing it need corrections if negative integers are introduced. In this short paper, we show how to overcome this difficulty and produce a right-to-left Jacobi symbol algorithm based on Bernstein-Yang.

The goal of the bounded storage model (BSM) is to construct unconditionally secure cryptographic protocols, by only restricting the storage capacity of the adversary, but otherwise giving it unbounded computational power. Here, we consider a streaming variant of the BSM, where honest parties can stream huge amounts of data to each other so as to overwhelm the adversary's storage, even while their own storage capacity is significantly smaller than that of the adversary. Prior works showed several impressive results in this model, including key agreement and oblivious transfer, but only as long as adversary's storage $m = O(n^2)$ is at most quadratically larger than the honest user storage $n$. Moreover, the work of Dziembowski and Maurer (DM) also gave a seemingly matching lower bound, showing that key agreement in the BSM is impossible when $m > n^2$. In this work, we observe that the DM lower bound only applies to a significantly more restricted version of the BSM, and does not apply to the streaming variant. Surprisingly, we show that it is possible to construct key agreement and oblivious transfer protocols in the streaming BSM, where the adversary's storage can be significantly larger, and even exponential $m = 2^{O(n)}$. The only price of accommodating larger values of $m$ is that the round and communication complexities of our protocols grow accordingly, and we provide lower bounds to show that an increase in rounds and communication is necessary. As an added benefit of our work, we also show that our oblivious transfer (OT) protocol in the BSM satisfies a simulation-based notion of security. In contrast, even for the restricted case of $m = O(n^2)$, prior solutions only satisfied a weaker indistinguishability based definition. As an application of our OT protocol, we get general multiparty computation (MPC) in the BSM that allows for up to exponentially large gaps between $m$ and $n$, while also achieving simulation-based security.

A randomness encoder is a generalization of encoding schemes with an efficient procedure for encoding \emph{uniformly random strings}. In this paper we continue the study of randomness encoders that additionally have the property of being continuous non-malleable. The beautiful notion of non-malleability for encoding schemes, introduced by Dziembowski, Pietrzak and Wichs (ICS’10), states that tampering with the codeword can either keep the encoded message identical or produce an uncorrelated message. Continuous non-malleability extends the security notion to a setting where the adversary can tamper the codeword polynomially many times and where we assume a self-destruction mechanism in place in case of decoding errors. Our contributions are: (1) two practical constructions of continuous non-malleable randomness encoders in the random oracle model, and (2) a new compiler from continuous non-malleable randomness encoders to continuousnon-malleable codes, and (3) a study of lower bounds for continuous non-malleability in the random oracle model.

Selective opening attacks (SOA) (for public-key encryption, PKE) concern such a multi-user scenario, where an adversary adaptively corrupts some fraction of the users to break into a subset of honestly created ciphertexts, and tries to learn the information on the messages of some unopened (but potentially related) ciphertexts. Until now, the notion of selective opening attacks is only considered in two settings: sender selective opening (SSO), where part of senders are corrupted and messages together with randomness for encryption are revealed; and receiver selective opening (RSO), where part of receivers are corrupted and messages together with secret keys for decryption are revealed. In this paper, we consider a more natural and general setting for selective opening security. In the setting, the adversary may adaptively corrupt part of senders and receivers \emph{simultaneously}, and get the plaintext messages together with internal randomness for encryption and secret keys for decryption, while it is hoped that messages of uncorrupted parties remain protected. We denote it as Bi-SO security since it is reminiscent of Bi-Deniability for PKE. We first formalize the requirement of Bi-SO security by the simulation-based (SIM) style, and prove that some practical PKE schemes achieve SIM-Bi-$\text{SO}$-CCA security in the random oracle model. Then, we suggest a weak model of Bi-SO security, denoted as SIM-wBi-$\text{SO}$-CCA security, and argue that it is still meaningful and useful. We propose a generic construction of PKE schemes that achieve SIM-wBi-$\text{SO}$-CCA security in the standard model and instantiate them from various standard assumptions. Our generic construction is built on a newly presented primitive, namely, universal$_{\kappa}$ hash proof system with key equivocability, which may be of independent interest.

We prove classical and quantum indifferentiability of a rate-1/3 compression function introduced by Shrimpton and Stam (ICALP '08). This construction was one of the first constructions based on three random functions that achieved optimal collision-resistance. We also prove that our result is tight, we define a classical and a quantum attackers that match the indifferentiability security level. Our tight indifferentiability results provide a negative result on the optimality of security of the construction by Shrimpton and Stam, security level of the strong indifferentiability notion is below that of collision-resistance. To arrive at these results, we generalize the results of Czajkowski, Majenz, Schaffner, and Zur (arXiv '19). Our generalization allows to analyze quantum security of constructions based on multiple independent random functions, something not possible before.

Many recent studies focus on dynamic searchable encryption (DSE), which provides efficient data-search and data-update services directly on outsourced private data. Most encryption schemes are not optimized for update-intensive cases, which say that the same data record is frequently added and deleted from the database. How to build an efficient and secure DSE scheme for update-intensive data is still challenging. We propose UI-SE, the first DSE scheme that achieves single-round-trip interaction, near-zero client storage, and backward privacy without any insertion patterns. UI-SE involves a new tree data structure, named OU-tree, which supports oblivious data updates without any access-pattern leakage. We formally prove that UI-SE is adaptively secure under Type-1$^-$ backward privacy, which is stronger than backward privacy proposed by Bost et al. in CCS 2017. Experimental data also demonstrate UI-SE has low computational overhead, low local disk usage, and high update performance on scalable datasets.

We generalize the knowledge extractor for constant-round special sound protocols presented by Wikström (2018) to a knowledge extractor for the corresponding non-interactive Fiat-Shamir proofs in the random oracle model and give an exact analysis of the extraction error and running time. Relative the interactive case the extraction error is increased by a factor $\ell$ and the running time is increased by a factor $O(\ell)$, where $\ell$ is the number of oracle queries made by the prover. Through carefully chosen notation and concepts, and a technical lemma, we effectively recast the extraction problem of the notoriously complex non-interactive case to the interactive case. Thus, our approach may be of independent interest.

An extractable one-way function (EOWF), introduced by Canetti and Dakdouk (ICALP 2008) and generalized by Bitansky et al. (SIAM Journal on Computing vol. 45), is an OWF that allows for efficient extraction of a preimage for the function. We study (generalized) EOWFs that have a public image verification algorithm. We call such OWFs verifiably-extractable and show that several previously known constructions satisfy this notion. We study how such OWFs relate to subversion zero-knowledge (Sub-ZK) NIZKs by using them to generically construct a Sub-ZK NIZK from a NIZK satisfying certain additional properties, and conversely show how to obtain them from any Sub-ZK NIZK. Prior to our work, the Sub-ZK property of NIZKs was achieved using concrete knowledge assumptions.

This paper introduces Verdict, a transparency dictionary, where an untrusted service maintains a label-value map that clients can query and update (foundational infrastructure for end-to-end encryption and other applications). To prevent unauthorized modifications to the dictionary, for example, by a malicious or a compromised service provider, Verdict produces publicly-verifiable cryptographic proofs that it correctly executes both reads and authorized updates. A key advance over prior work is that Verdict produces efficiently-verifiable proofs while incurring modest proving overheads. Verdict accomplishes this by composing indexed Merkle trees (a new SNARK-friendly data structure) with Phalanx (a new SNARK that supports amortized constant-sized proofs and leverages particular workload characteristics to speed up the prover). Our experimental evaluation demonstrates that Verdict scales to dictionaries with millions of labels while imposing modest overheads on the service and clients.

We study Multi-party computation (MPC) in the setting of subversion, where the adversary tampers with the machines of honest parties. Our goal is to construct actively secure MPC protocols where parties are corrupted adaptively by an adversary (as in the standard adaptive security setting), and in addition, honest parties' machines are compromised. The idea of reverse firewalls (RF) was introduced at EUROCRYPT'15 by Mironov and Stephens-Davidowitz as an approach to protecting protocols against corruption of honest parties' devices. Intuitively, an RF for a party $\mathcal{P}$ is an external entity that sits between $\mathcal{P}$ and the outside world and whose scope is to sanitize $\mathcal{P}$’s incoming and outgoing messages in the face of subversion of their computer. Mironov and Stephens-Davidowitz constructed a protocol for passively-secure two-party computation. At CRYPTO'20, Chakraborty, Dziembowski and Nielsen constructed a protocol for secure computation with firewalls that improved on this result, both by extending it to multi-party computation protocol, and considering active security in the presence of static corruptions. In this paper, we initiate the study of RF for MPC in the adaptive setting. We put forward a definition for adaptively secure MPC in the reverse firewall setting, explore relationships among the security notions, and then construct reverse firewalls for MPC in this stronger setting of adaptive security. We also resolve the open question of Chakraborty, Dziembowski and Nielsen by removing the need for a trusted setup in constructing RF for MPC. Towards this end, we construct reverse firewalls for adaptively secure augmented coin tossing and adaptively secure zero-knowledge protocols and obtain a constant round adaptively secure MPC protocol in the reverse firewall setting without setup. Along the way, we propose a new multi-party adaptively secure coin tossing protocol in the plain model, that is of independent interest.

Our context is anonymous encryption schemes hiding their receiver, but in a setting which allows authorities to reveal the receiver when needed. While anonymous Identity-Based Encryption (IBE) is a natural candidate for such fair anonymity (it gives trusted authority access by design), the de facto security standard (a.k.a. IND-ID-CCA) is incompatible with the ciphertext rerandomizability which is crucial to anonymous communication. Thus, we seek to extend IND-ID-CCA security for IBE to a notion that can be meaningfully relaxed for rerandomizability while it still protects against active adversaries. To the end, inspired by the notion of replayable adaptive chosen-ciphertext attack (RCCA) security (Canetti et al., Crypto'03), we formalize a new security notion called Anonymous Identity-Based RCCA (ANON-ID-RCCA) security for rerandomizable IBE and propose the first construction with rigorous security analysis. The core of our scheme is a novel extension of the double-strand paradigm, which was originally proposed by Golle et al. (CT-RSA'04) and later extended by Prabhakaran and Rosulek (Crypto'07), to the well-known Gentry-IBE (Eurocrypt'06). Notably, our scheme is the first IBE that simultaneously satisfies adaptive security, rerandomizability, and recipient-anonymity to date. As the application of our new notion, we design a new universal mixnet in the identity-based setting that does not require public key distribution (with fair anonymity). More generally, our new notion is also applicable to most existing rerandomizable RCCA-secure applications to eliminate the need for public key distribution infrastructure while allowing fairness.

In their pursuit to maximize their return on investment, cybercriminals will likely reuse as much as possible between their campaigns. Not only will the same phishing mail be sent to tens of thousands of targets, but reuse of the tools and infrastructure across attempts will lower their costs of doing business. This reuse, however, creates an effective angle for mitigation, as defenders can recognize domain names, attachments, tools, or systems used in a previous compromisation attempt, significantly increasing the cost to the adversary as it would become necessary to recreate the attack infrastructure each time. However, generating such cyber threat intelligence (CTI) is resource-intensive, so organizations often turn to CTI providers that commercially sell feeds with such indicators. As providers have different sources and methods to obtain their data, the coverage and relevance of feeds will vary for each of them. To cover the multitude of threats one organization faces, they are best served by obtaining feeds from multiple providers. However, these feeds may overlap, causing an organization to pay for indicators they already obtained through another provider. This paper presents a privacy-preserving protocol that allows an organization to query the databases of multiple data providers to obtain an estimate of their total coverage without revealing the data they store. In this way, a customer can make a more informed decision on their choice of CTI providers. We implement this protocol in Rust to validate its performance experimentally: When performed between three CTI providers who collectively have 20,000 unique indicators, our protocol takes less than 6 seconds to execute. The code for our experiments is freely available.

In many occasions, the knowledge error $\kappa$ of an interactive proof is not small enough, and thus needs to be reduced. This can be done generically by repeating the interactive proof in parallel. While there have been many works studying the effect of parallel repetition on the {\em soundness error} of interactive proofs and arguments, the effect of parallel repetition on the {\em knowledge error} has largely remained unstudied. Only recently it was shown that the $t$-fold parallel repetition of {\em any} interactive protocol reduces the knowledge error from $\kappa$ down to $\kappa^t +\nu$ for any non-negligible term $\nu$. This generic result is suboptimal in that it does not give the knowledge error $\kappa^t$ that one would expect for typical protocols, and, worse, the knowledge error remains non-negligible. In this work we show that indeed the $t$-fold parallel repetition of any $(k_1,\dots,k_{\mu})$-special-sound multi-round public-coin interactive proof optimally reduces the knowledge error from $\kappa$ down to $\kappa^t$. At the core of our results is an alternative, in some sense more fine-grained, measure of quality of a dishonest prover than its success probability, for which we show that it characterizes when knowledge extraction is possible. This new measure then turns out to be very convenient when it comes to analyzing the parallel repetition of such interactive proofs. While parallel repetition reduces the knowledge error, it is easily seen to {\em increase} the {\em completeness error}. For this reason, we generalize our result to the case of $s$-out-of-$t$ threshold parallel repetition, where the verifier accepts if $s$ out of $t$ of the parallel instances are accepting. An appropriately chosen threshold $s$ allows both the knowledge error and completeness error to be reduced simultaneously.

We introduce a novel framework for quantifying the bit security of security games. Our notion is defined with an operational meaning that a $\lambda$-bit secure game requires a total computational cost of $2^\lambda$ for winning the game with high probability, e.g., 0.99. We define the bit security both for search-type and decision-type games. Since we identify that these two types of games should be structurally different, we treat them differently but define the bit security using the unified framework to guarantee the same operational interpretation. The key novelty of our notion of bit security is to employ two types of adversaries: inner adversary and outer adversary. While the inner adversary plays a ``usual'' security game, the outer adversary invokes the inner adversary many times to amplify the winning probability for the security game. We find from our framework that the bit security for decision games can be characterized by the information measure called the Rényi divergence of order $1/2$ of the inner adversary. The conventional ``advantage,'' defined as the probability of winning the game, characterizes our bit security for search-type games. We present several security reductions in our framework for justifying our notion of bit security. Many of our results quantitatively match the results for the bit security notion proposed by Micciancio and Walter in 2018. In this sense, our bit security strengthens the previous notion of bit security by adding an operational meaning. A difference from their work is that, in our framework, the Goldreich-Levin theorem gives an optimal reduction only for ``balanced'' adversaries who output binary values in a balanced manner.

In the shuffle model for differential privacy, $n$ users locally randomize their data and submit the results to a trusted “shuffler” who mixes the results before sending them to a server for analysis. This is a promising model for real-world applications of differential privacy, as several recent results have shown that the shuffle model sometimes offers a strictly better privacy/utility tradeoff than what is possible in a purely local model. A downside of the shuffle model is its reliance on a trusted shuffler, and it is natural to try to replace this with a distributed shuffling protocol run by the users themselves. While it would of course be possible to use a fully secure shuffling protocol, one might hope to instead use a more-efficient protocol having weaker security guarantees. In this work, we consider a relaxation of secure shuffling called differential obliviousness that we prove suffices for differential privacy in the shuffle model. We also propose a differentially oblivious shuffling protocol based on onion routing that requires only $O(n \log n)$ communication while tolerating any constant fraction of corrupted users. We show that for practical settings of the parameters, our protocol outperforms existing solutions to the problem in some settings.

Anonymous message delivery systems, such as private messaging services and privacy-preserving payment systems, need a mechanism for recipients to retrieve the messages addressed to them, without leaking metadata or letting their messages be linked. Recipients could download all posted messages and scan for those addressed to them, but communication and computation costs are excessive at scale. We show how untrusted servers can detect messages on behalf of recipients, and summarize these into a compact encrypted digest that recipients can easily decrypt. These servers operate obliviously and do not learn anything about which messages are addressed to which recipients. Privacy, soundness, and completeness hold even if everyone but the recipient is adversarial and colluding (unlike in prior schemes). Our starting point is an asymptotically-efficient approach, using Fully Homomorphic Encryption and homomorphically-encoded Sparse Random Linear Codes. We then address the concrete performance using bespoke tailoring of lattice-based cryptographic components, alongside various algebraic and algorithmic optimizations. This reduces the digest size to a few bits per message scanned. Concretely, the servers' cost is ~$1 per million messages scanned, and the resulting digests can be decoded by recipients in ~20ms. Our schemes can thus practically attain the strongest form of receiver privacy for current applications such as privacy-preserving cryptocurrencies.

Let $As = b + e \bmod q$ be an LWE-instance with ternary keys $s,e \in \{0, \pm 1\}^n$. Let $s$ be taken from a search space of size $\mathcal{S}$. A standard Meet-in-the-Middle attack recovers $s$ in time $\mathcal{S}^{0.5}$. Using the representation technique, a recent improvement of May shows that this can be lowered to approximately $\mathcal{S}^{0.25}$ by guessing a sub-linear number of $\Theta(\frac{n}{\log n})$ coordinates from $e$. While guessing such an amount of $e$ can asymptotically be neglected, for concrete instantiations of e.g. NTRU, BLISS or GLP the additional cost of guessing leads to complexities around $\mathcal{S}^{0.3}$. We introduce a locality sensitive hashing (LSH) technique based on Odlyzko's work that avoids any guessing of $e$'s coordinates. This LSH technique involves a comparably small cost such that we can significantly improve on previous results, pushing complexities towards the asymptotic bound $\mathcal{S}^{0.25}$. Concretely, using LSH we lower the MitM complexity estimates for the currently suggested NTRU and NTRU Prime instantiations by a factor in the range $2^{20}-2^{49}$, and for BLISS and GLP parameters by a factor in the range $2^{18}-2^{41}$.

Vector commitment (VC) schemes allow one to commit concisely to an ordered sequence of values, so that the values at desired positions can later be proved concisely. In addition, a VC can be statelessly updatable, meaning that commitments and proofs can be updated to reflect changes to individual entries, using knowledge of just those changes (and not the entire vector). VCs have found important applications in verifiable outsourced databases, cryptographic accumulators, and cryptocurrencies. However, to date there have been relatively few post-quantum constructions, i.e., ones that are plausibly secure against quantum attacks. More generally, functional commitment (FC) schemes allow one to concisely and verifiably reveal various functions of committed data, such as linear functions (i.e., inner products, including evaluations of a committed polynomial). Under falsifiable assumptions, all known functional commitments schemes have been limited to ``linearizable'' functions, and there are no known post-quantum FC schemes beyond ordinary VCs. In this work we give post-quantum constructions of vector and functional commitments based on the standard Short Integer Solution lattice problem (appropriately parameterized): \begin{itemize} \item First, we present new statelessly updatable VCs with significantly shorter proofs than (and efficiency otherwise similar to) the only prior post-quantum, statelessly updatable construction (Papamanthou \etal, EUROCRYPT 13). Our constructions use private-key setup, in which an authority generates public parameters and then goes offline. \item Second, we construct functional commitments for \emph{arbitrary (bounded) Boolean circuits} and branching programs. Under falsifiable assumptions, this is the first post-quantum FC scheme beyond ordinary VCs, and the first FC scheme of any kind that goes beyond linearizable functions. Our construction works in a new model involving an authority that generates the public parameters and remains online to provide public, reusable ``opening keys'' for desired functions of committed messages. \end{itemize}

EasyCrypt is a formal verification tool used extensively for formalizing concrete security proofs of cryptographic constructions. However, the EasyCrypt formal logics consider only classical attackers, which means that post-quantum security proofs cannot be formalized and machine-checked with this tool. In this paper we prove that a natural extension of the EasyCrypt core logics permits capturing a wide class of post-quantum cryptography proofs, settling a question raised by (Unruh, POPL 2019). Leveraging our positive result, we implement EasyPQC, an extension of EasyCrypt for post-quantum security proofs, and use EasyPQC to verify post-quantum security of three classic constructions: PRF-based MAC, Full Domain Hash and GPV08 identity-based encryption.

Public knowledge about the structure of a cryptographic system is a standard assumption in the literature and algorithms are expected to guarantee security in a setting where only the encryption key is kept secret. Nevertheless, undisclosed proprietary cryptographic algorithms still find widespread use in applications both in the civil and military domains. Even though side-channel-based reverse engineering attacks that recover the hidden components of custom cryptosystems have been demonstrated for a wide range of constructions, the complete and practical reverse engineering of AES-128-like ciphers remains unattempted. In this work, we close this gap and propose the first practical reverse engineering of AES-128-like custom ciphers, i.e., algorithms that deploy undisclosed SubBytes, ShiftRows and MixColumns functions. By performing a side-channel-assisted differential power analysis, we show that the amount of traces required to fully recover the undisclosed components are relatively small, hence the possibility of a side-channel attack remains as a practical threat. The results apply to both 8-bit and 32-bit architectures and were validated on two common microcontroller platforms.

Significantly extending the framework of (Couteau and Hartmann, Crypto 2020), we propose a general methodology to construct NIZKs for showing that an encrypted vector $\vec{\chi}$ belongs to an algebraic set, i.e., is in the zero locus of an ideal $\mathscr{I}$ of a polynomial ring. In the case where $\mathscr{I}$ is principal, i.e., generated by a single polynomial $F$, we first construct a matrix that is a ``quasideterminantal representation'' of $F$ and then a NIZK argument to show that $F (\vec{\chi}) = 0$. This leads to compact NIZKs for general computational structures, such as polynomial-size algebraic branching programs. We extend the framework to the case where $\IDEAL$ is non-principal, obtaining efficient NIZKs for R1CS, arithmetic constraint satisfaction systems, and thus for $\mathsf{NP}$. As an independent result, we explicitly describe the corresponding language of ciphertexts as an algebraic language, with smaller parameters than in previous constructions that were based on the disjunction of algebraic languages. This results in an efficient GL-SPHF for algebraic branching programs.

The security proofs of leakage-resilient MACs based on symmetric building blocks currently rely on idealized assumptions that hardly translate into interpretable guidelines for the cryptographic engineers implementing these schemes. In this paper, we first present a leakage-resilient MAC that is both efficient and secure under standard and easily interpretable black box and physical assumptions. It only requires a collision resistant hash function and a single call per message authentication to a Tweakable Block Cipher ($\mathsf{TBC}$) that is unpredictable with leakage. This construction leverages two design twists: large tweaks for the $\mathsf{TBC}$ and a verification process that checks the inverse $\mathsf{TBC}$ against a constant. It enjoys beyond birthday security bounds. We then discuss the cost of getting rid of these design twists. We show that security can be proven without them as well. Yet, a construction without large tweaks requires stronger (non idealized) assumptions and may incur performance overheads if specialized $\mathsf{TBC}$s with large tweaks can be exploited, and a construction without twisted verification requires even stronger assumptions (still non idealized) and leads to more involved bounds. The combination of these results makes a case for our first pragmatic construction and suggests the design of $\mathsf{TBC}$s with large tweaks and good properties for side-channel countermeasures as an interesting challenge.

Decentralized finance (DeFi) refers to interoperable smart contracts running on distributed ledgers offering financial services beyond payments. Recently, there has been an explosion of DeFi applications centered on Ethereum, with close to a hundred billion USD in total assets deposited as of September 2021. These applications provide financial services such as asset management, trading, and lending. The wide adoption of DeFi has raised important concerns, and among them is the key issue of privacy---DeFi applications store account balances in the clear, exposing financial positions to public scrutiny. In this work, we propose a framework of anonymous and composable DeFi on public-state smart contract platforms. First, we define a cryptographic primitive called a flexible anonymous transaction (FLAX) system with two distinctive features: (1) transactions authenticate additional information known as ``associated data'' and (2) transactions can be applied flexibly via a parameter that is determined at processing time, e.g. during the execution time of smart contracts. Second, we design an anonymous token standard (extending ERC20), which admits composable usage of anonymous funds by other contracts. Third, we demonstrate how the FLAX token standard can realize privacy-preserving variants of the Ethereum DeFi ecosystem of today---we show contract designs for asset pools, decentralized exchanges, and lending, covering the largest DeFi projects to date including Curve, Uniswap, Dai stablecoin, Aave, Compound, and Yearn. Lastly, we provide formal security definitions for FLAX and describe instantiations from existing designs of anonymous payments such as Zerocash, RingCT, Quisquis, and Zether.

The problem of Byzantine Fault Tolerance (BFT) has received a lot of attention in the last 30 years. The seminal work by Fisher, Lynch, and Paterson (FLP) shows that there does not exist a deterministic BFT protocol in complete asynchronous networks against a single failure. In order to address this challenge, researchers have designed randomized BFT protocols in asynchronous networks and deterministic BFT protocols in partial synchronous networks. For both kinds of protocols, a basic assumption is that there is an adversary that controls at most a threshold number of participating nodes and that has a full control of the message delivery order in the network. Due to the popularity of Proof of Stake (PoS) blockchains in recent years, several BFT protocols have been deployed in the large scale of Internet environment. We analyze several popular BFT protocols such as Capser FFG / CBC-FBC for Ethereum 2.0 and GRANDPA for Polkadot. Our analysis shows that the security models for these BFT protocols are slightly different from the models commonly accepted in the academic literature. For example, we show that, if the adversary has a full control of the message delivery order in the underlying network, then none of the BFT protocols for Ethereum blockchain 2.0 and Polkadot blockchain could achieve liveness even in a synchronized network. Though it is not clear whether a practical adversary could {\em actually} control and re-order the underlying message delivery system (at Internet scale) to mount these attacks, it raises an interesting question on security model gaps between academic BFT protocols and deployed BFT protocols in the Internet scale. With these analysis, this paper proposes a Casper CBC-FBC style binary BFT protocol and shows its security in the traditional academic security model with complete asynchronous networks. Finally, we propose a multi-value BFT protocol XP for complete asynchronous networks and show its security in the traditional academic BFT security model.

A new interpretation of linear cryptanalysis is proposed. This 'geometric approach' unifies all common variants of linear cryptanalysis, reveals links between various properties, and suggests additional generalizations. For example, new insights into invariants corresponding to non-real eigenvalues of correlation matrices and a generalization of the link between zero-correlation and integral attacks are obtained. Geometric intuition leads to a fixed-key motivation for the piling-up principle, which is illustrated by explaining and generalizing previous results relating invariants and linear approximations. Rank-one approximations are proposed to analyze cell-oriented ciphers, and used to resolve an open problem posed by Beierle, Canteaut and Leander at FSE 2019. In particular, it is shown how such approximations can be analyzed automatically using Riemannian optimization.

In this work, we study the Time-Lock Encryption (TLE) cryptographic primitive. The concept of TLE involves a party initiating the encryption of a message that one can only decrypt after a certain amount of time has elapsed. Following the Universal Composability (UC) paradigm introduced by Canetti [IEEE FOCS 2001], we formally abstract the concept of TLE into an ideal functionality. In addition, we provide a standalone definition for secure TLE schemes in a game-based style and we devise a hybrid protocol that relies on such a secure TLE scheme. We show that if the underlying TLE scheme satisfies the standalone game-based security definition, then our hybrid protocol UC realises the TLE functionality in the random oracle model. Finally, we present Astrolabous, a TLE construction that satisfies our security definition, leading to the first UC realization of the TLE functionality. Interestingly, it is hard to prove UC secure any of the TLE construction proposed in the literature. The reason behind this difficulty relates to the UC framework itself. Intuitively, to capture semantic security, no information should be leaked regarding the plaintext in the ideal world, thus the ciphertext should not contain any information relating to the message. On the other hand, all ciphertexts will eventually open, resulting in a trivial distinction of the real from the ideal world in the standard model. We overcome this limitation by extending any secure TLE construction adopting the techniques of Nielsen [CRYPTO 2002] in the random oracle model. Specifically, the description of the extended TLE algorithms includes calls to the random oracle, allowing our simulator to equivocate. This extension can be applied to any TLE algorithm that satisfies our standalone game-based security definition, and in particular to Astrolabous.