We present HAETAE (Hyperball bimodAl modulE rejecTion signAture schemE), a new lattice-based signature scheme. Like the NIST-selected Dilithium signature scheme, HAETAE is based on the Fiat-Shamir with Aborts paradigm, but our design choices target an improved complexity/compactness compromise that is highly relevant for many space-limited application scenarios. We primarily focus on reducing signature and verification key sizes so that signatures fit into one TCP or UDP datagram while preserving a high level of security against a variety of attacks. As a result, our scheme has signature and verification key sizes up to 39% and 25% smaller, respectively, compared than Dilithium. We provide a portable, constant-time reference implementation together with an optimized implementation using AVX2 instructions and an implementation with reduced stack size for the Cortex-M4. Moreover, we describe how to efficiently protect HAETAE against implementation attacks such as side-channel analysis, making it an attractive candidate for use in IoT and other embedded systems.

In the last decade, zero-knowledge proof of knowledge protocols have been extensively studied to achieve active security of various cryptographic protocols. However, the existing solutions simply seek zero-knowledge for both message and randomness, which is an overkill in many applications since protocols may remain secure even if some information about randomness is leaked to the adversary. We develop this idea to improve the state-of-the-art proof of knowledge protocols for RLWE-based public-key encryption and BDLOP commitment schemes. In a nutshell, we present new proof of knowledge protocols without using noise flooding or rejection sampling which are provably secure under a computational hardness assumption, called Hint-MLWE. We also show an efficient reduction from Hint-MLWE to the standard MLWE assumption. Our approach enjoys the best of two worlds because it has no computational overhead from repetition (abort) and achieves a polynomial overhead between the honest and proven languages. We prove this claim by demonstrating concrete parameters and compare with previous results. Finally, we explain how our idea can be further applied to other proof of knowledge providing advanced functionality.

This paper introduces CLAASP, a Cryptographic Library for the Automated Analysis of Symmetric Primitives. The library is designed to be modular, extendable, easy to use, generic, efficient and fully automated. It is an extensive toolbox gathering state-of-the-art techniques aimed at simplifying the manual tasks of symmetric primitive designers and analysts. CLAASP is built on top of Sagemath and is open-source under the GPLv3 license. The central input of CLAASP is the description of a cryptographic primitive as a list of connected components in the form of a directed acyclic graph. From this representation, the library can automatically: (1) generate the Python or C code of the primitive evaluation function, (2) execute a wide range of statistical and avalanche tests on the primitive, (3) generate SAT, SMT, CP and MILP models to search, for example, differential and linear trails, (4) measure algebraic properties of the primitive, (5) test neural-based distinguishers. In this work, we also present a comprehensive survey and comparison of other software libraries aiming at similar goals as CLAASP.

The graphs ${\cal G}_F=\{(x,F(x)); x\in \mathbb{F}_2^n\}$ of those $(n,n)$-functions $F:\mathbb{F}_2^n\mapsto \mathbb{F}_2^n$ that are almost perfect nonlinear (in brief, APN; an important notion in symmetric cryptography) are, equivalently to their original definition by K. Nyberg, those Sidon sets (an important notion in combinatorics) $S$ in $({\Bbb F}_2^n\times {\Bbb F}_2^n,+)$ such that, for every $x\in {\Bbb F}_2^n$, there exists a unique $y\in {\Bbb F}_2^n$ such that $(x,y)\in S$. Any subset of a Sidon set being a Sidon set, an important question is to determine which Sidon sets are maximal relatively to the order of inclusion. In this paper, we study whether the graphs of APN functions are maximal (that is, optimal) Sidon sets. We show that this question is related to the problem of the existence / non-existence of pairs of APN functions lying at distance 1 from each others, and to the related problem of the existence of APN functions of algebraic degree $n$. We revisit the conjectures that have been made on these latter problems.

Accumulation is a simple yet powerful primitive that enables incrementally verifiable computation (IVC) without the need for recursive SNARKs. We provide a generic, efficient accumulation (or folding) scheme for any $(2k-1)$-move special-sound protocol with a verifier that checks $\ell$ degree-$d$ equations. The accumulation verifier only performs $k+2$ elliptic curve multiplications and $k+d+O(1)$ field/hash operations. Using the compiler from BCLMS21 (Crypto 21), this enables building efficient IVC schemes where the recursive circuit only depends on the number of rounds and the verifier degree of the underlying special-sound protocol but not the proof size or the verifier time. We use our generic accumulation compiler to build ProtoStar. ProtoStar is a non-uniform IVC scheme for Plonk that supports high-degree gates and (vector) lookups. The recursive circuit is dominated by $3$ group scalar multiplications and a hash of $d^*$ field elements, where $d^*$ is the degree of the highest gate. The scheme does not require a trusted setup or pairings, and the prover does not need to compute any FFTs. The prover in each accumulation/IVC step is also only logarithmic in the number of supported circuits and independent of the table size in the lookup.

The enumeration of all outputs of a given multivariate polynomial is a fundamental mathematical problem and is incorporated in some algebraic attacks on multivariate public key cryptosystems. For a degree-$d$ polynomial in $n$ variables over the finite field with $q$ elements, solving the enumeration problem classically requires $O\left(\tbinom{n+d}{d} \cdot q^n\right)$ operations. At CHES 2010, Bouillaguet et al. proposed a fast enumeration algorithm over the binary field $\mathbb{F}_2$. Their proposed algorithm covers all the inputs of a given polynomial following the order of Gray codes and is completed by $O(d\cdot2^n)$ bit operations. However, to the best of our knowledge, a result achieving the equivalent efficiency in general finite fields is yet to be proposed. In this study, we propose a novel algorithm that enumerates all the outputs of a degree-$d$ polynomial in $n$ variables over $\mathbb{F}_q$ with a prime number $q$ by $O(d\cdot q^n)$ operations. The proposed algorithm is constructed by using a lexicographic order instead of Gray codes to cover all the inputs. This result can be seen as an extension of the result of Bouillaguet et al. to general finite fields and is almost optimal in terms of time complexity. We can naturally apply the proposed algorithm to the case where $q$ is a prime power. Notably, our enumeration algorithm differs from the algorithm by Bouillaguet et al. even in the case of $q=2$.

The magic of Fully Homomorphic Encryption (FHE) is that it allows operations on encrypted data without decryption. Unfortunately, the slow computation time limits their adoption. The slow computation time results from the vast memory requirements (64Kbits per ciphertext), a bootstrapping key of 1.3 GB, and sizeable computational overhead (10240 NTTs, each NTT requiring 5120 32-bit multiplications). We accelerate the FHEW bootstrapping in hardware on a high-end U280 FPGA. To reduce the computational complexity, we propose a fast hardware NTT architecture modified from with support for negatively wrapped convolution. The IP module includes large I/O ports to the NTT accelerator and an index bit-reversal block. The total architecture requires less than 225000 LUTs and 1280 DSPs. Assuming that a fast interface to the FHEW bootstrapping key is available, the execution speed of FHEW bootstrapping can increase by at least 7.5 times.

In this paper, we show an in-place implementation of the ASCON linear layer. An in-place implementation is important in the context of quantum computing, we expect our work will be useful in quantum implementation of ASCON. In order to get the implementation, we first write the ASCON linear layer as a binary matrix; then apply two legacy algorithms (Gauss-Jordan elimination and PLU factorization) as well as our modified version of Xiang et al.'s algorithm/source-code (published in ToSC/FSE'20). Our in-place implementation takes 1595 CNOT gates and 119 quantum depth; and this is the first in-place implementation of the ASCON linear layer, to the best of our knowledge.

We propose a new cryptographic primitive called "verifiably encrypted threshold key derivation" (vetKD) that extends identity-based encryption with a decentralized way of deriving decryption keys. We show how vetKD can be leveraged on modern blockchains to build scalable decentralized applications (or "dapps") for a variety of purposes, including preventing front-running attacks on decentralized finance (DeFi) platforms, end-to-end encryption for decentralized messaging and social networks (SocialFi), cross-chain bridges, as well as advanced cryptographic primitives such as witness encryption and one-time programs that previously could only be built from secure hardware or using a trusted third party. And all of that by secret-sharing just a single secret key...

In a Multi-Client Functional Encryption (MCFE) scheme, $n$ clients each obtain a secret encryption key from a trusted authority. During each time step $t$, each client $i$ can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function $f$, and the functional key can be applied to a collection of $n$ clients’ ciphertexts encrypted to the same time step, resulting in the outcome of $f$ on the clients’ data. In this paper, we focus on MCFE for inner-product computations. If an MCFE scheme hides not only the clients’ data, but also the function $f$, we say it is function hiding. Although MCFE for inner-product computation has been extensively studied, how to achieve function privacy is still poorly understood. The very recent work of Agrawal et al. showed how to construct a function-hiding MCFE scheme for inner-product assuming standard bilinear group assumptions; however, they assume the existence of a random oracle and prove only a relaxed, selective security notion. An intriguing open question is whether we can achieve function-hiding MCFE for inner-product without random oracles. In this work, we are the first to show a function-hiding MCFE scheme for inner products, relying on standard bilinear group assumptions. Further, we prove adaptive security without the use of a random oracle. Our scheme also achieves succinct ciphertexts, that is, each coordinate in the plaintext vector encrypts to only $O(1$) group elements. Our main technical contribution is a new upgrade from single-input functional encryption for inner-products to a multi-client one. Our upgrade preserves function privacy, that is, if the original single-input scheme is function-hiding, so is the resulting multi-client construction. Further, this new upgrade allows us to obtain a conceptually simple construction.

The Meet-in-the-Middle (MITM) attack is one of the most powerful cryptanalysis techniques, as seen by its use in preimage attacks on MD4, MD5, Tiger, HAVAL, and Haraka-512 v2 hash functions and key recovery for full-round KTANTAN. An efficient approach to constructing MITM attacks is automation, which refers to modeling MITM characteristics and objectives into constraints and using optimizers to search for the best attack configuration. This work focuses on the simplification and renovation of the most advanced superposition framework based on Mixed-Integer Linear Programming (MILP) proposed at CRYPTO 2022. With the refined automation model, this work provides the first comprehensive analysis of the preimage security of hash functions based on all versions of the Rijndael block cipher, the origin of the Advanced Encryption Standard (AES), and improves the best-known results. Specifically, this work has extended the attack rounds of Rijndael 256-192 and 256-256, reduced the attack complexity of Rijndael 256-128 and 128-192 (AES192), and filled the gap of preimage security evaluation on Rijndael versions with a block size of 192 bits.

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security). While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security. We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of $n$-party access structures to $1.5^{n+o(n)}$, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in $\mathsf{P}$ and $\mathsf{NP}$.

SPEEDY is a family of ultra-lightweight block ciphers designed by Leander et al. at CHES 2021. There are three recommended variants denoted as SPEEDY-$r$-192 with $r$∈{5,6,7}. All of them support the 192-bit block and the 192-bit key. The main focus during its design is to ensure hardware-aware low latency, thus, whether it is designed to have enough security is worth to be studied. Recently, the full-round security of SPEEDY-7-192 is announced to be broken by Boura et al. at EUROCRYPT 2023 under the chosen-ciphertext setting, where a round-reduced attack on SPEEDY-6-192 is also proposed. However, no valid attack on SPEEDY-5-192 is given due to its more restricted security parameters. Up to now, the best key recovery attack on this variant only covers 3 rounds proposed by Rohit et al. at AFRICACRYPT 2022. In this paper, we give three full-round attacks on SPEEDY-7-192. Using the divide-and-conquer strategy and other new proposed techniques, we found a 5.5-round differential distinguisher which can be used to mount the first chosen-plaintext full-round key recovery attack. With a similar strategy, we also found a 5-round linear distinguisher which leads to the first full-round attack under the known-plaintext setting. Meanwhile, the 5.5-round differential distinguisher also helps us slightly improve the full-round attack in the chosen-ciphertext setting compared with the previous result. Besides, we also present a 4-round differential attack on SPEEDY-5-192, which is the best attack on this variant in terms of the number of rounds so far. A faster key recovery attack covering the same rounds is also given using a differential-linear distinguisher. Both attacks cannot threaten the full round security of SPEEDY-5-192.

In this paper, we provide experimental evidence for the benefits of multi-task learning in the context of masked AES implementations (via the ASCADv1-r and ASCADv2 databases). We develop an approach for comparing single-task and multi-task approaches rather than comparing specific resulting models: we do this by training many models with random hyperparameters (instead of comparing a few highly tuned models). We find that multi-task learning has significant practical advantages that make it an attractive option in the context of device evaluations: the multi-task approach leads to performant networks quickly in particular in situations where knowledge of internal randomness is not available during training.

Distributed integrated circuit (IC) supply chain has resulted in a myriad of security vulnerabilities including that of hardware Trojan (HT). An HT can perform malicious modifications on an IC design with potentially disastrous consequences, such as leaking secret information in cryptographic applications or altering operation instructions in processors. Due to the emergence of outsourced fabrication, an untrusted foundry is considered the most potent adversary in introducing an HT. This can be attributed to the asymmetric business model between the design house and the foundry; the design house is completely oblivious to the fabrication process, whereas the design IP is transparent to the foundry, thereby having full control over the layout. In order to address this issue, in this paper, we—for the first time—introduce a layout-level HT detection algorithm utilizing low-confidence classification and providing Trojan localization. We convert the IC layout to a graph and utilize Graph Neural Network (GNN)-based learning frameworks to flag any unrecognized suspicious region in the layout. The proposed framework is evaluated on AES and RS232 designs from the Trusthub benchmark suite, where it has been demonstrated to detect all nine HT-inserted designs. Finally, we open-source the full code-base for the research community at large.

In this paper, we propose the first linear two-party secure-computation private set intersection (PSI) protocol, in the semi-honest adversary model, computing the following functionality. One of the parties ($P_X$) inputs a set of items $X = \{x_j \mid 1 \le j \le n_X\}$, whereas the other party ($P_Y$) inputs a set of items $Y = \{y_i \mid 1\le i \le n_Y \}$ and a set of corresponding data pairs $D_Y = \{ (d_i^0,d_i^1) \mid 1 \le i \le n_Y\}$ having the same cardinality with $Y$. While $P_Y$ outputs nothing, $P_X$ outputs a set of data $D_X = \{ d_i^{b_i} \mid b_i = 1 \text{ if } y_i \in X, b_i = 0 \text{ otherwise}\}$. This functionality is generally required when the PSI protocol is used as a part of a larger secure two-party computation such as threshold PSI or any function of the intersection in general. In literature, there are linear circuit and secure-computation PSI proposals, such as Pinkas et al. PSI protocol (Eurocrypt 2019), our PSI protocol (CANS 2020) and Chandran et al. PSI protocol (PETS 2022), for similar functionalities but having a cuckoo table mapping in the functionality, which complicates the application of different secure computation techniques on top of the output of the PSI protocol. We also show that the idea in the construction of our secure-computation PSI protocol having the functionality mentioned above can be utilized to convert the existing circuit PSI and secure-computation PSI protocols into the protocols realizing the functionality not having the cuckoo table mapping. We provide this conversion method as a separate protocol, which is one of the main contributions of this work. While creating the protocol, as a side contribution, we provide a one-time batch oblivious programmable pseudo-random function based on garbled Bloom filters.

Online auctions have a steadily growing market size, creating billions of US dollars in sales value every year. To ensure fairness and auditability while preserving the bidder's privacy is the main challenge of an auction scheme. At the same time, utility driven blockchain technology is picking up the pace, offering transparency and data integrity to many applications. In this paper, we present a blockchain-based first price sealed-bid auction scheme. Our scheme offers privacy and public verifiability. It can be built on any public blockchain, which is leveraged to provide transparency, data integrity, and hence auditability. The inability to double spend on a blockchain is used to prevent bid replay attacks. Moreover, our scheme can achieve non-repudiation for both bidders and the auctioneer without revealing the bids and we encapsulate this concept inside the public verification of the auction. We propose to use ElGamal encryption and Bulletproofs to construct an efficient instantiation of our scheme. We also propose to use recursive zkSNARKs to reduce the number of comparison proofs from $N-1$ to $1$, where $N$ is the number of bidders.

This paper analyses the security of the so-called Milenage construction, developed by ETSI SAGE, when it is based on a non-one-to-one pseudo-random function (PRF) rather than a one-to-one pseudo-random permutation (PRP). It is shown that Milenage based on an $n$-bit random function and producing $t$ $n$-bit outputs, is indistinguishable from a random $tn$-bit function up to $q = O(2^{n/2}/t)$ queries. We also extend the existing security proof for PRP-based Milenage due to Gilbert by generalising the model and incorporating the Milenage message authentication function in the proof.

ChatGPT, which emerged at the end of 2022, has gained significant attention as a highly advanced conversational artificial intelligence service. Developed by OpenAI, ChatGPT is a natural language processing model. There are instances where individuals might want to attempt programming using ChatGPT. In this paper, we utilized the ChatGPT to implement a cryptographic algorithms. Despite numerous trial and error efforts, it was possible to implement cryptography through ChatGPT. This implies that even without extensive coding skill or programming knowledge, one can implement cryptography through ChatGPT if they understand the cryptographic structure. However, the ability to analyze the source code is essential, as it is necessary to identify incorrect parts within the implemented code.

Proof-of-stake systems require stakers to lock up their funds in order to participate in consensus validation. This leads to capital inefficiency, as locked capital cannot be invested in Decentralized Finance (DeFi). Liquid staking rewards stakers with fungible tokens in return for staking their assets. These fungible tokens can in turn be reused in the DeFi economy. However, liquid staking introduces unexpected risks, as all delegated stake is now fungible. This exacerbates the already existing Principal–Agent problem faced during any delegation, in which the interests of the delegator (the Principal) are not aligned with the interests of the validator (the Agent). In this paper, we study the Principal–Agent problem in the context of liquid staking. We highlight the dilemma between the choice of proportional representation (having one's stake delegated to one's validator of choice) and fair punishment (being economically affected only when one's choice is misinformed). We put forth an attack illustrating that these two notions are fundamentally incompatible in an adversarial setting. We then describe the mechanism of exempt delegations, used by some staking systems today, and devise a precise formula for quantifying the correct choice of exempt delegation which allows balancing the two conflicting virtues in the rational model.

We conduct a systematic examination of vector arithmetic for polynomial multiplications in software. Vector instruction sets and extensions typically specify a fixed number of registers, each holding a power-of-two number of bits, and support a wide variety of vector arithmetic on registers. Programmers then try to align mathematical computations with the vector arithmetic supported by the designated instruction set or extension. We delve into the intricacies of this process for polynomial multiplications. In particular, we introduce “vectorization- friendliness” and “permutation-friendliness”, and review “Toeplitz matrix- vector product” to systematically identify suitable mappings from homo- morphisms to vectorized implementations. To illustrate how the formalization works, we detail the vectorization of polynomial multiplication in $\mathbb{Z}_{4591}[x]/\left\langle x^{761} − x − 1 \right\rangle$ used in the parameter set sntrup761 of the NTRU Prime key encapsulation mechanism. For practical evaluation, we implement vectorized polynomial multipliers for the ring $\mathbb{Z}_{4591}[x]/\left\langle \Phi_{17} (x^{96}) \right\rangle$ with AVX2 and Neon. We benchmark our AVX2 implementation on Haswell and Skylake and our Neon implementation on Cortex-A72 and the “Firestorm” core of Apple M1 Pro. Our AVX2-optimized implementation is 1.99−2.16 times faster than the state-of-the-art AVX2-optimized implementation by [Bernstein, Brum- ley, Chen, and Tuveri, USENIX Security 2022] on Haswell and Skylake, and our Neon-optimized implementation is 1.29−1.36 times faster than the state-of-the-art Neon-optimized implementation by [Hwang, Liu, and Yang, ACNS 2024] on Cortex-A72 and Apple M1 Pro. For the overall scheme with AVX2, we reduce the batch key generation cycles (amortized with batch size 32) by 7.9%−12.0%, encapsulation cycles by 7.1%−10.3%, and decapsulation cycles by 10.7%−13.3% on Haswell and Skylake. For the overall performance with Neon, we reduce the encapsulation cycles by 3.0%−6.6% and decapsulation cycles by 12.8%−15.1% on Cortex-A72 and Apple M1 Pro.

This note introduces a public-key variant of TFHE. The output ciphertexts are of LWE type. Interestingly, the public key is shorter and the resulting ciphertexts are less noisy. The security of the scheme holds under the standard RLWE assumption. Several variations and extensions are also described.

We propose a secure multiparty signing protocol for the BBS+ signature scheme; in other words, an anonymous credential scheme with threshold issuance. We prove that due to the structure of the BBS+ signature, simply verifying the signature produced by an otherwise semi-honest protocol is sufficient to achieve composable security against a malicious adversary. Consequently, our protocol is extremely simple and efficient: it involves a single request from the client (who requires a signature) to the signing parties, two exchanges of messages among the signing parties, and finally a response to the client; in some deployment scenarios the concrete cost bottleneck may be the client's local verification of the signature that it receives. Furthermore, our protocol can be extended to support the strongest form of blind signing and to serve as a distributed evaluation protocol for the Dodis-Yampolskiy Oblivious VRF. We validate our efficiency claims by implementing and benchmarking our protocol.

In this paper we introduce a novel version of the Joye-Libert cryptosystem that allows users to decrypt without knowing the factorisation of the composite modulus. Then we use our construction as a building block for a threshold decryption protocol of the homomorphic Joye-Libert encryption scheme. Finally, we present several extensions of the threshold cryptosystem.

The Brakerski/Fan-Vercauteren (BFV) scheme is a state-of-the-art scheme in Fully Homomorphic Encryption based on the Ring Learning with Errors (RLWE) problem. Thus, ciphertexts contain an error that increases with each homomorphic operation and has to stay below a certain threshold for correctness. This can be achieved by setting the ciphertext modulus big enough. On the other hand, a larger ciphertext modulus decreases the level of security and computational efficiency, making parameter selection challenging. Our work aims to improve the bound on the ciphertext modulus, minimizing it. Our main contributions are the following. Primarily, we perform the first average-case analysis of the error growth for the BFV scheme, significantly improving its estimation. For a circuit with a multiplicative depth of only 5, our bounds are up to 25.2 bits tighter than previous analyses and within 1.2 bits of the experimentally observed values. % Secondly, we give a general way to bound the ciphertext modulus for correct decryption that allows closed formulas. % Finally, we use our theoretical advances and propose the first parameter generation tool for the BFV scheme. Here, we add support for arbitrary but use-case-specific circuits, as well as the ability to generate easy-to-use code snippets, making our theoretical work accessible to both researchers and practitioners.

In this paper we formally introduce a novel mode of operation based on the cipher block chaining mode. The main idea of this mode is to use a stateful block cipher instead of a stateless one. Afterwards, we show how to implement our proposal and present a performance analysis of our mode. Next, we provide a concrete security analysis by computing a tight bound on the success of adversaries based on their resources. The results of our performance and security analyses are that this novel mode is more secure than the cipher block chaining mode for large files, but the encryption/decryption time doubles/triples. Therefore, our novel mode is suitable for encrypting large files, when higher security is required, but speed is not paramount. Note that the changes required to transform the software implementations of the cipher block chaining mode into this new mode are minimal, and therefore transitioning to this new mode is straightforward.

Threshold signatures protect the signing key by sharing it among a group of signers so that an adversary must corrupt a threshold number of signers to be able to forge signatures. Existing threshold signatures with succinct signatures and constant verification times do not work if signers have different weights. Such weighted settings are seeing increasing importance in decentralized systems, especially in the Proof-of-Stake blockchains. This paper presents a new paradigm for threshold signatures for pairing- and discrete logarithm-based cryptosystems. Our scheme has a compact verification key consisting of only 7 group elements, and a signature consisting of 8 group elements. Verifying the signature requires 1 exponentiation and 13 bilinear pairings. Our scheme supports arbitrary weight distributions among signers and arbitrary thresholds. It requires non-interactive preprocessing after a universal powers-of-tau setup. We prove the security of our scheme in the Algebraic Group Model and implement it using golang. Our evaluation shows that our scheme achieves a comparable signature size and verification time to a standard (unweighted) threshold signature. Compared to existing multisignature schemes, our scheme has a much smaller public verification key.

In a vertical federated learning (VFL) system consisting of a central server and many distributed clients, the training data are vertically partitioned such that different features are privately stored on different clients. The problem of split VFL is to train a model split between the server and the clients. This paper aims to address two major challenges in split VFL: 1) performance degradation due to straggling clients during training; and 2) data and model privacy leakage from clients’ uploaded data embeddings. We propose FedVS to simultaneously address these two challenges. The key idea of FedVS is to design secret sharing schemes for the local data and models, such that information-theoretical privacy against colluding clients and curious server is guaranteed, and the aggregation of all clients’ embeddings is reconstructed losslessly, via decrypting computation shares from the non- straggling clients. Extensive experiments on various types of VFL datasets (including tabular, CV, and multi-view) demonstrate the universal advantages of FedVS in straggler mitigation and privacy protection over baseline protocols.

Modular arithmetic used for cryptography includes modular adding, modular subtracting, modular multiplying, modular inverting, modular exponentiating etc. In this paper, the authors well analyze the bit complexity of a bitwise modular operation and the time complexity of a non-bitwise modular operation. Besides discuss the clock cycles for one bytewise modular operation utilizing directives from the ATmel 8-bit AVR instruction set. Last, reveal that the ratio of derivate numbers of clock cycles for two modular operations under different modulus lengths is almost a constant.

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group action-based cryptography: we show that each finite group defines a group action relative to the semidirect product of the group by its automorphism group, and give security bounds on the resulting signature scheme in terms of the group-theoretic computational problem known as the Semidirect Discrete Logarithm Problem (SDLP). Crucially, we make progress towards being able to efficiently compute the novel group action, and give an example of a parameterised family of groups for which the group action can be computed for any parameters, thereby negating the need for expensive offline computation or inclusion of redundancy required in other schemes of this type.

Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.

In today’s interconnected world, data has become a valuable asset, leading to a growing interest in protecting it through techniques such as privacy-preserving computation. Two well-known approaches are multi-party computation and homomorphic encryption with use cases such as privacy-preserving machine learning evaluating or training neural networks. For multi-party computation, one of the fundamental arithmetic operations is the secure multiplication in the malicious security model and by extension the multiplication of matrices which is expensive to compute in the malicious model. Transferring the problem of secure matrix multiplication to the homomorphic domain enables savings in communication complexity, reducing the main bottleneck. In this work, we implement and optimize the homomorphic generation of matrix triples. We provide an open-source implementation for the leveled BGV (Brakerski Gentry Vaikuntanathan) scheme supporting plaintext moduli of arbitrary size using state-of-the-art implementation techniques. We also provide a new, use-case specific approach to parameter generation for leveled BGV-like schemes heuristically optimizing for computation time and taking into account architecture-specific constraints. Finally, we provide an in-depth analysis of the homomorphic circuit enabling the re-use of key switching keys and eliminating constant multiplications, combining our results in an implementation to generate homomorphic matrix triples for arbitrary plaintext moduli. Our implementation is publicly available and up to $2.1\times$ faster compared to previous work while also providing new time-memory trade-offs for different computing environments. Furthermore, we implement and evaluate additional, use-case specific optimization opportunities such as matrix slicing for the matrix triple generation.

This paper presents a dynamic, real-time approach to detecting anomalous blockchain transactions. The proposed tool, BlockGPT, generates tracing representations of blockchain activity and trains from scratch a large language model to act as a real-time Intrusion Detection System. Unlike traditional methods, BlockGPT is designed to offer an unrestricted search space and does not rely on predefined rules or patterns, enabling it to detect a broader range of anomalies. We demonstrate the effectiveness of BlockGPT through its use as an anomaly detection tool for Ethereum transactions. In our experiments, it effectively identifies abnormal transactions among a dataset of 68M transactions and has a batched throughput of 2284 trans- actions per second on average. Our results show that, BlockGPT identifies abnormal transactions by ranking 49 out of 124 attacks among the top-3 most abnormal transactions interacting with their victim contracts. This work makes contributions to the field of blockchain transaction analysis by introducing a custom data encoding compatible with the transformer architecture, a domain-specific tokenization technique, and a tree encoding method specifically crafted for the Ethereum Virtual Machine (EVM) trace representation.

Public-key encryption with keyword search (PEKS) was first proposed by Boneh et al. (EUROCRYPT 2004), achieving the ability to search for ciphertext files. Nevertheless, it is vulnerable to inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search (PAEKS), introduced by Huang et al. (Inf. Sci. 2017), on the other hand, is secure against IKGA. Nonetheless, it is susceptible to quantum computing attacks. Liu et al. and Cheng et al. addressed this problem by reducing to the lattice hardness (AsiaCCS 2022, ESORICS 2022). Furthermore, several scholars pointed out that the threat of secret key exposure delegates a severe and realistic concern, potentially leading to privacy disclosure (EUROCRYPT 2003, Compt. J. 2022). As a result, research focusing on mitigating key exposure and resisting quantum attacks for the PAEKS primitive is far-reaching. In this work, we present the first generic construction and instantiation of forward-secure PAEKS primitive based on lattice hardness without trusted authorities, mitigating the secret key exposure while ensuring quantum-safe properties. We extend the scheme of Liu et al. (AsiaCCS 2022), and formalize a novel post-quantum PAEKS construction, namely FS-PAEKS. To begin with, we introduce the binary tree structure to represent the time periods, along with a lattice basis extension algorithm, and SamplePre algorithm to obtain the post-quantum one-way secret key evolution, allowing users to update their secret keys periodically. Furthermore, our scheme is proven to be IND-CKA and IND-IKGA secure in a quantum setting. In addition, we also compare the security of our primitive in terms of computational complexity and communication overhead with other top-tier schemes. Ultimately, we demonstrate two potential applications of FS-PAEKS.

Authenticated Encryption (AE) achieves privacy and authenticity with a single scheme. It is possible to obtain an AE scheme gluing together an encryption scheme (privacy secure) and a Message Authentication Code (authenticity secure). This approach is called generic composition and its security has been studied by Namprempre et al. [NRS14]. They looked into all the possible gluings of an encryption scheme with a secure MAC to obtain a nonce-based AE-scheme. The encryption scheme is either IV-based (that is, with an additional random input, the initialization vector [IV]) or nonce-based (with an input to be used once, the nonce). Nampremepre et al. assessed the security/insecurity of all possible composition combinations except for 4 (N4, A10, A11 and A12). Berti et al. [BPP18a] showed that N4 is insecure and that the remaining modes (A10, A11, and A12) are either all secure or insecure. Here, we prove that these modes are all insecure with a counterexample.

The estimation of the computational complexity of hard problems is essential for determining secure parameters for cryptographic systems. To date, those estimations are often performed in an ad-hoc manner. This led to a scattered landscape of available estimation scripts, with multiple scripts for the same problem with varying outputs. Overall, this complicates the task of reaching consensus on the hardness of cryptographic problems. Furthermore, for designers it makes it difficult to gather precise information on the concrete difficulty of the underlying problems. Especially in the light of the still ongoing NIST PQC standardization effort and the upcoming call for post-quantum secure digital signature schemes there is a pressing need for a reliable point of access for concrete security estimates. In this work we present the first open-source software library entirely dedicated to cryptographic hardness estimation, the $\texttt{CryptographicEstimators}$ library. In contrast to most previous estimators, this library follows a modern object-oriented software architecture, which provides a wide variety of features. Overall the design is optimized to ease extending existing estimators by new algorithms and makes it simple to integrate completely new estimators. In this work we further specify the algorithmic cost model underlying the estimators. In order to provide a starting point for the project, we gathered and integrated estimators for six different hardness assumptions, including the syndrome decoding problem, the multivariate quadratic problem, the code equivalence problem, the permuted kernel problem and different flavors thereof. In our effort of gathering those estimation scripts, we also normalized those estimates to fit into the cost model and to measure the same unit operations.

Wave is a provably EUF-CMA (existential unforgeability under adaptive chosen message attacks) digital signature scheme based on codes \cite{DST19a}. It is an hash-and-sign primitive and its security is built according to a GPV-like framework \cite{GPV08} under two assumptions related to coding theory: (i) the hardness of finding a word of prescribed Hamming weight and prescribed syndrome, and (ii) the pseudo-randomness of ternary generalized $(U|U+V)$ codes. Forgery attacks (i)---or message attacks---consist in solving the ternary decoding problem for large weight \cite{BCDL19}, while, to the best of our knowledge, key attacks (ii) will try to exhibit words that are characteristic of $(U|U+V)$ codes, which are called type-U or type-V codewords in the present paper. In the current state-of-the-art, the best known attacks both reduce to various flavours of Information Set Decoding (ISD) algorithms for different regime of parameters. In this paper we give estimates for the complexities of the best known ISD variants for those regimes. Maximizing the computational effort, thus the security, for both attacks lead to conflicting constraints on the parameters. We provide here a methodology to derive optimal trade-offs for selecting parameters for the Wave signature scheme achieving a given security. We apply this methodology to the current state-of-the-art and propose some effective parameters for Wave. For $\lambda=128$ bits of classical security, the signature is $737$ bytes long, scaling linearly with the security, and the public key size is $3.6$ Mbytes, scaling quadratically with the security.

Proof-carrying data (PCD) is a powerful cryptographic primitive that allows mutually distrustful parties to perform distributed computation in an efficiently verifiable manner. Known constructions of PCD are obtained by recursively-composing SNARKs or related primitives. SNARKs with desirable properties such as transparent setup are constructed in the random oracle model. However, using such SNARKs to construct PCD requires heuristically instantiating the oracle and using it in a non-black-box way. Chen, Chiesa and Spooner (EC'22) constructed SNARKs in the low-degree random oracle model, circumventing this issue, but instantiating their model in the real world appears difficult. In this paper, we introduce a new model: the arithmetized random oracle model (AROM). We provide a plausible standard-model (software-only) instantiation of the AROM, and we construct PCD in the AROM, given only a standard-model collision-resistant hash function. Furthermore, our PCD construction is for arbitrary-depth compliance predicates. We obtain our PCD construction by showing how to construct SNARKs in the AROM for computations that query the oracle, given an accumulation scheme for oracle queries in the AROM. We then construct such an accumulation scheme for the AROM. We give an efficient "lazy sampling" algorithm (an emulator) for the ARO up to some error. Our emulator enables us to prove the security of cryptographic constructs in the AROM and that zkSNARKs in the ROM also satisfy zero-knowledge in the AROM. The algorithm is non-trivial, and relies on results in algebraic query complexity and the combinatorial nullstellensatz.

Verifiable Computation (VC) schemes provide a mechanism for verifying the output of a remotely executed program. These are used to support computing paradigms wherein a computationally restricted client, the Verifier, wishes to delegate work to a more powerful but untrusted server, the Prover. The Verifier wishes to detect any incorrect results, be they accidental or malicious. The current state-of-the-art is only close-to-practical, usually because of a computationally demanding setup which must be amortised across repeat executions. We present a VC scheme for verifying the output of arithmetic circuits with a small one-time setup, KGen, independent of the size of the circuit being verified, and a insignificantly small constant program specific setup, ProbGen. To our knowledge our VC scheme is the first built from the hardness of integer factoring, a standard cryptographic assumption. Our scheme has the added novelty that the proofs are simply the raw output of the target computation, and the Prover is in effect blind to the fact they are taking part in a VC scheme at all. Although our scheme has worse asymptotic performance than the state-of-the-art it is particularly well suited for verifying one-shot programs and the output of large integer polynomial evaluation.

Fair Exchange (FE) protocols are a class of cryptographic protocol in which two parties, X and Y , exchange some secret data, where the ability of each party to receive secret data is contingent on having sent secret data of their own. When exchanging secret data without the support of FE protocols, whoever sends their secret first makes themselves vulnerable to the possibility that the other participant will cheat and won’t send their secret in return. It is widely believed that FE protocols satisfying the soundness notion of Strong Fairness require a third party arbitrator trusted by both X and Y , however in this paper we construct an FE scheme satisfying a notion of Strong Fairness with no third party involvement. This is achieved by embracing nondeterminism and slightly relaxing the definitions of security from the perfect to the computational domain. The protocol presented in this paper allows two parties running interactive processes to exchange secrets, safe in the knowledge that either both secrets will change hands, or neither will, without the involvement of a trusted third party. The security of the protocol presented in this work reduces to the strength of an underlying symmetric authenticated encryption scheme.

Conflict-free Replicated Data Types (CRDTs) are a very popular class of distributed data structures that strike a compromise between strong and eventual consistency. Ensuring the protection of data stored within a CRDT, however, cannot be done trivially using standard encryption techniques, as secure CRDT protocols would require replica-side computation. This paper proposes an approach to lift general-purpose implementations of CRDTs to secure variants using secure multiparty computation (MPC). Each replica within the system is realized by a group of MPC parties that compute its functionality. Our results include: i) an extension of current formal models used for reasoning over the security of CRDT solutions to the MPC setting; ii) a MPC language and type system to enable the construction of secure versions of CRDTs and; iii) a proof of security that relates the security of CRDT constructions designed under said semantics to the underlying MPC library. We provide an open-source system implementation with an extensive evaluation, which compares different designs with their baseline throughput and latency.

Despite offering numerous advantages, public decentralized cryptocurrencies such as Bitcoin suffer from scalability issues such as high transaction latency and low throughput. The vast array of so-called Layer-2 solutions tackling the scalability problem focus on throughput, and consider latency as a secondary objective. However, in the context of retail payments, instant finality of transactions is arguably a more pressing concern, besides the overarching concern for privacy. In this paper, we provide an overlay network that allows privacy-friendly low latency payments in a retail market. Our approach follows that of a recent work called Snappy, which achieved low latency but exposed identities of customers and their transaction histories. Our construction ensures this data is kept private, while providing merchants with protection against double-spending attacks. Although our system is still based upon customers registering with a collateral, crucially this collateral is reusable over time. The technical novelty of our work comes from randomness-reusable threshold encryption (RRTE), a cryptographic primitive we designed specifically for the following features: our construction provably guarantees payments to merchants, preserves the secret identity of honest customers and prevents their transactions from being linked. We also present an implementation of our construction, showing its capacity for fast global payments in a retail setting with a delay of less than 1 second.

The original NTRU cryptosystem from 1998 can be considered the starting point of the great success story of lattice-based cryptography. Modern NTRU versions like NTRU-HPS and NTRU-HRSS are round-3 finalists in NIST's selection process, and also Crystals-Kyber and especially Falcon are heavily influenced by NTRU. Coppersmith and Shamir proposed to attack NTRU via lattice basis reduction, and variations of the Coppersmith-Shamir lattice have been successfully applied to solve official NTRU challenges by Security Innovations, Inc. up to dimension $n=173$. In our work, we provide the tools to attack modern NTRU versions, both by the design of a proper lattice basis, as well as by tuning the modern BKZ with lattice sieving algorithm from the G6K library to NTRU needs. Let $n$ be prime, $\Phi_n := (X^n-1)/(X-1)$, and let $\mathbb{Z}_q[X]/(\Phi_n)$ be the cyclotomic ring. As opposed to the common belief, we show that switching from the Coppersmith-Shamir lattice to a basis for the cyclotomic ring provides benefits. To this end, we slightly enhance the LWE with Hints framework by Dachman-Soled, Ducas, Gong, Rossi with the concept of projections against almost-parallel hints. Using our new lattice bases, we set the first cryptanalysis landmarks for NTRU-HPS with $n \in [101,171]$ and for NTRU-HRSS with $n \in [101,211]$. As a numerical example, we break our largest HPS-171 instance using the cyclotomic ring basis within $83$ core days, whereas the Coppersmith-Shamir basis requires $172$ core days. We also break one more official NTRU challenges by Security Innovation, Inc., originally worth 1000\$, in dimension $n=181$ in $20$ core years.

MQ-Sign is a variant of the UOV singature scheme proposed by Shim et al. It has been suggested as a candidate for the standardization of post-quantum cryptography in Republic of Korea (known as KpqC). However, recently Aulbach et al. proposed a practical key recovery attack against MQ-Sign-RS and MQ-Sign-SS with a simple secret key $\mathcal{S}$. In this paper, we propose another attack that is valid for the case of a general secret key $\mathcal{S}$.

The neural-differential distinguisher proposed by Gohr boosted the development of neural aided differential attack. As another significant cryptanalysis technique, linear attack has not been developing as rapidly in combination with deep learning technology as differential attack. In 2020, Hou et al. proposed the first neural-linear attack with one bit key recovery on 3, 4 and 5-round DES and restricted multiple bits recovery on 4 rounds, where the effective bits in one plain-ciphertext pair are spliced as one data sample. In this paper, we compare the neural-linear cryptanalysis with neural-differential cryptanalysis and propose a new data preprocessing algorithm depending on their similarities and differences. We call the new data structure distribution data. Basing on it, we mount our key recovery on round-reduced DES—first, we raise the accuracy of the neural-linear distinguisher by about 50%. Second, our distinguisher improves the effectiveness of one bit key recovery against 3, 4 and 5-round DES than the former one, and attack 6-round DES with success rate of 60.6% using 2048 plain-ciphertext pairs. Third, we propose a real multiple bit key recovery algorithm, leading neural-linear attack from theory to practice.

In this work we are interested in evaluating the possibility of extracting information from radio-enabled embedded-systems from a long distance. That is, our focus is capturing information from sources in the micrometer to tens of centimeters scale, such as intra- or inter- device busses, board-level routing traces etc. Moreover, we focus on distances in the range of millimeters to tens of centimeters from the (on-chip or on-board) embedded-system Tx Antenna to the signal source. Side-channels denotes presence of information in illegitimate channels. Side-channel analysis (SCA) attacks typically require statistical analysis and many leakage traces, focusing on micrometer level signals (sources) which emanate direct Near-Field information up to centimeters-level distances. In the same context (Near-Field and micrometer-level) simple power analysis (SPA) like attacks typically extract either direct raw information from one or few leakages or utilize statistical analysis on various samples from the same trace, similarly to horizontal attacks. Lately, radio-enabled systems were shown to emanate to a large distance (Far-Field), information from micrometer level sources, such as CPU processing, through the RF Tx Antenna: so far, SCA-like statistical analysis were shown. On the other hand, various reports exist on direct information eavesdropping/ sniffing or data exfiltration, emanated from centimeter to tens of centimeters scale sources, e.g., SATA, USB, Power-lines, Serial interface, Air-Gap systems, Screens and even optical fibers. All these elements are typically being used as a source and a direct Tx Antenna (huge, several to tens of centimeters) of the sensitive information. These antennas typically transmit information to short distances and the decay is very steep (proportional to $r^{-2}$-$r^{-3}$ depending on various factors and models). To the best of our knowledge, we report here for the first time an alarming security challenge: any signal in the embedded system, from serial ports, DMA-controlled memory-access, JTAG and SPI interfaces, on-board signals with galvanic connection to the Tx Antenna-chip and \emph{on-board signals without galvanic connection to the Tx Antenna-chip itself, all leak direct information up to tens of centimeters from source to the Tx Antenna}. This alarming situation induce signal-integrity implications within the embedded system, and significant implications relating to device-isolation and user-isolation, it may also affect standards and specifications for e.g., electromagnetic compatibility (EMC), on-board signal shielding, electromagnetic and RF interference (EMI, RFI), cross-talk, and generally design-for-manufacturing (DFM) guidelines for both intra-IC and PCB board. We demonstrate such direct readout of signals with commercial and low-cost equipment indicating how problematic the situation is. The existence of such leakage is demonstrated both over an ultra-low-cost platform such as the nRF52832(nRF) embedded-system and on a more advanced ESP32-c3-devkitc-02 board which is far more widespread in ISM radio applications and meets certification like FCC and CE (as compared to the nRF device). We have constructed an experiment to demonstrate leakage scenarios from (1) on- and (2) off-chip, on-board or (3) signals without galvanic connection to the RF front-end chip, showing the severity of the leakage, repetitively and systematic nature of the phenomena over various devices. We further demonstrate how sophisticated adversaries can build a code-injection Gadget which can carry sensitive-data and modulate it to be best extracted by the RF-channel. The main observation we push forward is that unless concrete interference and isolation standards appear with security metrics in mind, which are significantly different than ones needed for communication, it would be hard to prevent such leakages.

Distributed Oblivious Random Access Memory (DORAM) is a secure multiparty protocol that allows a group of participants holding a secret-shared array to read and write to secret-shared locations within the array. The efficiency of a DORAM protocol is measured by the amount of communication and computation required per read/write query into the array. DORAM protocols are a necessary ingredient for executing Secure Multiparty Computation (MPC) in the RAM model. Although DORAM has been widely studied, all existing DORAM protocols have focused on the setting where the DORAM servers are semi-honest. Generic techniques for upgrading a semi-honest DORAM protocol to the malicious model typically increase the asymptotic communication complexity of the DORAM scheme. In this work, we present a 3-party DORAM protocol which requires $O((\kappa + D)\log N)$ communication and computation per query, for a database of size $N$ with $D$-bit values, where $\kappa$ is the security parameter. Our hidden constants in a big-O nation are small. We show that our protocol is UC-secure in the presence of a malicious, static adversary. This matches the communication and computation complexity of the best semi-honest DORAM protocol, and is the first malicious DORAM protocol with this complexity.

Cryptographic hash functions are used inside many applications that critically rely on their resistance against cryptanalysis attacks and the correctness of their implementations. Nevertheless, vulnerabilities in cryptographic hash function implementations can remain unnoticed for more than a decade, as shown by the recent discovery of a buffer overflow in the implementation of SHA-3 in the eXtended Keccak Code Package (XKCP), impacting Python, PHP, and several other software projects. This paper explains how this buffer overflow vulnerability in XKCP was found. More generally, we explore the application of formal methods to the five finalist submission packages to the NIST SHA-3 competition, allowing us to (re-)discover vulnerabilities in the implementations of Keccak and BLAKE, and also discover a previously undisclosed vulnerability in the implementation of Grøstl. We also show how the same approach rediscovers a vulnerability affecting 11 out of the 12 implemented cryptographic hash functions in Apple's CoreCrypto library. Our approach consists of removing certain lines of code and then using KLEE as a tool to prove functional equivalence. We discuss the advantages and limitations of our approach and hope that our attempt to consolidate some earlier approaches can lead to new insights.

Due to the significant development of the intelligence industry worldwide, various initiatives have increasingly recognized the value of the Internet of Things (IoT). IoT systems, however, are often hin- dered by fundamental challenges, such as the need for a central server to manage them. Decentralizing these systems can be achieved through the use of blockchains. Recently, there has been an increase in the popularity of blockchain in various fields, such as banking, IoT, and the intelligence industry, and human societies have taken notice of it. One of the main problems is with the scalability of such systems as the network size grows. This paper examines how to overcome this challenge in blockchain-based IoT systems. We introduce a sharding-based blockchain that is lightweight and scalable. In the proposed method, the nodes are assigned to a number of shards based on their history of activity. As part of this study, the Improved Byzantine Fault Tolerance with Graceful performance Degradation (IGDBFT) consensus algorithm is introduced within the proposed scheme for intra-shard consensus. A solution to storing blocks and cross-shard transactions has been developed using a global chain containing parent blocks in the cloud layer. Finally, we analyze the security and efficiency of our scheme and compare our sharding-based protocol with previous protocols.

Central Bank Digital Currency (CBDC) is in the phase of discussion in most of countries. In this paper, we consider the security issues of centralized retail CBDC. Our focus is on the design and analysis of the underlying cryptographic protocol. The main security requirements against the protocol are transaction anonymity and protection against tax evasion. The protocol provides security guarantees in case of the strongest model of an execution environment which is the general concurrent environment. We apply the Universal Composition (UC) methodology of Canetti [3],[4]. At the time of this writing, we are not aware of any published CBDC protocol with an aim to provide secure compositional guarantees.

There are lots of Random Key Generators, In this paper, we gave a new construction of Randomized Bit Generator by using Algebraic number theory, which is quite easy to compute and also we keep the security of this generator in our mind. we discussed its applications as a secret key generator being a randomized bit generator in encryption schemes and hash functions. We tried to make it Quantumly secure by randomizing it and extending its parameters to see it as a Quantum Random key generator.

We introduce HyperNova, a new recursive argument for proving incremental computations whose steps are expressed with CCS (Setty et al. ePrint 2023/552), a customizable constraint system that simultaneously generalizes Plonkish, R1CS, and AIR without overheads. HyperNova makes four contributions, each resolving a major problem in the area of recursive arguments. First, it provides a folding scheme for CCS where the prover's cryptographic cost is a single multi-scalar multiplication (MSM) of size equal to the number of variables in the constraint system, which is optimal when using an MSM-based commitment scheme. The folding scheme can fold multiple instances at once, making it easier to build generalizations of IVC such as PCD. Second, when proving program executions on stateful machines (e.g., EVM, RISC-V), the cost of proving a step of a program is proportional only to the size of the circuit representing the instruction invoked by the program step ("a la carte" cost profile). Third, we show how to achieve zero-knowledge for "free" and without the need to employ zero-knowledge SNARKs: we show that Nova's folding scheme has a blinding property that can be used to "randomize" IVC proofs and, more generally, to add zero-knowledge to non-ZK SNARKs, via a protocol we call NovaBlindFold. This highlights a new application of folding schemes. Fourth, we show how to efficiently instantiate HyperNova over a cycle of elliptic curves. For this, we provide a general technique, which we refer to as CycleFold, that applies to all modern folding-scheme-based recursive arguments.

Private messaging systems that use a bulletin board, like privacy-preserving blockchains, have been a popular topic during the last couple of years. In these systems, typically a private message is posted on the board for a recipient and the privacy requirement is that no one can determine the sender and the recipient of the message. Until recently, the efficiency of these recipients was not considered, and the party had to perform a naive scan of the board to retrieve their messages. More recently, works like Fuzzy Message Detection (FMD), Private Signaling (PS), and Oblivious Message Retrieval (OMR) have studied the problem of protecting recipient privacy by outsourcing the message retrieval process to an untrusted server. However, FMD only provides limited privacy guarantees, and PS and OMR greatly lack scalability. In this work, we present a new construction for private signaling which is both asymptotically superior and concretely orders of magnitude faster than all prior works while providing full privacy. Our constructions make use of a trusted execution environment (TEE) and an Oblivious RAM to improve the computation complexity of the server. We also improve the privacy guarantees by keeping the recipient hidden even during the retrieval of signals from the server. Our proof-of-concept open-source implementation shows that for a server serving a million recipients and ten million messages, it only takes $< 60$ milliseconds to process a sent message, and $< 6$ seconds to process a retrieval (of 100 signals) request from a recipient.

In this work, we initiate a study of $K$-NIKE protocols in the fine-grained setting, in which there is a polynomial gap between the running time of the honest parties and that of the adversary. Our goal is to show the possibility, or impossibility, of basing such protocols on weaker assumptions than those of $K$-NIKE for $K \geq 3$. Our contribution is threefold. - We show that random oracles can be used to obtain fine-grained $K$-NIKE protocols for every constant $K$. In particular, we show how to generalize Merkle's two-party protocol to $K$ parties in such a way that the honest parties ask $n$ queries each, while the adversary needs $n^{K/(K-1)}$ queries to the random oracle to find the key. - We then improve the security by further using algebraic structures, while avoiding pairings. In particular, we show that there is a 4-party NIKE in Shoup's generic group model with a quadratic gap between the number of queries by the honest parties vs. that of the adversary. - Finally, we show a limitation of using purely algebraic methods for obtaining $3$-NIKE. In particular, we show that any $n$-query $3$-NIKE protocol in Maurer's generic group model can be broken by a $O(n^2)$-query attacker. Maurer's GGM is more limited compared with Shoup's both for the parties and the adversary, as there are no explicit labels for the group elements. Despite being more limited, this model still captures the Diffie Hellman protocol. Prior to our work, it was open to break $3$-NIKE protocols in Maurer's model with any polynomial number of queries.

Commitments are fundamental in cryptography. In the classical world, commitments are equivalent to the existence of one-way functions. It is also known that the most desired form of commitments in terms of their round complexity, i.e., non-interactive commitments, cannot be built from one-way functions in a black-box way [Mahmoody-Pass, Crypto'12]. However, if one allows the parties to use quantum computation and communication, it is known that non-interactive commitments (to classical bits) are in fact possible [Koshiba-Odaira, Arxiv'11 and Bitansky-Brakerski, TCC'21]. We revisit the assumptions behind non-interactive commitments in a quantum world and study whether they can be achieved using quantum computation and classical communication based on a black-box use of one-way functions. We prove that doing so is impossible unless the Polynomial Compatibility Conjecture [Austrin et al. Crypto'22] is false. We further extend our impossibility to protocols with quantum decommitments. This complements the positive result of Bitansky and Brakerski [TCC'21], as they only required a classical decommitment message. Because non-interactive commitments can be based on injective one-way functions, assuming the Polynomial Compatibility Conjecture, we also obtain a black-box separation between one-way functions and injective one-way functions (e.g., one-way permutations) even when the construction and the security reductions are allowed to be quantum. This improves the separation of Cao and Xue [Theoretical Computer Science'21] in which they only allowed the security reduction to be quantum. At a technical level, we prove that sampling oracles at random from ``sufficiently large'' sets (of oracles) will make them one-way against polynomial quantum-query adversaries who also get arbitrary polynomial-size quantum advice about the oracle. This gives a natural generalization of the recent results of Hhan et al.[Asiacrypt'19] and Chung et al. [FOCS'20].

We study sufficient conditions for compiling simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP prove systems, such as Plonk and Marlin. To instantiate our methodology we additionally prove that KZG commitments satisfy our simulation extractability requirement, despite being naturally malleable. To this end, we design a relaxed notion of simulation extractability that matches how KZG commitments are used and optimized in real-world prove systems. Only the proof that KZG satisfies this relaxed simulation extractability property relies on the algebraic group model (AGM) and random oracle (RO). We thus isolate the use of (and thus the reliance on) these strong heuristics.

The increased popularity of Machine Learning as a Service (MLaaS) makes the privacy of user data and network weights a critical concern. Using Torus FHE (TFHE) offers a solution for privacy-preserving computation in a cloud environment by allowing computation directly over encrypted data. However, software TFHE implementations of cyphertext-cyphertext multiplication needed when both input data and weights are encrypted are either lacking or are too slow. This paper proposes a new way to improve the performance of such multiplication by applying carry save addition. Its theoretical speedup is proportional to the bit width of the plaintext integer operands. This also speeds up multi-operand summation. A speedup of 15x is obtained for 16-bit multiplication on a 64-core processor, when compared to previous results. Multiplication also becomes more than twice as fast on a GPU if our approach is utilized. This leads to much faster dot product and convolution computations, which combine multiplications and a multi-operand sum. A 45x speedup is achieved for a 16-bit, 32-element dot product and a ~30x speedup for a convolution with a 32x32 filter size.

We propose hinTS --- a new threshold signature scheme built on top of the widely used BLS signatures. Our scheme enjoys the following attractive features: \begin{itemize} \item A {\em silent setup} process where the joint public key of the parties is computed as a deterministic function of their locally computed public keys. \item Support for {\em dynamic} choice of thresholds and signers, after the silent setup, without further interaction. \item Support for {\em general} access policies; in particular, native support for {\em weighted} thresholds with zero additional overhead over standard threshold setting. \item Strong security guarantees, including proactive security and forward security. \end{itemize}We prove the security of our scheme in the algebraic group model and provide implementation and extensive evaluation. Our scheme outperforms all prior proposals that aim to avoid distributed key generation in terms of aggregation time, signature size, and verification time. As an example, the aggregation time for 1000 signers is under 0.5 seconds, while both signing and verification are constant time algorithms, taking roundly 1 ms and 17.5 ms respectively. The key technical contribution of our work involves the design of special-purpose succinct proofs to {\em efficiently} prove the well-formedness of aggregated public keys. Our solution uses public ``hints'' released by the signers as part of their public keys (hence the name hinTS).

Plaintext structures are a commonly-used technique for improving differential cryptanalysis. Generally, there are two types of plaintext structures: multiple-differential structures and truncated-differential structures. Both types have been widely used in cryptanalysis of S-box-based ciphers while for SPECK, an Addition-Rotation-XOR (ARX) cipher, the truncated-differential structure has not been used so far. In this paper, we investigate the properties of modular addition and propose a method to construct truncated-differential structures for SPECK. Moreover, we show that a combination of both types of structures is also possible for SPECK. For recovering the key of SPECK, we propose dedicated algorithms and apply them to various differential distinguishers, which helps to obtain a series of improved attacks on all variants of SPECK. Notably, on SPECK128, the time complexity of the attack can be reduced by a factor up to 2^15. The results show that the combination of both structures helps to improve the data and time complexity at the same time, as in the cryptanalysis of S-box-based ciphers.

This paper presents the first decentralized multi-authority attribute-based inner product functional encryption (MA-ABIPFE) schemes supporting vectors of a priori unbounded lengths. The notion of AB-IPFE, introduced by Abdalla et al. [ASIACRYPT 2020], combines the access control functionality of attribute-based encryption (ABE) with the possibility of evaluating linear functions on encrypted data. A decentralized MA-ABIPFE defined by Agrawal et al. [TCC 2021] essentially enhances the ABE component of AB-IPFE to the decentralized multi-authority setting where several authorities can independently issue user keys involving attributes under their control. In MA-ABIPFE for unbounded vectors (MA-ABUIPFE), encryptors can encrypt vectors of arbitrary length under access policies of their choice whereas authorities can issue secret keys to users involving attributes under their control and vectors of arbitrary lengths. Decryption works in the same way as for MA-ABIPFE provided the lengths of the vectors within the ciphertext and secret keys match. We present two MA-ABUIPFE schemes supporting access policies realizable by linear secret sharing schemes (LSSS), in the significantly faster prime-order bilinear groups under decisional assumptions based on the target groups which are known to be weaker compared to their counterparts based in the source groups. The proposed schemes demonstrate different trade-offs between versatility and underlying assumptions. The first scheme allows each authority to control a bounded number of attributes and is proven secure under the well-studied decisional bilinear Diffie-Hellman (DBDH) assumption. On the other hand, the second scheme allows authorities to control exponentially many attributes, that is, supports large attribute universe, and is proven secure under a non-interactive q-type variant of the DBDH assumption called L-DBDH, similar to what was used in prior large-universe multi-authority ABE (MA-ABE) construction. When compared with the only known MA-ABIPFE scheme due to Agrawal et al. [TCC 2021], our schemes offer significantly higher efficiency while offering greater flexibility and security under weaker assumptions at the same time. Moreover, unlike Agrawal et al., our schemes can support the appearance of the same attributes within an access policy arbitrarily many times. Since efficiency and practicality is the prime focus of this work, we prove the security of our constructions in the random oracle model against static adversaries similar to prior works on MA-ABE with similar motivations and assumptions. On the technical side, we extend the unbounded IPFE techniques of Dufour-Sans and Pointcheval [ACNS 2019] to the context of MA-ABUIPFE by introducing a novel hash-decomposition technique.

Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource. First, we construct a one-shot (i.e., single message) string oblivious transfer (OT) protocol with random receiver bit in the shared EPR pairs model, assuming the (sub-exponential) hardness of LWE. Building on this, we show that {\em secure teleportation through quantum channels} is possible. Specifically, given the description of any quantum operation $Q$, a sender with (quantum) input $\rho$ can send a single classical message that securely transmits $Q(\rho)$ to a receiver. That is, we realize an ideal quantum channel that takes input $\rho$ from the sender and provably delivers $Q(\rho)$ to the receiver without revealing any other information. This immediately gives a number of applications in the shared EPR pairs model: (1) non-interactive secure computation of unidirectional \emph{classical} randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a non-interactive \emph{zero-knowledge} state synthesis protocol. Next, we construct a two-round (round-optimal) secure multiparty computation protocol for classical functionalities in the shared EPR pairs model that is \emph{unconditionally-secure} in the (quantum-accessible) random oracle model. Classically, both of these results cannot be obtained without some form of correlated randomness shared between the parties, and the only known approach is to have a trusted dealer set up random (string) OT correlations. In the quantum world, we show that shared EPR pairs (which are simple and can be deterministically generated) are sufficient. At the heart of our work are novel techniques for making use of entangling operations to generate string OT correlations, and for instantiating the Fiat-Shamir transform using correlation-intractability in the quantum setting.

Secure Multi-Party Computation (MPC) is continuously becoming more and more practical. Many optimizations have been introduced, making MPC protocols more suitable for solving real-world problems. However, the MPC protocols and optimizations are usually implemented as a standalone proof of concept or in an MPC framework and are tightly coupled with special-purpose circuit formats, such as Bristol Format. This makes it very hard and time-consuming to re-use algorithmic advances and implemented applications in a different context. Developing generic algorithmic optimizations is exceptionally hard because the available MPC tools and formats are not generic and do not provide the necessary infrastructure. In this paper, we present FUSE: A Framework for Unifying and Optimizing Secure Multi-Party Computation Implementations with Efficient Circuit Storage. FUSE provides a flexible intermediate representation (FUSE IR) that can be used across different platforms and in different programming languages, including C/C++, Java, Rust, and Python. We aim at making MPC tools more interoperable, removing the tight coupling between high-level compilers for MPC and specific MPC protocol engines, thus driving knowledge transfer. Our framework is inspired by the widely known LLVM compiler framework. FUSE is portable, extensible, and it provides implementation-agnostic optimizations. As frontends, we implement HyCC (CCS'18), the Bristol circuit format, and MOTION (TOPS'22), meaning that these can be automatically converted to FUSE IR. We implement several generic optimization passes, such as automatic subgraph replacement and vectorization, to showcase the utility and efficiency of our framework. Finally, we implement as backends MOTION and MP-SPDZ (CCS'20), so that FUSE IR can be run by these frameworks in an MPC protocol, as well as other useful backends for JSON output and the DOT language for graph visualization. With FUSE, it is possible to use any implemented frontend with any implemented backend and vice-versa. FUSE IR is not only efficient to work on and much more generic than any other format so far -- supporting, e.g., function calls, hybrid MPC protocols as well as user-defined building blocks, and annotations -- while maintaining backwards-compatibility, but also compact, with smaller storage size than even minimalistic formats such as Bristol already for a few hundred operations.

Physically Unclonable Functions (PUFs) are being proposed as a low cost alternative to permanently store secret keys or provide device authentication without requiring non-volatile memory, large e-fuses or other dedicated processing steps. In the literature, PUFs are split into two main categories. The so-called strong PUFs are mainly used for authentication purposes, hence also called authentication PUFs. They promise to be lightweight by avoiding extensive digital post-processing and cryptography. The so-called weak PUFs, also called key generation PUFs, can only provide authentication when combined with a cryptographic authentication protocol. Over the years, multiple research results have demonstrated that Strong PUFs can be modeled and attacked by machine learning techniques. Hence, the general assumption is that the security of a strong PUF is solely dependent on its security against machine learning attacks. The goal of this paper is to debunk this myth, by analyzing and breaking three recently published Strong PUFs (Suresh et al., VLSI Circuits 2020; Liu et al., ISSCC 2021; and Jeloka et al., VLSI Circuits 2017). The attacks presented in this paper have practical complexities and use generic symmetric key cryptanalysis techniques.

Fully Homomorphic Encryption (FHE) inherently lacks data integrity mechanisms, allowing a malicious server to arbitrarily tamper with the data associated with FHE computations on its end. A series of works named reaction attacks further demonstrates that a malicious server can exploit this lack of integrity checks to carry out interactive full-key recovery attacks on state-of-the-art FHE schemes. In this paper, we propose an efficient solution to this problem by utilizing the concept of the Merkle tree. Our solution uses cryptographic hash functions to ensure the integrity of data involved in FHE computations. The efficiency of our solution comes from the lower sizes and ease of computations of the hash values, which subsequently leads to a reduction in both the network and computation overhead. Given that protecting the entire FHE circuit can lead to tremendous network overhead, we further perform scheme-specific optimizations by identifying a small portion of the FHE circuit, protecting which is sufficient to thwart these reaction-based attacks. Finally, we propose a framework that evaluates different FHE schemes based on the overhead that will be incurred when protecting these schemes through our solution. Our framework can be leveraged by application developers to choose an optimal FHE scheme in terms of both performance and overhead.

We present a framework for building practical anonymous credential schemes based on the hardness of lattice problems. The running time of the prover and verifier is independent of the number of users and linear in the number of attributes. The scheme is also compact in practice, with the proofs being as small as a few dozen kilobytes for arbitrarily large (say up to $2^{128}$) users with each user having several attributes. The security of our scheme is based on a new family of lattice assumptions which roughly states that given short pre-images of random elements in some set $S$, it is hard to create a pre-image for a fresh element in such a set. We show that if the set admits efficient zero-knowledge proofs of knowledge of a commitment to a set element and its pre-image, then this yields practically-efficient privacy-preserving primitives such as blind signatures, anonymous credentials, and group signatures. We propose a candidate instantiation of a function from this family which allows for such proofs and thus yields practical lattice-based primitives.

We develop a simple compiler that generically adds publicly-verifiable deletion to a variety of cryptosystems. Our compiler only makes use of one-way functions (or one-way state generators, if we allow the public verification key to be quantum). Previously, similar compilers either relied on the use of indistinguishability obfuscation (Bartusek et. al., ePrint:2023/265) or almost-regular one-way functions (Bartusek, Khurana and Poremba, arXiv:2303.08676).

User authentication and message confidentiality are the basic security requirements of high-end applications such as multicast communication and distributed systems. Several efficient signature-then-encrypt cryptographic schemes have been proposed to offer these security requirements with lower computational cost and communication overhead. However, signature-then-encryption techniques take more computation time than signcryption techniques. Signcryption accomplishes both digital signature and public key encryption functions in a single logical step and at a much lower cost than ``signature followed by encryption.'' Several signcryption schemes based on bilinear pairing operations have been proposed. Similarly, anonymous multi-receiver encryption has recently risen in prominence in multicast communication and distributed settings, where the same messages are sent to several receivers but the identity of each receiver should remain private. Anonymous multi-receiver encryption allows a receiver to obtain the plaintext by decrypting the ciphertext using their own private key, while their identity is kept secret to anyone, including other receivers. Among the Certificateless Multi-receiver Encryption (CLMRE) schemes that have been introduced, Hung et al. proposed an efficient Anonymous Multireceiver Certificateless Encryption (AMCLE) scheme ensuring confidentiality and anonymity based on bilinear pairings and is secure against IND-CCA and ANON-CCA. In this paper, we substantially extend Hung et al.’s multireceiver certificateless encryption scheme to a Multireceiver Certificateless Signcryption (MCLS) scheme that provides confidentiality along with authentication. We show that, as compared to Hung et al.’s encryption scheme, our signcryption scheme requires only three additional multiplication operations for signcryption and unsigncryption phases. Whereas, the signcryption cost is linear with the number of designated receivers while the unsigncryption cost remains constant for each designated receiver. We compare the results with other existing single receiver and multireceiver signcryption schemes in terms of number of operations, exemption of key escrow problem, and public key settings. The scheme proposed in this paper is more efficient for single and multireceiver signcryption schemes while providing exemption from the key escrow problem, and working in certificateless public key settings.

We prove that perfectly-secure optimally-resilient secure Multi-Party Computation (MPC) for a circuit with $C$ gates and depth $D$ can be obtained in $O((Cn+n^4 + Dn^2)\log n)$ communication complexity and $O(D)$ expected time. For $D \ll n$ and $C\geq n^3$, this is the first perfectly-secure optimal-resilient MPC protocol with linear communication complexity per gate and constant expected time complexity per layer. Compared to state-of-the-art MPC protocols in the player elimination framework [Beerliova and Hirt TCC'08, and Goyal, Liu, and Song CRYPTO'19], for $C>n^3$ and $D \ll n$, our results significantly improve the run time from $\Omega(n+D)$ to expected $O(D)$ while keeping communication complexity at $O(Cn\log n)$. Compared to state-of-the-art MPC protocols that obtain an expected $O(D)$ time complexity [Abraham, Asharov, and Yanai TCC'21], for $C>n^3$, our results significantly improve the communication complexity from $O(Cn^4\log n)$ to $O(Cn\log n)$ while keeping the expected run time at $O(D)$. One salient part of our technical contribution is centered around a new primitive we call "detectable secret sharing". It is perfectly-hiding, weakly-binding, and has the property that either reconstruction succeeds or $O(n)$ parties are (privately) detected. On the one hand, we show that detectable secret sharing is sufficiently powerful to generate multiplication triplets needed for MPC. On the other hand, we show how to share $p$ secrets via detectable secret sharing with communication complexity of just $O(n^4\log n+p \log n)$. When sharing $p\geq n^4$ secrets, the communication cost is amortized to just $O(1)$ field elements per secret. Our second technical contribution is a new Verifiable Secret Sharing protocol that can share $p$ secrets at just $O(n^4\log n+pn\log n)$ word complexity. When sharing $p\geq n^3$ secrets, the communication cost is amortized to just $O(n)$ filed elements per secret. The best prior required $\Omega(n^3)$ communication per secret.

In post-quantum cryptography, hash-based signature schemes are attractive choices because of the weak assumptions. Most existing hash-based signature schemes are proven secure against post-quantum chosen message attacks (CMAs), where the adversaries are able to execute quantum computations and classically query to the signing oracle. In some cases, the signing oracle is also considered quantum-accessible, meaning that the adversaries are able to send queries with superpositions to the signing oracle. Considering this, Boneh and Zhandry [BZ13] propose a stronger security notion called existential unforgeability under quantum chosen message attacks (EUF-qCMA). We call it quantum-access security (or Q2 security in some literature). The quantum-access security of practical signature schemes is lacking in research, especially of the hash-based ones. In this paper, we analyze the quantum-access security of hash-based signature schemes in two directions. First, we show concrete quantum chosen message attacks (or superposition attacks) on existing hash-based signature schemes, such as SPHINCS and SPHINCS+. The complexity of the attacks is obviously lower than that of optimal classical chosen message attacks, implying that quantum chosen message attacks are more threatening than classical ones to these schemes. Second, we propose a simple variant of SPHINCS+ and give security proof against quantum chosen message attacks. As far as we know, it is the first practical hash-based stateless signature scheme against quantum chosen message attacks with concrete provable security.

Federated learning (FL) has gained widespread popularity in a variety of industries due to its ability to locally train models on devices while preserving privacy. However, FL systems are susceptible to i) privacy inference attacks and ii) poisoning attacks, which can compromise the system by corrupt actors. Despite a significant amount of work being done to tackle these attacks individually, the combination of these two attacks has received limited attention in the research community. To address this gap, we introduce SAFEFL, a secure multiparty computation (MPC)-based framework designed to assess the efficacy of FL techniques in addressing both privacy inference and poisoning attacks. The heart of the SAFEFL framework is a communicator interface that enables PyTorch-based implementations to utilize the well established MP-SPDZ framework, which implements various MPC protocols. The goal of SAFEFL is to facilitate the development of more efficient FL systems that can effectively address privacy inference and poisoning attacks.

This paper introduces a secure and efficient hybrid scheme based on polar codes, called as HES-PC. The proposed HES-PC contains of two other mechanisms: a key encapsulation mechanism based on polar codes, called as KEM-PC, a data encapsulation mechanism based on polar codes, called as DEM-PC. In fact, the symmetric key is exchanged between the legitimate partners by exploiting the KEM-PC. Also, secure polar encoding/successive cancelation (SC) decoding is enhanced between the honest parties by using DEM-PC.

Thus far, several papers reported concrete resource estimates of Shor's quantum algorithm for solving the elliptic curve discrete logarithm problem (ECDLP). In this paper, we study quantum FLT-based inversion algorithms over binary elliptic curves. There are two major algorithms proposed by Banegas et al. and Putranto et al., where the former and latter algorithms achieve fewer numbers of qubits and smaller depths of circuits, respectively. We propose two quantum FLT-based inversion algorithms that essentially outperform previous FLT-based algorithms and compare the performance for NIST curves of the degree $n$. Specifically, for all $n$, our first algorithm achieves fewer qubits than Putranto et al.'s one without sacrificing the number of Toffoli gates and the depth of circuits, while our second algorithm achieves smaller depths of circuits without sacrificing the number of qubits and Toffoli gates. For example, when $n = 571$, the number of qubits of our first algorithm is 74 \% of that of Putranto et al.'s one, while the depth of our second algorithm is 83 \% of that of Banegas et al.'s one. The improvements stem from the fact that FLT-based inversions can be performed with arbitrary sequences of addition chains for $n - 1$ although both Banegas et al. and Putranto et al. follow fixed sequences that were introduced by Itoh and Tsujii's classical FLT-based inversion. In particular, we analyze how several properties of addition chains, which do not affect the computational resources of classical FLT-based inversions, affect the computational resources of quantum FLT-based inversions and find appropriate sequences.

This paper introduces customizable constraint system (CCS), a generalization of R1CS that can simultaneously capture R1CS, Plonkish, and AIR without overheads. Unlike existing descriptions of Plonkish and AIR, CCS is not tied to any particular proof system. Furthermore, we observe that the linear-time polynomial IOP for R1CS in Spartan (CRYPTO 20) extends easily to CCS, and when combined with a polynomial commitment scheme, it yields a family of SNARKs for CCS, which we refer to as SuperSpartan. SuperSpartan supports high-degree constraints without its prover incurring cryptographic costs that scale with the degree of constraints (only field operations scale with the constraint degree). Moreover, as in Spartan, it does not employ superlinear-time and hard-to-distribute operations such as FFTs. Similar properties were achieved for Plonkish by HyperPlonk (EUROCRYPT 23) via a different route. However, it is unclear how to prove CCS instances (or even R1CS instances) with HyperPlonk (or Plonk itself), without overheads. Furthermore, unlike HyperPlonk, SuperSpartan can prove uniform instances of CCS (including AIR) without requiring a linear-time preprocessing for the verifier, and for those instances, SuperSpartan provides “free” addition gates. SuperSpartan for AIR is the first SNARK for AIR with a linear-time prover, transparent and sublinear-time pre-processing, polylogarithmic proof size, and plausible post-quantum security. In particular, SuperSpartan for AIR provides a faster prover than existing transparent SNARKs for AIR (which are sometimes referred to as STARKs).

We introduce a novel template attack for secret key recovery in Kyber, leveraging side-channel information from polynomial multiplication during decapsulation. Conceptually, our attack exploits that Kyber's incomplete number-theoretic transform (NTT) causes each secret coefficient to be used multiple times, unlike when performing a complete NTT. Our attack is a single trace \emph{known} ciphertext attack that avoids machine-learning techniques and instead relies on correlation-matching only. Additionally, our template generation method is very simple and easy to replicate, and we describe different attack strategies, varying on the number of templates required. Moreover, our attack applies to both masked implementations as well as designs with multiplication shuffling. We demonstrate its effectiveness by targeting a masked implementation from the \emph{mkm4} repository. We initially perform simulations in the noisy Hamming-Weight model and achieve high success rates with just $13\,316$ templates while tolerating noise values up to $\sigma=0.3$. In a practical setup, we measure power consumption and notice that our attack falls short of expectations. However, we introduce an extension inspired by known online template attacks, enabling us to recover $128$ coefficient pairs from a single polynomial multiplication. Our results provide evidence that the incomplete NTT, which is used in Kyber-768 and similar schemes, introduces an additional side-channel weakness worth further exploration.

We will revisit recent techniques and results on the cryptoanalysis of local pseudorandom number generators (PRGs). By doing so, we will achieve a new attack on PRGs whose time complexity only depends on the algebraic degree of the PRG. Concretely, for PRGs $F : \{0,1\}^n\rightarrow \{0,1\}^{n^{1+e}}$, we will give an algebraic algorithm that distinguishes between random points and image points of $F$, whose time complexity is bounded by \[\exp(O(\log(n)^{\deg F /(\deg F - 1)} \cdot n^{1-e/(\deg F -1)} ))\] and whose advantage is at least $1 - o(1)$ in the worst case. To the best of the author's knowledge, this attack outperforms current attacks on the pseudorandomness of local random functions with guaranteed noticeable advantage and gives a new baseline algorithm for local PRGs. Furthermore, this is the first subexponential attack that is applicable to polynomial PRGs of constant degree over fields of any size with a guaranteed noticeable advantage. We will extend this distinguishing attack further to achieve a search algorithm that can invert a uniformly random constant-degree map $F : \{0,1\}^n\rightarrow \{0,1\}^{n^{1+e}}$ with high advantage in the average case. This algorithm has the same runtime complexity as the distinguishing algorithm.

In this paper we study non-trivial self-pairings with cyclic domains that are compatible with isogenies between elliptic curves oriented by an imaginary quadratic order $\mathcal{O}$. We prove that the order $m$ of such a self-pairing necessarily satisfies $m \mid \Delta_\mathcal{O}$ (and even $2m \mid \Delta_\mathcal{O} $ if $4 \mid \Delta_\mathcal{O}$ and $4m \mid \Delta_\mathcal{O}$ if $8 \mid \Delta_\mathcal{O}$) and is not a multiple of the field characteristic. Conversely, for each $m$ satisfying these necessary conditions, we construct a family of non-trivial cyclic self-pairings of order $m$ that are compatible with oriented isogenies, based on generalized Weil and Tate pairings. As an application, we identify weak instances of class group actions on elliptic curves assuming the degree of the secret isogeny is known. More in detail, we show that if $m^2 \mid \Delta_\mathcal{O}$ for some prime power $m$ then given two primitively $\mathcal{O}$-oriented elliptic curves $(E, \iota)$ and $(E',\iota') = [\mathfrak{a}] (E,\iota)$ connected by an unknown invertible ideal $\mathfrak{a} \subseteq \mathcal{O}$, we can recover $\mathfrak{a}$ essentially at the cost of a discrete logarithm computation in a group of order $m^2$, assuming the norm of $\mathfrak{a}$ is given and is smaller than $m^2$. We give concrete instances, involving ordinary elliptic curves over finite fields, where this turns into a polynomial time attack. Finally, we show that these self-pairings simplify known results on the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves.

In this paper, we study the compartment-based and hierarchical delegation of signing power of the verifiable accountable subgroup multi-signature (vASM). ASM is a multi-signature in which the participants are accountable for the resulting signature, and the number of participants is not fixed. After Micali et al.’s and Boneh et al.’s ASM schemes, the verifiable-ASM (vASM) scheme with a verifiable group setup and more efficient verification phase was proposed recently. The verifiable group setup in vASM verifies the participants at the group setup phase. In this work, we show that the vASM scheme can also be considered as a proxy signature in which an authorized user (original signer, designator) delegates her signing rights to a single (or a group of) unauthorized user(s) (proxy signer). Namely, we propose four new constructions with the properties and functionalities of an ideal proxy signature and a compartment-based/hierarchical structure. In the first construction, we apply the vASM scheme recursively; in the second one, we use Shamir’s secret sharing (SSS) scheme; in the third construction, we use SSS again but in a nested fashion. In the last one, we use the hierarchical threshold secret sharing (HTSS) scheme for delegation. Then, we show the affiliation of our constructions to proxy signatures and compare our constructions with each other in terms of efficiency and security. Finally we compare the vASM scheme with the existing pairing-based proxy signature schemes.

Zero-knowledge (ZK) proof systems have emerged as a promising solution for building security-sensitive applications. However, bugs in ZK applications are extremely difficult to detect and can allow a malicious party to silently exploit the system without leaving any observable trace. This paper presents Coda, a novel statically-typed language for building zero-knowledge applications. Critically, Coda makes it possible to formally specify and statically check properties of a ZK application through a rich refinement type system. One of the key challenges in formally verifying ZK applications is that they require reasoning about polynomial equations over large prime fields that go beyond the capabilities of automated theorem provers. Coda mitigates this challenge by generating a set of Coq lemmas that can be proven in an interactive manner with the help of a tactic library. We have used Coda to re-implement 79 arithmetic circuits from widely-used Circom libraries and applications. Our evaluation shows that Coda makes it possible to specify important and formally verify correctness properties of these circuits. Our evaluation also revealed 6 previously-unknown vulnerabilities in the original Circom projects.

As the technical feasibility of a quantum computer becomes more and more likely, post-quantum cryptography algorithms are receiving particular attention in recent years. Among them, code-based cryptosystems were first considered unsuited for hardware and embedded software implementations because of their very large key sizes. However, recent work has shown that such implementations are practical, which also makes them susceptible to physical attacks. In this article, we propose a horizontal correlation attack on the Classic McEliece cryptosystem, more precisely on the matrix-vector multiplication over $\mathbb{F}_2$ that computes the shared key in the encapsulation process. The attack is applicable in the broader context of Niederreiter-like code-based cryptosystems and is independent of the code structure, i.e. it does not need to exploit any particular structure in the parity check matrix. Instead, we take advantage of the constant time property of the matrix-vector multiplication over $\mathbb{F}_2$. We extend the feasibility of the basic attack by leveraging information-set decoding methods and carry it out successfully on the reference embedded software implementation. Interestingly, we highlight that implementation choices, like the word size or the compilation options, play a crucial role in the attack success, and even contradict the theoretical analysis.

The universal thresholdizer, introduced at CRYPTO'18, is a cryptographic scheme that transforms any cryptosystem into a threshold variant, thereby enhancing its applicability in threshold cryptography. It enables black-box construction of one-round threshold signature schemes based on the Learning with Errors problem, and similarly, facilitates one-round threshold ciphertext-attack secure public key encryption when integrated with non-threshold schemes. Current constructions of universal thresholdizer are fundamentally built upon linear secret sharing schemes. One approach employs Shamir's secret sharing, which lacks compactness and results in ciphertext sizes of $O(N \log N)$, and another approach uses $\{0,1\}$-linear secret sharing scheme ($\{0,1\}$-LSSS), which is compact but induces high communication costs due to requiring $O(N^{5.3})$ secret shares. In this work, we introduce a communication-efficient universal thresholdizer by revising the linear secret sharing scheme. We propose a specialized linear secret sharing scheme, called TreeSSS, which reduces the number of required secret shares $O(N^{3+o(1)})$ while maintaining the compactness of the universal thresholdizer. TreeSSS can also serve as a subroutine for constructing lattice based $t$-out-of-$N$ threshold cryptographic primitives such as threshold fully homomorphic encryptions and threshold signatures. In this context, TreeSSS offers the advantage of lower communication overhead due to the reduced number of secret shares involved.

Fully Homomorphic Encryption enables the evaluation of an arbitrary computable function over encrypted data. Among all such functions, particular interest goes for integer arithmetics. In this paper, we present a bundle of methods for fast arithmetic operations over encrypted data: addition/subtraction, multiplication, and some of their special cases. On top of that, we propose techniques for signum, maximum, and rounding. All methods are specifically tailored for computations with data encrypted with the TFHE scheme (Chillotti et al., Asiacrypt '16) and we mainly focus on parallelization of non-linear homomorphic operations, which are the most expensive ones. This way, evaluation times can be reduced significantly, provided that sufficient parallel resources are available. We implement all presented methods in the Parmesan Library and we provide an experimental evaluation. Compared to integer arithmetics of the Concrete Library, we achieve considerable speedups for all comparable operations. Major speedups are achieved for the multiplication of an encrypted integer by a cleartext one, where we employ special addition-subtraction chains, which save a vast amount of homomorphic operations.

Two fundamental properties of quantum states that quantum information theory explores are pseudorandomness and provability of destruction. We introduce the notion of quantum pseudorandom states with proofs of destruction (PRSPD) that combines both these properties. Like standard pseudorandom states (PRS), these are efficiently generated quantum states that are indistinguishable from random, but they can also be measured to create a classical string. This string is verifiable (given the secret key) and certifies that the state has been destructed. We show that, similarly to PRS, PRSPD can be constructed from any post-quantum one-way function. As far as the authors are aware, this is the first construction of a family of states that satisfies both pseudorandomness and provability of destruction. We show that many cryptographic applications that were shown based on PRS variants using quantum communication can be based on (variants of) PRSPD using only classical communication. This includes symmetric encryption, message authentication, one-time signatures, commitments, and classically verifiable private quantum coins.

In this paper we introduce a multistep generalization of the guess-and-determine or hybrid strategy for solving a system of multivariate polynomial equations over a finite field. In particular, we propose performing the exhaustive evaluation of a subset of variables stepwise, that is, by incrementing the size of such subset each time that an evaluation leads to a polynomial system which is possibly unfeasible to solve. The decision about which evaluation to extend is based on a preprocessing consisting in computing an incomplete Grobner basis after the current evaluation, which possibly generates linear polynomials that are used to eliminate further variables. If the number of remaining variables in the system is deemed still too high, the evaluation is extended and the preprocessing is iterated. Otherwise, we solve the system by a complete Grobner basis computation. Having in mind cryptanalytic applications, we present an implementation of this strategy in an algorithm called MultiSolve which is designed for polynomial systems having at most one solution. We prove explicit formulas for its complexity which are based on probability distributions that can be easily estimated by performing the proposed preprocessing on a testset of evaluations for different subsets of variables. We prove that an optimal complexity of MultiSolve is achieved by using a full multistep strategy with a maximum number of steps and in turn the standard guess-and-determine strategy, which essentially is a strategy consisting of a single step, is the worst choice. Finally, we extensively study the behaviour of MultiSolve when performing an algebraic attack on the well-known stream cipher Trivium.

This paper explores the design space of vector-optimized polynomial multiplications in the lattice-based key-encapsulation mechanisms NTRU and NTRU Prime. Since NTRU and NTRU Prime do not support straightforward applications of number– theoretic transforms, the state-of-the-art vector code either resorted to Toom–Cook, or introduced various techniques for coefficient ring extensions. All these techniques lead to a large number of small-degree polynomial multiplications, which is the bottleneck in our experiments. For NTRU Prime, we show how to reduce the number of small-degree polynomial multiplications to nearly 1/4 times compared to the previous vectorized code with the same functionality. Our transformations are based on careful choices of FFTs, including Good–Thomas, Rader’s, Schönhage’s, and Bruun’s FFTs. For NTRU, we show how to deploy Toom-5 with 3-bit losses. Furthermore, we show that the Toeplitz matrix–vector product naturally translates into efficient implementations with vector-by-scalar multiplication instructions which do not appear in all prior vector-optimized implementations. We choose the ARM Cortex-A72 CPU which implements the Armv8-A architecture for experiments, because of its wide uses in smartphones, and also the Neon vector instruction set implementing vector-by-scalar multiplications that do not appear in most other vector instruction sets like Intel’s AVX2. Even for platforms without vector-by-scalar multiplications, we expect significant improvements compared to the state of the art, since our transformations reduce the number of multiplication instructions by a large margin. Compared to the state-of-the-art optimized implementations, we achieve 2.18× and 6.7× faster polynomial multiplications for NTRU and NTRU Prime, respectively. For full schemes, we additionally vectorize the polynomial inversions, sorting network, and encoding/decoding subroutines in NTRU and NTRU Prime. For ntruhps2048677, we achieve 7.67×, 2.48×, and 1.77× faster key generation, encapsulation, and decapsulation, respectively. For ntrulpr761, we achieve 3×, 2.87×, and 3.25× faster key generation, encapsulation, and decapsulation, respectively. For sntrup761, there are no previously optimized implementations and we significantly outperform the reference implementation.

We present an optimized constant-time implementation of the MAYO signature scheme on ARMv7-M. MAYO is a novel multivariate proposal based on the trapdoor function of the Unbalanced Oil and Vinegar scheme. Our implementation builds on existing techniques for UOV-based schemes and introduces a new approach for evaluating the polar forms of quadratic maps. We modify MAYO's original parameters to achieve greater benefits from the proposed optimizations, resulting in slightly larger keys and shorter signatures for the same level of security. We evaluate the optimized implementation with the new parameters on the STM32H753ZIT6 microcontroller and measure its performance for the signing and verification procedures. At NIST security level I, signing requires approximately 43M cycles, and verification requires approximately 6M cycles. Both are 2.6 times faster than the results obtained from the original parameters.

Assume that we have a group $G$ of known order $q$, in which we want to solve discrete logarithms (dlogs). In 1994, Maurer showed how to compute dlogs in $G$ in poly time given a Diffie-Hellman (DH) oracle in $G$, and an auxiliary elliptic curve $\hat E(\mathbb{F}_q)$ of smooth order. The problem of Maurer's reduction of solving dlogs via DH oracles is that no efficient algorithm for constructing such a smooth auxiliary curve is known. Thus, the implications of Maurer's approach to real-world applications remained widely unclear. In this work, we explicitly construct smooth auxiliary curves for $13$ commonly used, standardized elliptic curves of bit-sizes in the range $[204,256]$, including e.g., NIST P-256, Curve25519, SM2 and GOST R34.10. For all these curves we construct a corresponding cyclic auxiliary curve $\hat E(\mathbb{F}_q)$, whose order is $39$-bit smooth, i.e., its largest factor is of bit-length at most $39$ bits. This in turn allows us to compute for all divisors of the order of $\hat E(\mathbb{F}_q)$ exhaustively a codebook for all discrete logarithms. As a consequence, dlogs on $\hat E(\mathbb{F}_q)$ can efficiently be computed in a matter of seconds. Our resulting codebook sizes for each auxiliary curve are less than 29 TByte individually, and fit on our hard disk. We also construct auxiliary curves for NIST P-384 and NIST P-521 with a $65$-bit and $110$-bit smooth order. Further, we provide an efficient implementation of Maurer's reduction from the dlog computation in $G$ with order $q$ to the dlog computation on its auxiliary curve $\hat E(\mathbb{F}_q)$. Let us provide a flavor of our results, e.g., when $G$ is the NIST P-256 group, the results for other curves are similar. With the help of our codebook for the auxiliary curve $\hat E(\mathbb{F}_q)$, and less than 24,000 calls to a DH oracle in $G$ (that we simulate), we can solve discrete logarithms on NIST P-256 in around 30 secs. From a security perspective, our results show that for current elliptic curve standards the difficulty of solving DH is practically tightly related to the difficulty of computing dlogs. Namely, unless dlogs are easy to compute on these curves $G$, we provide a very concrete security guarantee that DH in $G$ must also be hard. From a cryptanalytic perspective, our results show a way to efficiently solve discrete logarithms in the presence of a DH oracle.

We present a general compiler to add the publicly verifiable deletion property for various cryptographic primitives including public key encryption, attribute-based encryption, and quantum fully homomorphic encryption. Our compiler only uses one-way functions, or more generally hard quantum planted problems for NP, which are implied by one-way functions. It relies on minimal assumptions and enables us to add the publicly verifiable deletion property with no additional assumption for the above primitives. Previously, such a compiler needs additional assumptions such as injective trapdoor one-way functions or pseudorandom group actions [Bartusek-Khurana-Poremba, CRYPTO 2023]. Technically, we upgrade an existing compiler for privately verifiable deletion [Bartusek-Khurana, CRYPTO 2023] to achieve publicly verifiable deletion by using digital signatures.

Arithmetization-Oriented primitives are the building block of advanced cryptographic protocols such as Zero-Knowledge proof systems. One approach to designing such primitives is the HADES design strategy which aims to provide an efficient way to instantiate generalizing substitution-permutation networks to include partial S-box rounds. A notable instance of HADES, introduced by Grassi \emph{et al.} at USENIX Security '21, is Poseidon. Because of its impressive efficiency and low arithmetic complexity, Poseidon is a popular choice among the designers of integrity-proof systems. An updated version of Poseidon, namely, Poseidon2 was published at AfricaCrypt '23 aiming to improve the efficiency of Poseidon by optimizing its linear operations. In this work, we show some caveats in the security argument of HADES against algebraic attacks and quantify the complexity of Gr\"{o}bner basis attacks. We show that the complexity of the attack is lower than claimed with the direct implication that there are cases where the recommended number of rounds is insufficient for meeting the claimed security. Concretely, the complexity of a Gr\"{o}bner basis attack for an instance of Poseidon with 1024 bits of security is 731.77 bits and the original security argument starts failing already at the 384-bit security level. Since the security of Poseidon2 is derived from the security of Poseidon, the same analysis applies to the instances of Poseidon2. The results were shared with the designers and the security arguments were updated accordingly.

We present new protocols for *Asynchronous Verifiable Secret Sharing* for Shamir (i.e., threshold $t<n$) sharing of secrets. Our protocols: * Use only "lightweight" cryptographic primitives, such as hash functions; * Can share secrets over rings such as $\mathbb{Z}_{p^k}$ as well as finite fields $\mathbb{F}_q$; * Provide *optimal resilience*, in the sense that they tolerate up to $t < n/3$ corruptions, where $n$ is the total number of parties; * Are *complete*, in the sense that they guarantee that if any honest party receives their share then all honest parties receive their shares; * Employ *batching* techniques, whereby a dealer shares many secrets in parallel, and achieves an amortized communication complexity that is linear in $n$, at least on the "happy path", where no party *provably* misbehaves.

Gadget decomposition is widely used in lattice based cryptography, especially homomorphic encryption (HE) to keep the noise growth slow. If it is randomized following a subgaussian distribution, it is called subgaussian (gadget) decomposition which guarantees that we can bound the noise contained in ciphertexts by its variance. This gives tighter and cleaner noise bound in average case, instead of the use of its norm. Even though there are few attempts to build efficient such algorithms, most of them are still not practical enough to be applied to homomorphic encryption schemes due to somewhat high overhead compared to the deterministic decomposition. Furthermore, there has been no detailed analysis of existing works. Therefore, HE schemes use the deterministic decomposition algorithm and rely on a Heuristic assumption that every output element follows a subgaussian distribution independently. In this work, we introduce a new practical subgaussian gadget decomposition algorithm which has the least overhead (less than 14\%) among existing works for certain parameter sets, by combining two previous works. In other words, we bring an existing technique based on an uniform distribution to a simpler and faster design (PKC' 22) to exploit parallel computation, which allows to skip expensive parts due to pre-computation, resulting in even simpler and faster algorithm. When the modulus is large (over 100-bit), our algorithm is not always faster than the other similar work. Therefore, we give a detailed comparison, even for large modulus, with all the competitive algorithms for applications to choose the best algorithm for their choice of parameters.

Anonymous message delivery, as in private communication and privacy-preserving blockchain applications, ought to protect recipient metadata: a message should not be inadvertently linkable to its destination. But how can messages then be delivered to each recipient, without each recipient scanning all messages? Recent work constructed Oblivious Message Retrieval (OMR) protocols that outsource this job to untrusted servers in a privacy-preserving manner. We consider the case of group messaging, where each message may have multiple recipients (e.g., in a group chat or blockchain transaction). Direct use of prior OMR protocols in the group setting increases the servers' work linearly in the group size, rendering it prohibitively costly for large groups. We thus devise new protocols where the servers' cost grows very slowly with the group size, while recipients' cost is low and independent of the group size. Our approach uses Fully Homomorphic Encryption and other lattice-based techniques, building on and improving on prior work. The efficient handling of groups is attained by encoding multiple recipient-specific clues into a single polynomial or multilinear function that can be efficiently evaluated under FHE, and via preprocessing and amortization techniques. We formally study several variants of Group Oblivious Message Retrieval (GOMR) and describe corresponding GOMR protocols. Our implementation and benchmarks show, for parameters of interest, cost reductions of orders of magnitude compared to prior schemes. For example, the servers' cost is ${\sim}\$3.36$ per million messages scanned, where each message may address up to $15$ recipients.

Recent work on dynamic structured and searchable symmetric encryption has focused on achieving the notion of forward-privacy. This is mainly motivated by the claim that forward-privacy protects against adaptive file injection attacks (Zhang, Katz, Papamanthou, Usenix Security, 2016). In this work, we revisit the notion of forward-privacy in several respects. First, we observe that forward-privacy does not necessarily guarantee security against adaptive file injection attacks if a scheme reveals other leakage patterns like the query equality. We then propose a notion of security called correlation security which generalizes forward privacy. We then show how correlation security can be used to formally define security against different kinds of injection attacks. We then propose the first injection-secure multi-map encryption encryption scheme and use it as a building block to design the first injection-secure searchable symmetric encryption (SSE) scheme; which solves one of the biggest open problems in the field. Towards achieving this, we also propose a new fully-dynamic volume-hiding multi-map encryption scheme which may be of independent interest.

Implementation of Fully Homomorphic Encryption (FHE) is challenging. Especially when considering hardware acceleration, the major performance bottleneck is data transfer. Here we propose an algebraic framework called Heterogenous Lattice Graph (HLG) to build and process computing graphs in Residue Number System (RNS), which is the basis of high performance implementation of mainstream FHE algorithms. There are three main design goals for HLG framework: • Design a dedicated IR (HLG IR) for RNS system, here splitting and combination of data placeholders has practical implications in an algebraic sense. Existing IRs cannot efficiently support these operations. • Lower the technical barriers for both crypto researchers and hardware engineers by decoupling front-end cryptographic algorithms from the back-end hardware platforms. The algorithms and solutions built on HLG framework can be written once and run everywhere. Researchers and engineers don’t need to understand each other. • Try to reduce the cost of data transfer between CPU and GPU/FPGA/dedicated hardware, by providing the intermediate representation (IR) of the computing graph for hardware compute engine, which allows task scheduling without help from CPU. We have implemented CKKS algorithm based on HLG framework, together with a compute engine for multiple CPU cores. Experiment shows that we can outperform SEAL v3 Library in several use cases in multi-threading scenarios.

This report addresses the development of a pseudo random bit generator (PRBG) for constraint silicon devices. NIST.SP800-22 "Statistical test suite for Pseudo Random Generators" suggests a suite of tests that can confirm or deny the randomness of a given bit sequence. However, although providing a “pass / fail” criteria for the property of randomness of an arbitrary sequence, it is hard to get from the NIST suite the sense for the “level of randomness” for a given sequence, a measure that is sometimes required for the development process of PRBG. This post suggests a tool that can measure randomness, and therefore allows gradual changes in the PRBG algorithm, that helps trading power / time / area constraints versus quantifiable measure of the resulting randomness. Keywords: Binomial distribution, commutative distribution function (CDF), PRBG, Bernoulli density

Garbled circuits are a fundamental cryptographic primitive that allows two or more parties to securely evaluate an arbitrary Boolean circuit without revealing any information beyond the output using a constant number of communication rounds. Garbled circuits have been introduced by Yao (FOCS’86) and generalized to the multi-party setting by Beaver, Micali and Rogaway (STOC’90). Since then, several works have improved their efficiency by providing different garbling schemes and several implementations exist. Starting with the seminal Fairplay compiler (USENIX Security’04), several implementation frameworks decoupled the task of compiling the function to be evaluated into a Boolean circuit from the engine that securely evaluates that circuit, e.g., using a secure two-party computation protocol based on garbled circuits. In this paper, we show that this decoupling of circuit generation and evaluation allows a subtle attack on several prominent garbling schemes. It occurs when violating the implicit assumption on the circuit that gates have different input wires which is most often not explicitly specified in the respective papers. The affected garbling schemes use separate calls to a deterministic encryption function for the left and right input wire of a gate to derive pseudo-random encryption pads that are XORed together. When a circuit contains a gate where the left and right input wire are the same, these two per-wire encryption pads cancel out and we demonstrate that this can result in a complete break of privacy. We show how the vulnerable garbling schemes can be fixed easily.

In this paper, we explore the feasibility of reliable and private communication in dynamic networks, where in each round the adversary can choose which direct peer-to-peer links are available in the network graph, under the sole condition that the graph is k-connected at each round (for some k). We show that reliable communication is possible in such a dynamic network if and only if k > 2t. We also show that if k = cn > 2t for a constant c, we can achieve reliable communication with polynomial round and communication complexity. For unconditionally private communication, we show that for a passive adversary, k > t is sufficient (and clearly necessary). For an active adversary, we show that k > 2t is sufficient for statistical security (and clearly necessary), while k > 3t is sufficient for perfect security. We conjecture that, in contrast to the static case, k > 2t is not enough for perfect security, and we give evidence that the conjecture is true. Once we have reliable and private communication between each pair of parties, we can emulate a complete network with secure channels, and we can use known protocols to do secure computation.

It is a long-standing open problem whether the Minimum Circuit Size Problem ($\mathrm{MCSP}$) and related meta-complexity problems are NP-complete. Even for the rare cases where the NP-hardness of meta-complexity problems are known, we only know very weak hardness of approximation. In this work, we prove NP-hardness of approximating meta-complexity with nearly-optimal approximation gaps. Our key idea is to use *cryptographic constructions* in our reductions, where the security of the cryptographic construction implies the correctness of the reduction. We present both conditional and unconditional hardness of approximation results as follows. $\bullet$ Assuming subexponentially-secure witness encryption exists, we prove essentially optimal NP-hardness of approximating conditional time-bounded Kolmogorov complexity ($\mathrm{K}^t(x \mid y)$) in the regime where $t \gg |y|$. Previously, the best hardness of approximation known was a $|x|^{1/ \mathrm{poly}(\log \log |x|)}$ factor and only in the sublinear regime ($t \ll |y|$). $\bullet$ Unconditionally, we show near-optimal NP-hardness of approximation for the Minimum Oracle Circuit Size Problem (MOCSP), where Yes instances have circuit complexity at most $2^{\varepsilon n}$, and No instances are essentially as hard as random truth tables. Our reduction builds on a witness encryption construction proposed by Garg, Gentry, Sahai, and Waters (STOC'13). Previously, it was unknown whether it is NP-hard to distinguish between oracle circuit complexity $s$ versus $10s\log N$. $\bullet$ Finally, we define a "multi-valued" version of $\mathrm{MCSP}$, called $\mathrm{mvMCSP}$, and show that w.p. $1$ over a random oracle $O$, $\mathrm{mvMCSP}^O$ is NP-hard to approximate under quasi-polynomial-time reductions with $O$ oracle access. Intriguingly, this result follows almost directly from the security of Micali's CS proofs (Micali, SICOMP'00). In conclusion, we give three results convincingly demonstrating the power of cryptographic techniques in proving NP-hardness of approximating meta-complexity.

Gradient Boosting Decision Tree (GBDT) and its variants are widely used in industry, due to their strong interpretability. Secure multi-party computation allows multiple data owners to compute a function jointly while keeping their input private. In this work, we present Squirrel, a two-party GBDT training framework on a vertically split dataset, where two data owners each hold different features of the same data samples. Squirrel is private against semi-honest adversaries, and no sensitive intermediate information is revealed during the training process. Squirrel is also scalable to datasets with millions of samples even under a Wide Area Network (WAN). Squirrel achieves its high performance via several novel co-designs of the GBDT algorithms and advanced cryptography. Especially, 1) we propose a new and efficient mechanism to hide the sample distribution on each node using oblivious transfer. 2) We propose a highly optimized method for gradient aggregation using lattice-based homomorphic encryption (HE). Our empirical results show that our method can be three orders of magnitude faster than the existing HE approaches. 3) We propose a novel protocol to evaluate the sigmoid func- tion on secretly shared values, showing 19×-200×-fold im- provements over two existing methods. Combining all these improvements, Squirrel costs less than 6 seconds per tree on a dataset with 50 thousands samples which outperforms Pivot (VLDB 2020) by more than 28×. We also show that Squirrel can scale up to datasets with more than one million samples, e.g., about 170 seconds per tree over a WAN.

A line of recent work has highlighted the importance of context commitment security, which asks that authenticated encryption with associated data (AEAD) schemes will not decrypt the same adversarially-chosen ciphertext under two different, adversarially-chosen contexts (secret key, nonce, and associated data). Despite a spate of recent attacks, many open questions remain around context commitment; most obviously nothing is known about the commitment security of important schemes such as CCM, EAX, and SIV. We resolve these open questions, and more. Our approach is to, first, introduce a new framework that helps us more granularly define context commitment security in terms of what portions of a context are adversarially controlled. We go on to formulate a new notion, called context discoverability security, which can be viewed as analogous to preimage resistance from the hashing literature. We show that unrestricted context commitment security (the adversary controls all of the two contexts) implies context discoverability security for a class of schemes encompassing most schemes used in practice. Then, we show new context discovery attacks against a wide set of AEAD schemes, including CCM, EAX, SIV, GCM, and OCB3, and, by our general result, this gives new unrestricted context commitment attacks against them. Finally, we consider restricted context commitment security for the original SIV mode, for which no prior attack techniques work (including our context discovery based ones). We are nevertheless able to give a novel $O(2^{n/3})$ attack using Wagner's k-tree algorithm for the generalized birthday problem.

Recent work in the design of rate $1 - o(1)$ lattice-based cryptosystems have used two distinct design paradigms, namely replacing the noise-tolerant encoding $m \mapsto (q/2)m$ present in many lattice-based cryptosystems with a more efficient encoding, and post-processing traditional lattice-based ciphertexts with a lossy compression algorithm, using a technique very similar to the technique of ``vector quantization'' within coding theory. We introduce a framework for the design of lattice-based encryption that captures both of these paradigms, and prove information-theoretic rate bounds within this framework. These bounds separate the settings of trivial and non-trivial quantization, and show the impossibility of rate $1 - o(1)$ encryption using both trivial quantization and polynomial modulus. They furthermore put strong limits on the rate of constructions that utilize lattices built by tensoring a lattice of small dimension with $\mathbb{Z}^k$, which is ubiquitous in the literature. We additionally introduce a new cryptosystem, that matches the rate of the highest-rate currently known scheme, while encoding messages with a ``gadget'', which may be useful for constructions of Fully Homomorphic Encryption.