Contrastive learning is a powerful technique for discovering meaningful data representations by optimizing objectives based on $\textit{contrastive information}$, often given as a set of weighted triplets $\{(x_i, y_i^+, z_{i}^-)\}_{i = 1}^m$ indicating that an "anchor" $x_i$ is more similar to a "positive" example $y_i$ than to a "negative" example $z_i$. The goal is to find representations (e.g., embeddings in $\mathbb{R}^d$ or a tree metric) where anchors are placed closer to positive than to negative examples. While finding $\textit{global}$ optima of contrastive objectives is $\mathsf{NP}$-hard, the complexity of finding $\text{\textit{local}}$ optima---representations that do not improve by local search algorithms such as gradient-based methods---remains open. Our work settles the complexity of finding local optima in various contrastive learning problems by proving $\mathsf{PLS}$-hardness in discrete settings (e.g., maximize satisfied triplets) and $\mathsf{CLS}$-hardness in continuous settings (e.g., minimize Triplet Loss), where $\mathsf{PLS}$ (Polynomial Local Search) and $\mathsf{CLS}$ (Continuous Local Search) are well-studied complexity classes capturing local search dynamics in discrete and continuous optimization, respectively. Our results imply that no polynomial time algorithm (local search or otherwise) can find a local optimum for various contrastive learning problems, unless $\mathsf{PLS}\subseteq\mathsf{P}$ (or $\mathsf{CLS}\subseteq \mathsf{P}$ for continuous problems). Even in the unlikely scenario that $\mathsf{PLS}\subseteq\mathsf{P}$ (or $\mathsf{CLS}\subseteq \mathsf{P}$), our reductions imply that there exist instances where local search algorithms need exponential time to reach a local optimum, even for $d=1$ (embeddings on a line).

Abstract Precise forecasting of photovoltaic (PV) power generation upholds flexibility and reliability within the power grid. Due to the data security dilemma of previous forecasting methods, federated learning (FL) has been widely studied for its ability to train models without sharing training data. However, the incorrect behavior from untrusted devices and servers in traditional FL frameworks can undermine the integrity of the global model, precipitating inaccurate power generation forecasting. Therefore, we propose a blockchain-enabled trusted Byzantine-robust FL framework, called TBFL, designed for decentralized and privacy-preserving PV power generation forecasting. Specifically, this framework features a trusted supervision mechanism, which can effectively eliminate malicious gradients to achieve a high-quality model. In addition, a multilevel differential privacy scheme is designed to strike a balance between privacy protection and model accuracy. Finally, a model clipping algorithm based on neuronal similarity is implemented to optimize both the duration and consumption associated with local device training. Comprehensive experimental outcomes demonstrate that the framework TBFL can successfully improve robustness, and achieve similar efficiency as FedAvg while maintaining a high forecasting accuracy.

Vehicular ad-hoc networks (VANETs) can help facilitate traffic flow, reduce accidents, and enhance the driving experience. However, VANETs have some problems in terms of the authenticity and integrity of transmitted information and the preservation of vehicles’ privacy. Many certificateless aggregate signature (CLAS) schemes have been proposed to address these concerns. Nevertheless, most of these schemes suffer from security and efficiency challenges, such as the inability to resist forgery attacks and high computation costs. Recently, an efficient CLAS scheme with conditional privacy protection has been put forward by Chen et al. However, there is a security flaw in this scheme. In this paper, we give a specific attack algorithm to indicate that Chen et al.’s proposal cannot resist a public key replacement attack initiated by external adversaries and then put forward a security-enhanced scheme. Furthermore, an efficient invalid signature identification algorithm is designed to identify invalid signatures after an aggregate verification has failed. Through rigorous security analysis, it has been verified that the scheme put forward can satisfy the fundamental security requirements of VANETs. Compared with other related schemes, our proposal improves efficiency while providing privacy and security guarantees for VANETs.

Abstract This paper proposes a new method to find high-probability truncated differentials using matrix muliplication. For Markov cipher with similar round function, suppose that the transition probability matrix of round function is $\mathcal{D}$, then $\mathcal{D}^{r}$ contains all the differential probabilities of an $r$-round block cipher. To reduce the matrix dimension, we consider the word-oriented truncated differential and the truncated transition probability matrix $\mathcal{T}$. Regardless of the effect of the $S$-box, we focus on whether there is a non-zero difference on one cell instead of the value of the difference. In this case, the matrix dimension reduces significantly and we can calculate $\mathcal{T}^{r}$ using a workstation. Then all the $r$-round truncated differential probabilities can be found from $\mathcal{T}^{r}$. And the probability in $\mathcal{T}^{r}$ is the probability of the whole truncated differential hull but not a single or several truncated differential characteristics. Besides, we make a more accurate probability estimation of the truncated differential of lightweight block cipher. Combined with the truncated differential hull, we found some longer truncated differential distinguishers. And as $\mathcal{T}^{r}$ stores all the truncated differential probabilities, we can also find all the impossible truncated differentials.

In 2018, Pott et al. investigated vectorial functions with maximal number of bent components. They found one class of binomial functions attaining the upper bound. They also proposed an open problem regarding monomial functions that have the maximal number of bent components. In this paper, we solve this open problem. Specifically, we prove that if$k\geq 2$, then$x^{s(2^{k}+1)}$are the only monomial functions over$\mathbb {F}_{2^{2k}}$that have the maximal number of bent components, where$s\in \{1, 2, 2^{2}, \ldots, 2^{k-1}\}$. As a consequence, we also solve an open problem of Ness and Helleseth about the cross-correlation function between two sequences in 2006.

We improve Wu and Wang’s method for finding impossible differentials of block cipher structures. This improvement is more general than Wu and Wang’s method where it can find more impossible differentials with less time. We apply it on Gen-CAST256, Misty, Gen-Skipjack, Four-Cell, Gen-MARS, SMS4, MIBS, Camellia⁎ , LBlock, E2, and SNAKE block ciphers. All impossible differentials discovered by the algorithm are the same as Wu’s method. Besides, for the 8-round MIBS block cipher, we find 4 new impossible differentials, which are not listed in Wu and Wang’s results. The experiment results show that the improved algorithm can not only find more impossible differentials, but also largely reduce the search time.

Security concerns of RFID systems engaged a lot of researchers to design and to cryptanalyze RFID mutual authentication protocols. A suitable mutual authentication protocol for an RFID system should provide mutual authentication along with user privacy. In addition, such protocol must be resistant to active and passive attacks, e.g. man-in-the-middle attack, reply attack, reader-/tag-impersonation, denial of service and traceability attack. Among them, tag-impersonation refers to a process that the adversary's tag fools the legitimate reader to authenticate it as a valid tag. In this paper we exam the security of two RFID mutual authentication protocols, i.e., [6] and [17], under tag impersonation attack. We found that these two protocols share a same vulnerability in each session, the tag and the reader generates a random value respectively and they use the exclusive or (XOR) of those random values in the authentication process. We exploit this vulnerability to present two effective and efficient tag impersonation attacks against these protocols, e.g., the success probabilities of our attacks are "1" and the complexity is at most two runs of each protocol. At last, we exhibit the improved version of these protocols, which are immune from tag impersonation attacks.

The family of WG stream ciphers has good randomness properties. In this paper, we parameterize WG-7 stream cipher for RFID tags, where the modest computation/storage capabilities and the necessity to keep their prices low present a challenging problem that goes beyond the well-studied cryptography. The rigorous security analysis of WG-7 indicates that it is secure against time/memory/data trade off attack, differential attack, algebraic attack, correlation attack and Discrete Fourier Transform (DFT) attack. Furthermore, we offer efficient implementation of WG-7 on the 4-bit microcontroller ATAM893-D and the 8-bit microcontroller ATmega8 from ATmel. The experimental results show that WG-7 outperforms most of previous proposals in terms of throughput and implementation complexity. Moreover, we propose a mutual authentication protocol based on WG-7, which provides the untraceability, resistance of tag impersonation and reader impersonation. With its verified cryptographic properties, low implementation complexity and ideal throughput, WG-7 is a promising candidate for RFID applications.