There is a growing trend to outsource the inference task of large transformer models to cloud servers. However, this poses a severe threat to users’ private data as they are exposed to cloud servers after uploading. Although several works attempted to provide private inference for transformer models, their hundreds of communication rounds limit the application scenarios. Motivated by the desire to minimize round complexity, we propose CipherFormer, a novel transformer private inference scheme using homomorphic encryption and garbled circuits. We present a protocol for quickly computing homomorphic matrix multiplications. We then modify the attention mechanism and design the corresponding garbled circuits. Furthermore, we show how to use a lightweight attention mechanism and mixed-bitwidth to reduce the inference latency while maintaining accuracy. In comparison with an advanced homomorphic encryption scheme on text classification tasks, our model improves accuracy by 3% to 11% while performing private inference with a 7.7x-11.9x speedup.

Isogeny-based cryptography is famous for its short key size. As one of the most compact digital signatures, SQIsign (Short Quaternion and Isogeny Signature) is attractive among post-quantum cryptography, but it is inefficient compared to other post-quantum competitors because of complicated procedures in the ideal-to-isogeny translation, which is the efficiency bottleneck of the signing phase. In this paper, we recall the current implementation of SQIsign and mainly focus on how to improve the execution of the ideal-to-isogeny translation in SQIsign. Specifically, we demonstrate how to utilize the reduced Tate pairing to save one of the two elliptic curve discrete logarithms. In addition, the efficient implementation of the remainder discrete logarithm computation is explored. We speed up other procedures in the ideal-to-isogeny translation with various techniques as well. It should be noted that our improvements also benefit the performance of key generation and verification in SQIsign. In the instantiation with$ {p_{1973}}$, the improvements lead to a speedup of 5.47%, 8.80% and 25.34% for key generation, signature and verification, respectively.

In recent years, the isogeny-based protocol, namely supersingular isogeny Diffie-Hellman (SIDH) has become highly attractive for its small public key size. In addition, one can utilize several techniques to further compress the public key. However, compared to other post-quantum protocols, the computational cost of SIDH is relatively high, and so is that of its public-key compression. On the other hand, the storage for pairing computation and discrete logarithms to speed up the current implementation of the key compression is somewhat large. In this paper, we mainly improve the performance of public-key compression of SIDH, especially the efficiency and the storage of pairing computation involved. Our experimental results show that the memory requirement for pairing computation is reduced by a factor of about 1.5. Meanwhile, the instantiation of public-key compression of SIDH is$6.95\%--10.44\%$faster than the current state-of-the-art. Although SIKE is broken now, the techniques in this paper may benefit other isogeny-based cryptosystems which are still secure.

With the development of IoT techniques, urban computing has become an emerging topic in academia and industry. The goal of urban computing is to address some issues of urban planning by using the big data generated in urban facilities. The massive trajectory data processing is viewed as an important issue in urban computing. To satisfy the storage and processing requirements of massive trajectory data, a distributed system is usually adopted. However, existing distributed systems face challenges of data locality aware partitioning and various trajectory queries. In this paper, we propose a distributed framework of massive trajectory data analysis based on HBase, to realize spatio-temporal query more effectively. We first design a temporal-based pre-partitioning strategy to improve the performance of data written. Then we develop a Multi-Level Index to speed up the process of spatio-temporal query. Extensive experiments on real trajectory datasets demonstrate that the proposed framework significantly improves efficiency and usability.

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybrid weighted arithmetic mean to the interval-valued intuitionistic fuzzy environments.

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a nonmembership function, and a hesitancy function, is a generalization of a fuzzy set. Various aggregation operators are defined for AIFSs to deal with multicriteria decision-making problems in which there exists a prioritization of criteria. However, these existing intuitionistic fuzzy prioritized aggregation operators are not monotone with respect to the total order on Atanassov’s intuitionistic fuzzy values (AIFVs), which is undesirable. We propose an intuitionistic fuzzy prioritized arithmetic mean based on the Łukasiewicz triangular norm, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a consumer selects a car to illustrate the validity and applicability of the proposed method aggregation operator.

Interval-valued intuitionistic fuzzy preference relation is a useful tool to express decision maker's interval-valued intuitionistic fuzzy preference information over criteria in the process of multi-criteria decision making. How to derive the priority weights from an interval-valued intuitionistic fuzzy preference relation is an interesting and important issue in decision making with interval-valued intuitionistic fuzzy preference relation(s). In this paper, some new concepts such as interval-valued interval fuzzy sets, interval-valued interval fuzzy preference relation and consistent interval-valued intuitionistic fuzzy preference relation, are defined, and the equivalent interval-valued interval fuzzy preference relation of interval-valued intuitionistic fuzzy preference relation is given. Then a method for estimating criteria weights from interval- valued intuitionistic fuzzy preference relations is developed, two numerical examples are provided to illustrate the developed method.

We define some operations over Atanassov's intuitionistic fuzzy sets (AIFSs), such as Einstein intersection, Einstein product, Einstein scalar multiplication and Einstein exponentiation, etc., and then define new concentration and dilation of AIFSs. These definitions will be useful while dealing with various linguistic hedges like “very”, “more or less”, “highly”, “very very” etc., involved in the problems under intuitionistic fuzzy environment. We also prove some propositions and present some examples in this context.

Aggregation of fuzzy information is a new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, which has attracted significant interest from researchers in recent years. In this paper, we treat the intuitionistic fuzzy aggregation operators with the help of Einstein operations. We first introduce some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication. Then, we develop some intuitionistic fuzzy aggregation operators, such as the intuitionistic fuzzy Einstein weighted averaging operator and the intuitionistic fuzzy Einstein ordered weighted averaging operator, which extend the weighted averaging operator and the ordered weighted averaging operator to aggregate Atanassov's intuitionistic fuzzy values, respectively. We further establish various properties of these operators and analyze the relations between these operators and the existing intuitionistic fuzzy aggregation operators. Moreover, we give some numerical examples to illustrate the developed aggregation operators. Finally, we apply the intuitionistic fuzzy Einstein weighted averaging operator to multiple attribute decision making with intuitionistic fuzzy information.

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the decision information in the process of decision making. In this article, we investigate the decision making problems in which all the information provided by the decision maker is expressed as interval type-2 fuzzy decision matrix where each of the elements is characterized by interval type-2 fuzzy set, and the information about attribute weights is partially known, which may be constructed by various forms. We first utilize the average centroid measure to calculate the average centroid of each attribute value and construct the average centroid matrix of the interval type-2 fuzzy decision matrix. Based on the average centroid matrix and the given attribute weight information, we establish some optimization models to determine the weights of attributes. Furthermore, we develop a procedure to identify the best alternative(s). Finally, we give an illustrative example.

Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations. Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. © 2011 Wiley Periodicals, Inc.