In recent years, Industrial Internet of Things (IIoT) technologies based on group information sharing have been widely applied in industrial manufacturing and global trade due to their real-time, secure, and interoperable characteristics. However, most of these technologies rely on group key negotiation protocols, which suffer from drawbacks such as high overhead, weak security, and low scalability. Therefore, designing secure and efficient group key negotiation protocols has become a scientific challenge that needs to be addressed. In this paper, a fully structured group key negotiation protocol is proposed using the mathematical structure of balanced incomplete block designs and an elliptic curve Qu-Vanstone (ECQV) authentication protocol. Firstly, to reduce the computational overhead of the protocol, the ECQV authentication protocol is utilized to avoid performing pairing operations. Then, to prove the security of the protocol, security proofs are conducted based on the elliptic curve decisional Diffie–Hellman assumption. Lastly, to reduce the communication overhead and improve the scalability of the protocol, an extension to existing group key negotiation protocols is proposed using asymmetric balanced incomplete block designs, increasing the supported number of members from https://www.w3.org/1998/Math/MathML" display="inline"> q 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003466284/c64b8b66-5b04-4d90-b345-58effd21948c/content/math6_1.tif "/> to https://www.w3.org/1998/Math/MathML" display="inline"> q 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003466284/c64b8b66-5b04-4d90-b345-58effd21948c/content/math6_2.tif "/> and https://www.w3.org/1998/Math/MathML" display="inline"> q 2 + q + 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003466284/c64b8b66-5b04-4d90-b345-58effd21948c/content/math6_3.tif "/> . Experimental results demonstrate that the proposed protocol can reduce computational overhead to https://www.w3.org/1998/Math/MathML" display="inline"> O n n m https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003466284/c64b8b66-5b04-4d90-b345-58effd21948c/content/math6_4.tif "/> and communication overhead to https://www.w3.org/1998/Math/MathML" display="inline"> O n n https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003466284/c64b8b66-5b04-4d90-b345-58effd21948c/content/math6_5.tif "/> . The protocol ensures resistance against chosen plaintext attacks while allowing flexible adaptation of the number of participants in group key negotiation protocols, thereby enhancing both the security and efficiency of the protocol.
In the Internet of Things (IoT) environment, more types of devices than ever before are connected to the internet to provide IoT services. Smart devices are becoming more intelligent and improving performance, but there are devices with little computing power and low storage capacity. Devices with limited resources will have difficulty applying existing public key cryptography systems to provide security. Therefore, communication protocols for various kinds of participating devices should be applicable in the IoT environment, and these protocols should be lightened for resources-restricted devices. Security is an essential element in the IoT environment, so for secure communication, it is necessary to perform authentication between the communication objects and to generate the session key. In this paper, we propose two kinds of lightweight authentication and key agreement schemes to enable fast and secure authentication among the objects participating in the IoT environment. The first scheme is an authentication and key agreement scheme with limited resource devices that can use the elliptic curve Qu-Vanstone (ECQV) implicit certificate to quickly agree on the session key. The second scheme is also an authentication and key agreement scheme that can be used more securely, but slower than first scheme using certificateless public key cryptography (CL-PKC). In addition, we compare and analyze existing schemes and propose new schemes to improve security requirements that were not satisfactory.
The n -puzzle is a classical problem for modeling algorithms. For n -puzzle there are https://www.w3.org/1998/Math/MathML" display="inline"> n + 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_1.tif "/> different objects: n cells and one empty cell. Each object can be coded by https://www.w3.org/1998/Math/MathML" display="inline"> ρ = ⌈ log 2 n + 1 ⌉ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_2.tif "/> qubits and a configuration of https://www.w3.org/1998/Math/MathML" display="inline"> n + 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_3.tif "/> objects can be represented by a register of https://www.w3.org/1998/Math/MathML" display="inline"> z := ρ ⋅ ( n + 1 ) https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_4.tif "/> qubits https://www.w3.org/1998/Math/MathML" display="inline"> | x ⟩ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_5.tif "/> . The function https://www.w3.org/1998/Math/MathML" display="inline"> g ( x ) https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_6.tif "/> is represented a unitary operator T . T acts on the https://www.w3.org/1998/Math/MathML" display="inline"> z + 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_7.tif "/> qubits with https://www.w3.org/1998/Math/MathML" display="inline"> x ∈ B z https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_8.tif "/> and https://www.w3.org/1998/Math/MathML" display="inline"> c ∈ B 1 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_9.tif "/> https://www.w3.org/1998/Math/MathML" display="block"> T ⋅ | x ⟩ | c ⟩ = | x ⟩ | f ( x ) ⊕ c ⟩ . https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003374404/4745344c-4074-4386-85e6-ca8a3849de1f/content/math10_10.tif "/>
In this chapter, the simplest quantum measurement situation, i.e., where the state is an eigenvector of the observable to be measured, is considered. The states are therefore non-superimposed and measurement Axiom 3.2 of Section 13.7 in the previous chapter is applicable. We consider states in https://www.w3.org/1998/Math/MathML" display="inline"> ℂ 2 , ℂ 2 ⊗ ℂ 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math14_1.tif "/> and https://www.w3.org/1998/Math/MathML" display="inline"> ℂ 2 ⊗ ℂ 2 ⊗ ℂ 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math14_2.tif "/> . The generalisation to https://www.w3.org/1998/Math/MathML" display="inline"> ⊗ n ℂ 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003264569/7139ce19-0d58-4a0c-820f-b76fb033e438/content/math14_3.tif "/> is then clear.
The IoT-enabled Smart Grid uses IoT smart devices to collect the private electricity data of consumers and send it to service providers over the public network, which leads to some new security problems. To ensure the communication security in a smart grid, many researches are focusing on using authentication and key agreement protocols to protect against cyber attacks. Unfortunately, most of them are vulnerable to various attacks. In this paper, we analyze the security of an existent protocol by introducing an insider attacker, and show that their scheme cannot guarantee the claimed security requirements under their adversary model. Then, we present an improved lightweight authentication and key agreement protocol, which aims to enhance the security of IoT-enabled smart grid systems. Furthermore, we proved the security of the scheme under the real-or-random oracle model. The result shown that the improved scheme is secure in the presence of both internal attackers and external attackers. Compared with the original protocol, the new protocol is more secure, while keeping the same computation efficiency. Both of them are 0.0552 ms. The communication of the new protocol is 236 bytes, which is acceptable in smart grids. In other words, with similar communication and computation cost, we proposed a more secure protocol for smart grids.
The Industrial Internet of Things (IIoT) is the application of the Internet of Things (IoT) in the industrial field. IIoT allows users to remotely access industrial equipment and the data in it, which also brings certain challenges to the security of industrial data. Authentication and key agreement protocols are very effective security technologies in the matter of protecting industrial data. There is a large amount of research work on authentication protocols in IIoT, but most of the protocols have security weaknesses. Recently, Rafique et al. proposed a multi-factor protocol in IIoT that can accomplish authentication and session key establishment through a gateway. Rafique et al. claimed that their protocol is secure, unfortunately, we carefully analyze the protocol of Rafique et al. and find some security flaws, i.e., it is vulnerable to insider attack and known session-specific temporary information (KSSTI) attack, and unable to provide forward security. We explore the factors of insecurity and propose an enhanced multi-factor secure authentication and key agreement protocol in IIoT. The new protocol improves the security of the protocol while using only symmetric cryptography, hash function, and XOR operation. Formal security analysis and informal security discussions demonstrate that the new protocol is resistant to a variety of known attacks. After performance analysis, our protocol has lower computational cost, and increases no significant communication cost, while providing more secure and robust properties.
In this chapter we are going to explicitly identify the parameter, t , from Chapter 4 as a continuous variable that corresponds to time in a physical system. This will enable us to show how natural number dynamics can be converted into Hamiltonian form and thus develop dynamical equations that can be applied to physical systems, that form the basis for standard quantum mechanics. It is instructive to begin with a single category system with n items. We will take the system to be bosonic so that n can be any natural number. We then simply parameterize the variable ξ with t , as we did for the multi-category case, by writing https://www.w3.org/1998/Math/MathML" display="inline"> ξ = ω 0 t https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377504/0865e0f9-b6f9-4666-9620-3b3ea10ce510/content/math5_1.tif "/> , where ω 0 , is a constant angular frequency. Eq. (3.14) can then be transformed into a time evolution S-type equation applied to an eigenfunction, https://www.w3.org/1998/Math/MathML" display="inline"> Φ n https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377504/0865e0f9-b6f9-4666-9620-3b3ea10ce510/content/math5_2.tif "/> of the operator https://www.w3.org/1998/Math/MathML" display="inline"> N ^ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377504/0865e0f9-b6f9-4666-9620-3b3ea10ce510/content/math5_3.tif "/> . Comparing the result with Eq. (4.9) , one then gets 5.1 https://www.w3.org/1998/Math/MathML" display="block"> i d Φ n d t = Ω ^ Φ n = ω 0 N ^ Φ n , https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003377504/0865e0f9-b6f9-4666-9620-3b3ea10ce510/content/math5_4.tif "/>