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# Attribute-Based Authentication Scheme from Partial Encryption for Lattice with Short Key

School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen, 333403, China

* Corresponding Author: Shuhua Wang. Email:

*Computers, Materials & Continua* **2023**, *75*(1), 67-80. https://doi.org/10.32604/cmc.2023.035337

**Received** 17 August 2022; **Accepted** 13 October 2022; **Issue published** 06 February 2023

## Abstract

Wireless network is the basis of the Internet of things and the intelligent vehicle Internet. Due to the complexity of the Internet of things and intelligent vehicle Internet environment, the nodes of the Internet of things and the intelligent vehicle Internet are more vulnerable to malicious destruction and attacks. Most of the proposed authentication and key agreement protocols for wireless networks are based on traditional cryptosystems such as large integer decomposition and elliptic curves. With the rapid development of quantum computing, these authentication protocols based on traditional cryptography will be more and more threatened, so it is necessary to design some authentication and key agreement protocols that can resist quantum attacks. In this paper, an anti-quantum authentication scheme for wireless networks based on lattice cryptosystem is constructed. In the attribute-based authentication scheme, the length of the authenticated public-private key pair depends on the maximum order and complexity of the formula in the algorithm. In the attribute-based authentication scheme, there is a certain correlation between the authenticated data and the attribute value of the user in the scheme. We show that the attribute-based authentication scheme gives an attribute-based with smaller public-private key pairs. The security of the attribute-based authentication scheme is based on the sub-exponential hard problem of the LWE (Learning With Errors). The*Q*-

*poly*made by the adversary in the scheme, and our attribute-based authentication scheme guarantees that private data about user attributes and ciphertext cannot be obtained by malicious attackers.

## Keywords

There are many attributes-based authentication schemes proposed in protocols related to wireless networks and information security, such as references [1–4]. However, most of the proposed authentication and key agreement protocols for wireless networks are based on traditional cryptosystems such as large integer decomposition and elliptic curves. With the rapid development of quantum computing, these authentication protocols based on traditional cryptography will be more and more threatened. These attribute-based authentication schemes will not be secure in the post-quantum era. At present, the widely used anti-quantum cryptosystem is an anti-quantum algorithm based on lattice cryptosystem and coding-related problems. With the rapid development of quantum computer, the anti-quantum algorithm based on lattice cryptosystem will attract more researchers. For the related security protocols based on lattice cryptosystem [5–7], the anti-quantum performance of the protocols is based on the related difficult problems such as the shortest vector and learning with errors in a lattice-based cryptosystem. The authentication and key agreement protocol based on lattice cryptosystem can also resist various threats brought by quantum computers in the post-quantum era, and can ensure the security of wireless networks, which is a hot issue in anti-quantum algorithms [8–15]. The difficult problem of a lattice-based cryptosystem is that it plays a key role in information security in wireless networks in the future quantum era [16–18]. Based on the difficult problems of lattice-based cryptosystem, many fully homomorphic encryption schemes [19–24] and public-key encryption schemes [25–27] are presented.

In the past decade, many schemes of anti-quantum authentication and security protocols based on the difficult problems of lattice cryptosystem have been proposed [28–34]. In 2016, Bansarkhani et al. [5]. Based on lattice cryptosystem, a new anti-quantum authentication signature protocol is proposed, and the authentication protocol is applied to block chain security. In 2018, Behina et al. [35]. From the difficult problem of lattice-based cryptosystem, an effective key searchable security authentication scheme is proposed, the key searchable security authentication scheme uses a new strategy to search keywords such as keys. In 2019, Fukumitsu et al. [7]. Based on the difficulty of lattice cryptosystem, a secure and efficient authentication signature protocol is proposed, which is proved to be secure in the random model, which is a three-round scheme with the public key aggregation with the security proof, A group signatures scheme without NIZK (Non-Interactive Zero Knowledge) base on lattice was designed [36], but this group signatures scheme requires a combination of attribute-based encryption and signatures. Ma et al. [10]. Based on lattice cipher, an effective anti-quantum authentication signature protocol for blockchains is proposed, which is a four-round scheme with the key aggregation and Tso et al. [12]. An effective anti-quantum blind signature protocol based on attributes from lattices is proposed, which is the attribute-based signature. In 2020, Kansal et al. [9]. Based on the difficulty of lattice cryptosystem, an effective anti-quantum authentication signature scheme is proposed, which is a round optimal secure authentication scheme. In 2020, Sun et al. [37]. Proposed an effective anti-quantum lattice cipher group signature authentication protocol based on zero knowledge proofs. Canard et al. [38]. Proposed an anti-quantum group signature authentication protocol with secure data fixed length based on lattice cryptosystem. The protocol is proved to be secure under the standard model. In 2020, Doss et al. [39]. Proposed a secure and effective meme optimization method based on lattice public key cryptosystem, which is used to transmit important medical privacy information in block chain and the internet of things that can resist the key exchange. The application of the attribute-based authentication scheme also includes hierarchical electronic voting for multiple regions, robust reversible audio watermarking for telemedicine and privacy protection, and much more [40]. At present, many scholars are studying anti-quantum secure signature and authentication protocols based on lattice cryptosystem, such as the quantum-resistant batch verifiable data privacy security authentication protocol of VANETs (Vehicular Ad Hoc Networks) using lattice [8].

Hence, it is of great significance to construct a secure authentication protocol based on the difficult problem of lattice cryptosystem. In this paper, an effective attribute-based authentication protocol is proposed, which supports full homomorphic encryption of information. The length of the public-private key pair in this protocol is short, and the corresponding computational overhead is reduced.

The general definition in these lattices can be expressed as: randomly select a prime number

Definition 1 (

where

Connection with lattices. Suppose

There is a C-bounded Gaussian distribution

Lemma 1 ([31])

Randomly select the matrixes C in

Suppose

Lemma 2 ([31])

Randomly select the matrixes C in

Suppose

Lemma 3 [29]

1.

2.

3 Attribute-Based Authentication Scheme

Based on the partial hidden predicate encryption protocol based on the difficult problem of lattice cryptosystem, a new attribute-based anti-quantum authentication protocol (

In the section, it is proposed that the public key, common parameter, and master key of all users are generated by the algorithm

1. Randomly select some important parameters

2. Choose some important random matrices:

3. Sampling matrix with algorithm

4. The algorithm outputs some parameters and the most important core key of the scheme:

The private key of the scheme for the user is generated using those public parameters generated above, where

1. Compute the parameter

2. Sample a random subset

3. Sampling the key with algorithm

4. Let

Take Alice and Bob as an example, Alice and Bob are necessary to authenticate each other before finally generating a symmetric key for communication, which is jointly generated by the Alice private attributes

1. Sample a Gaussian parameter

2. Choose a security hash function

3. Compute the message

4. Select a parameter b, and set

5. Random sampling t matrices

6. Random sampling l matrices

7. Finally, out the encrypted ciphertext

1. Based on these parameters

2. Compute:

3. If

Then set

4. Compute the partial communication key associated with Alice:

The partial communication key associated with the Bob negotiation process is as follows: Alice uses the hash function

1. Sample a Gaussian parameter

2. Compute the message

3. Select a parameter

4. Random sampling t matrices

5. Random sampling l matrices

6. Choose a hash algorithm

7. Compute the symmetric communication key with Bob:

8. Out the ciphertext

1. Using

2. Compute

3. Round computes each datum of

Then set

4. Compute the partial communication key associated with Bob:

5. Compute the symmetric communication key with Bob:

Finally, the whole attribute-based authentication Scheme is over, and Alice and Bob can communicate securely with the authentication symmetric key

The correctness of Alice to Bob’s partial authentication in the

If

Compute

If the first

Otherwise, if

Therefore, with overwhelming probability from the No.1 to No.

The security of Bob to Alice’s other partial authentication in the

So, the symmetric communication key of Bob and Alice is:

The specific process of the security of Alice to Bob’s partial authentication in the

Proof. First, we describe the auxiliary evaluation algorithms of the proof.

1. Sampling matrix with algorithm

2. Random sample l parameters

3. Random sample t parameters

4. Random choose some subsets

5. Sample some random matrices

6. Sample the private key

7. Output necessary public key of our scheme as

And the most important core key of our scheme as

1. Sample a Gaussian parameter

2. Select a parameter

3. Compute the

4. Random sampling t matrices

5. Final output the encrypted ciphertext

1. Compute the key corresponding to

2. We know that

1) A

Let

Therefore that:

Return

2) The

Now, we describe a sim algorithm, which claims that the result of the real algorithm is indistinguishable from game simulation through the following hybrids.

(1). The first case that satisfies indistinguishable situation is the following two simulation algorithm:

Algorithm 0: The realistic simulation.

Algorithm 1: The simulation

(2). The second case that satisfies indistinguishable situation is the following two simulation algorithm:

Algorithm 1: This algorithm is the same as algorithm 1 in the first case.

Algorithm 2: The game simulation

(3). The third case that satisfies indistinguishable situation is the following two simulation algorithm:

Algorithm 2: This algorithm is the same as algorithm 2 in the second case.

Algorithm 3: The game simulation

(4). The fourth case that satisfies indistinguishable situation is the following two simulation algorithm:

Algorithm 3: This algorithm is the same as algorithm 3 in the third case.

Algorithm 4: The algorithm

(5). The fifth case that satisfy indistinguishable situation is the following two simulation algorithm:

Algorithm 4: This algorithm is the same as algorithm 4 in the fourth case.

Algorithm 5: The game simulation

(6). The sixth case that satisfy indistinguishable situation is the following two ism algorithm:

Algorithm 5: This algorithm is the same as algorithm 5 in the fifth case.

Algorithm 6: The game simulation

(7). The seventh case that satisfy indistinguishable situation is the following two ism algorithm:

Algorithm 6: This algorithm is the same as algorithm 6 in the sixth case.

Algorithm 7: The game simulation

A detailed proof of indistinguishability (1) –(7) is provided in the references [23,29]. The security of Bob with Alice's other partial authentication in the

Next, we compare our attribute-based authentication scheme with other related secret key schemes [6,13,14,22]. We mainly focus on the computational costs, storage overhead, and several security properties.

As depicted in Table 1, we compare the storage overhead and other related secret key schemes. The public key parameter' size is

In Table 2, the SM represents the standard model, and the SCPA represents the selective chosen plaintext attack, the NTRU represents the number theory research unit, and the CVP represents the closest vector problem. We compare the security properties and other related secret key schemes, according to the Table 1, Li et al. [13] is more effectivie than our attribute-based authentication scheme over lattice in terms of computational storage, which is based on NTRU lattice, so it lacks provable security. Gentry et al. [22], Wang et al. [14] and Brakerski et al. [6] Schemes are slightly weaker than our attribute-based authentication scheme over lattice in terms of computational complexity and storage. Moreover, our scheme is based on partially hiding predicate encryption, so the key size is also efficient, and our scheme is provably security of

Based on the

Funding Statement: This work was supported by the Special Project for Scientific and Technological Cooperation of Jiangxi Province [no. 20212BDH80021].

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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## Cite This Article

W. Yu and S. Wang, "Attribute-based authentication scheme from partial encryption for lattice with short key,"*Computers, Materials & Continua*, vol. 75, no.1, pp. 67–80, 2023.