Quantum technique for access control in cloud computing II: Encryption and key distribution

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Abstract

This is the second paper of the series of papers dealing with access control problems in cloud computing by adopting quantum techniques. In this paper we study the application of quantum encryption and quantum key distribution in the access control problem. We formalize our encryption scheme and protocol for key distribution in the setting of categorical quantum mechanics (CQM). The graphical language of CQM is used in this paper. The quantum scheme/protocol we propose possesses several advantages over existing schemes/protocols proposed in the state of the art for the same purpose. They are informationally secure and implementable by the current technology.

Introduction

This is the second paper of the series of papers dealing with access control problems in cloud computing by adopting quantum technique (Sun et al., submitted for publication). A simple model for the access control problem in cloud computing is shown in Fig. 1. Such a model has three components: data owner, cloud and data user. The data owner places on the cloud the encrypted data (bit or qubits) which the user wants to access. Upon receiving a data access request from the user, the data owner employs an access control policy to decide whether the user should be granted the access. Afterwards, if the access control policy says that the access should be granted to the user, then the data owner sends the corresponding key and a certificate to the user. Finally, the user sends the certificate to the cloud and gets the encrypted data, upon the successful verification of the certificate by the cloud.

In the first paper of this series (Sun et al., submitted for publication), we developed quantum imperative logic as a formal language for the specification of access control policies, which helps the owner in deciding whether to grant access to the user or not. But how to grant certain access to a user? Cryptography offers a convenient tool for solving this problem. Many cryptographic solutions to the access-granting problem have been proposed (Akl and Taylor, 1983, Castiglione et al., 2016a, Castiglione et al., 2016b, Castiglione et al., 2017, Liu et al., 2017a, Liu et al., 2017b). The basic idea is: first encrypt all resource, then assign keys for decryption to those users who are permitted to access. More precisely, suppose we have resources {data1,,datan}. We first use key1,,keyn to encrypt those data. So we have Enckey1(data1),, Enckeyn(datan). Then we assign keyi to a user iff the user is permitted to access datai. Therefore, encryption and key distribution plays a pivotal role in granting access. In this paper, we develop quantum techniques for encryption and key distribution, using the framework of categorical quantum mechanics (CQM).

The structure of the rest of this paper is as follows: we provide some background knowledge on categorical quantum mechanics in Section 2. Then we introduce encryption by complementary observables in Section 3. We present our quantum protocol for key distribution in Section 4. We discuss related works in Section 5 and conclude this paper in Section 6.

Section snippets

Categorical quantum mechanics

Categorical quantum mechanics (Abramsky and Coecke, 2004, Coecke and Perdrix, 2010, Coecke et al., 2011, Coecke et al., 2016, Coecke and Duncan, 2011, Bian and Wang, 2015, Coecke and Kissinger, 2017) concerns the study of quantum computation and quantum foundations using category theory, as well as the graphical language closely related to category theory. Composition of quantum systems in CQM is treated as a primitive connective, which is conveniently described by dagger symmetric monoidal

Encryption by complementary observables

Definition 12

observable structure (Coecke and Duncan, 2011)

An observable structure in a -SMC is a dagger commutative Frobenius algebra (A,m,u) such that mm=1A. Graphically,

An observable structure (A,m,u) induce a self-dual when setting ηA=mu.

Example 6

Consider the object C2 in FinHilb, let

  • 1.

    mz:C2C2C2::{|0|00|1|11

  • 2.

    uz:CC2::1|0+|1

Then Oz=(C2,mz,uz) is an observable structure.

Example 7

For C2 in FinHilb, let

  • 1.

    mx:C2C2C2::{|+|++||

  • 2.

    ux:CC2::1|++|

Then Ox=(C2,mx,ux) is an observable structure.

Example 8

For C2 in FinHilb, let |i=12(|0+i|1) and |i¯=12(

Key distribution: generalized quantum three-pass protocol

A three-pass protocol in cryptography (Massey, 1988) is a protocol which enables one party to securely send a message to a second party by exchanging three encrypted messages. The essential idea of the three-pass protocol is that each party has private keys for encryption and decryption and they use their keys independently, first to encrypt the message, and then to decrypt the message.

Informally, the three-pass protocol for Alice to secretly send an object to Bob works as follows

  • 1.

    Alice puts the

Related work

The quantum one-time pad encryption scheme (Boykin and Roychowdhury, 2003) is probably the most well-known encryption scheme in quantum cryptography. The key space for quantum one-time pad is {I,X,Z,XZ}. While this key space is much like a result of trial and error, our encryption scheme is more systematic and has a deeper theoretic background, besides ensuring the same security as quantum one-time pad.

The first and yet most influential protocol for quantum key distribution is developed by

Conclusion

In this paper we study the application of quantum encryption and quantum key distribution in the access control problem. The quantum scheme/protocol we propose in this paper has various advantages over existing schemes/protocols proposed for the same purpose. They are informationally secure and implementable by the current technology. We remark that implementing quantum cryptographic protocols is much easier than building quantum computers. Many quantum cryptographic protocols have been

Acknowledgment

The names of the authors are ordered anti-alphabetically. Xin Sun is also affilliated with the John Paul II Catholic University of Lublin. Xin Sun and Piotr Kulicki has been supported by the National Science Centre of Poland (BEETHOVEN, UMO-2014/15/G/HS1/04514).

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