A quantum group signature scheme with reusable keys based on four-particle Cluster states

With the continuous development of quantum technology, the quantum signature as an application of quantum cryptography has received great attention. In this paper, we propose a public-key quantum group blind signature scheme based on single-qubit rotations. In this scheme, the group manager generates a public key. Each group member randomly generates his own private key according to the public key. The signer uses his private key and random sequence to generate the signature. The verifier uses the public key to verify the correctness of the quantum signature. The public and private keys can be reused, which simplifies the key management of the signature system. In this scheme, the random sequence is used to enhance the security of the scheme. At the same time, the quantum efficiency is improved by using single-qubit rotations. The security analysis shows that our scheme can ensure the security of the keys, the unforgeability and the non-deniability of the signature.

Host Identity Protocol (HIP) gives cryptographically veriable identities to hosts. These identities are based on public key cryptography and consist of public and private keys. Public keys can be stored, together with corresponding IP addresses, in DNS servers. When entities are negotiating on a HIP connection, messages are signed with private keys and verified with public keys. Even if this system is quite secure, there are some vulnerabilities concerning the authenticity of public keys. We examine various possibilities to derive trust in public parameters. These are DNSSEC, public key certificates (PKI), identity based cryptography (IBE) and certificate-less public key cryptography (CL-PKC). Both IBE and CL-PKC seem to offer better properties than DNSSEC and PKI, but experimental evaluation is needed, before we can make final conclusions.

Host Identity Protocol (HIP) gives cryptographically verifiable identities to hosts. These identities are based on public key cryptography and consist of public and private keys. Public keys can be stored, together with corresponding IP addresses, in DNS servers. When entities are negotiating on a HIP connection, messages are signed with private keys and verified with public keys. Even if this system is quite secure, there is some vulnerability concerning the authenticity of public keys. The authors examine some possibilities to derive trust in public parameters. These are DNSSEC and public key certificates (PKI). Especially, the authors examine how to implement certificate handling and what is the time complexity of using and verifying certificates in the HIP Base Exchange. It turned out that certificates delayed the HIP Base Exchange only some milliseconds compared to the case where certificates are not used. In the latter part of our article the authors analyze four proposed HIP multicast models and how they could use certificates. There are differences in the models how many times the Base Exchange is performed and to what extent existing HIP specification standards must be modified.

The introduction of public key cryptography (PKC) was a critical advance in IT security. In contrast to symmetric key cryptography, it enables confidential communication between entities in open networks, in particular the Internet, without prior contact. Beyond this PKC also enables protection techniques that have no analogue in traditional cryptography, most importantly digital signatures which for example support Internet security by authenticating software downloads and updates. Although PKC does not require the confidential exchange of secret keys, proper management of the private and public keys used in PKC is still of vital importance: the private keys must remain private, and the public keys must be verifiably authentic. So understanding so-called public key infrastructures (PKIs) that manage key pairs is at least as important as studying the ingenious mathematical ideas underlying PKC. In this book the authors explain the most important concepts underlying PKIs and discuss relevant standards, implementations, and applications. The book is structured into chapters on the motivation for PKI, certificates, trust models, private keys, revocation, validity models, certification service providers, certificate policies, certification paths, and practical aspects of PKI. This is a suitable textbook for advanced undergraduate and graduate courses in computer science, mathematics, engineering, and related disciplines, complementing introductory courses on cryptography. The authors assume only basic computer science prerequisites, and they include exercises in all chapters and solutions in an appendix. They also include detailed pointers to relevant standards and implementation guidelines, so the book is also appropriate for self-study and reference by industrial and academic researchers and practitioners.

Chapter 9 - Public Key Algorithms

In this paper we propose three public key BE schemes that have efficient complexity measures. The first scheme, called the BE-PI scheme, has O(r) header size, O(1) public keys and O(logN) private keys per user, where r is the number of revoked users. This is the first public key BE scheme that has both public and private keys under O(logN) while the header size is O(r). These complexity measures match those of efficient secret key BE schemes.Our second scheme, called the PK-SD-PI scheme, has O(r) header size, O(1) public key and O(log2 N) private keys per user. They are the same as those of the SD scheme. Nevertheless, the decryption time is remarkably O(1). This is the first public key BE scheme that has O(1) decryption time while other complexity measures are kept low. The third scheme, called, the PK-LSD-PI scheme, is constructed in the same way, but based on the LSD method. It has O(r/ε) ciphertext size and O(log1 + ε N) private keys per user, where 0 < ε< 1. The decryption time is also O(1).Our basic schemes are one-way secure against full collusion of revoked users in the random oracle model under the BDH assumption. We can modify our schemes to have indistinguishably security against adaptive chosen ciphertext attacks.KeywordsBroadcast encryptionpolynomial interpolationcollusion

SummaryZigBee is a wireless network technology suitable for applications requiring lower bandwidth, low energy consumption and small packet size. Security has been one of the challenges in ZigBee networks. Public Key Infrastructure (PKI) provides a binding of entities with public keys through a Certifying Authority (CA). Public key cryptography using public–private key pairs can be used for ensuring secure transmission in a network. But large size of public and private keys and memory limitations in ZigBee devices pose a problem for using PKI to secure communication in ZigBee networks. In this paper, we propose a PKI enabled secure communication schema for ZigBee networks. Limited memory and power constraints of end devices restrict them from storing public keys of all other devices in the network. Large keys cannot be communicated due to limited power of the nodes and small transmission packet size. The proposed schema addresses these limitations. We propose two algorithms for sending and receiving the messages. The protocols for intercommunication between the network entities are also presented. Minor changes have been introduced in the capabilities of devices used in the ZigBee networks to suit our proposed scheme. Network adaptations depending on different scenarios are discussed. The approach adopted in this paper is to alter the communication flow so as to necessitate minimum memory and computational requirements at the resource starved end points. In the proposed PKI implementation, end devices store the public keys of only the coordinator which in turn holds public keys of all devices in the network. All communication in our scheme is through the coordinator, which in the event of failure is re‐elected through an election mechanism. The performance of the proposed scheme was evaluated using a protocol analyzer in home automation and messenger applications. Results indicate that depending on the type of application, only a marginal increase in latency of 2 to 5 ms is introduced for the added security. Layer wise traffic and packets captured between devices were analyzed. Channel utilization, message length distribution and message types were also evaluated. The proposed protocol's performance was found to be satisfactory on the two tested applications. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Chapter 12 - Creating a Public Key Infrastructure with Certificate Services

Modern internet communications and electronic transactions rely heavily on the use of public key cryptosystems. Two famous examples are the RSA cryptosystem (RSA), and the elliptic curve cryptosystem (ECC). Such cryptosystems have the advantage that they do not require the sender and recipient of confidential messages to have met beforehand and exchanged secret key material. Instead, the person wishing to receive confidential messages creates a pair of matching public and private cryptographic keys, posts their public key for all to see, but keeps their private key secret. Anyone wishing to send the author of the public key a confidential message uses the posted public key to encrypt a message, and transmits the encrypted message via a potentially insecure classical communications channel. Upon receipt, the legitimate recipient uses his matching private key to unscramble the encrypted message.

In the fuzzy identity-based encryption scheme, a trusted KGC (key generation center) is needed to generate the corresponding private key corresponding to the user's biometric public key. In order to deal with the decentralization problem and the verification problem of the users identity, we propose a public key encryption model based on transformed biometrics. In this model, the user uses the transformed biometrics as his public key and his inherent real biometrics as his private key. In order to protect the user's biometrics information from being leaked, we take some appropriate security measures such as biometric template protection technology and irreversible random conversion technology. These operations are performed locally by the user, and once the public key is generated, the random transformation matrix is deleted or destroyed. The user connects the device serial number in parallel with the modulus N as the input value of the SHA-256 function and uses the output message digest as the public information. The user uses the inner product encryption to complete the encryption process. In this model, the security parameter and the private keys do not require any trusted organization for their generation, and these sensitive information does not need to be transmitted over a public network. The communication parties do not need to know the public key information of the other party in advance. When the user needs to transmit the secret message, the user can query the corresponding public key and related information. We have effectively linked the biological identities with the digital identities. Our thorough analysis shows that the proposed encryption model is both secure and efficient for an encryption algorithm.

Elliptic Curve Cryptography (ECC) uses two keys private key and public key and is considered as a public key cryptographic algorithm that is used for both authentication of a person and confidentiality of data. Either one of the keys is used in encryption and other in decryption depending on usage. Private key is used in encryption by the user and public key is used to identify user in the case of authentication. Similarly, the sender encrypts with the private key and the public key is used to decrypt the message in case of confidentiality. Choosing the private key is always an issue in all public key Cryptographic Algorithms such as RSA, ECC. If tiny values are chosen in random the security of the complete algorithm becomes an issue. Since the Public key is computed based on the Private Key, if they are not chosen optimally they generate infinity values. The proposed Modified Elliptic Curve Cryptography uses selection in either of the choices; the first option is by using Particle Swarm Optimization and the second option is by using Cuckoo Search Algorithm for randomly choosing the values. The proposed algorithms are developed and tested using sample database and both are found to be secured and reliable. The test results prove that the private key is chosen optimally not repetitive or tiny and the computations in public key will not reach infinity.

For secret message transfer through computer, every message is encrypted following a scrambling rule and the coded message is decrypted if the scrambling rule (i.e., the encryption key) is known. For a computer, the message (M), the key (K) and the coded message (C) are all numbers, expressed as strings of 0's and 1's. The one-way modulo function (which enables us to determine uniquely the RHS form the LHS, but not the other way round) and the difficulty of the obtaining two large prime factors ( p and q ) of a number N = p × q are combined to create an asymmetric key. Different keys are used for encryption and decryption. Public Key and Private Key Everybody knows my public key (like my telephone number). Anyone can send me an encrypted message using my public key, but only I can decipher it by using my private key. RSA, or Rivest, Shamir, Adleman, algorithm, reported in 1976. depends on the difficulty of getting back two very large prime numbers p and q from their product N . N (known to all) serves as the public key and p, q (known only to me) comprise my private key. Martin Gardner (1977) asked the readers of Scientific American to find the two prime factors of a large number consisting of 129 digits.

Based on the Hadamard and Hπ/4 operators, a new quantum signature scheme is proposed. In our scheme, the signer's private key is generated by a trusted private key generator (PKG), while the identity information of the signer is used as the corresponding public key. Both of the private key and public key of the signer are classical bit strings, which can be easily stored and reused. Given a quantum signature, anyone can verify the validity of the quantum signature with the signer's identity. Therefore, our scheme is a public-key quantum signature without a digital certificate, which has the merits of an identity-based cryptosystem and can simplify the key management of the quantum signature system. On the other hand, our scheme need not use any quantum swap test during the signature verification phase. Furthermore, by the signature proof, our scheme can arbitrate the potential disputation of losing quantum signature, which cannot be arbitrated in most of the quantum signature schemes. So our scheme has the property of strong non-repudiation. It also has the security properties of information-theoretic security, unforgeability, etc. Our scheme can achieve a high efficiency of 70%. Therefore, our quantum signature scheme is more secure, practicable, and efficient than the similar schemes.

Sensor devices in the Wireless Sensor Network (WSN) are commonly subjected to various forms of attacks, such as flood attacks, eavesdropping attacks, etc. When an attacker compromises a sensor device, the sensor device's data contents become non-confidential and are grabbed by the attacker, putting the entire network at risk. As a result, to prevent key leaks in WSN networks, this paper proposes a Token with Secret and Public Keys Sharing (TSP-KS) algorithm. In the existence of attackers, cryptography is used to provide secure communication. A traditional public-key cryptosystem is appropriate in cryptography since it does not need the sender and receiver to supply the same secret to communicate without risk. However, they frequently rely on complex mathematical calculations, making them far less capable than equivalent symmetric-key cryptosystems. The high cost of encrypting long messages with public-key cryptography could be problematic in a wide range of applications. A hybrid system deals with it using a combination of the two. In WSN, Admin creates a token, a secret key, a public key, and a private key. Here, the token is used for access control in sensor devices and the administrator, the secret and public keys are utilized for packet encryption in sensor devices and the base station, and the private key is utilized for decryption in the administrator. Admin shares token with secret and public key for sensor devices and base station for encryption purposes. As a result, the TSP-KS algorithm was utilized to securely share these token with secret and public keys for sensor devices and base station over a distributed way. Experimental results demonstrate that the TSP-KS algorithm securely shares a token with a secret and public key.

This paper describes an implementation of location-based encryption using a public key cryptosystem based on the rank error correcting codes. In any code based cryptosystem, public and private keys are in the form of matrices based over the finite field. This work proposes an algorithm for calculating public and private key matrices based on the geographic location of the intended receiver. The main idea is to calculate a location specific parity check matrix and then corresponding public key. Data is encrypted using public key. Some information about the parity check matrix along with other private keys are sent to receiver as cipher-text, encrypted with another instance of the public or GPT cryptosystem using public key of the receiver. The proposed scheme also introduces a method of calculating different parity check matrix for each user.