Quantum asymmetric key crypto scheme using Grover iteration

Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science. An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed. Depending on the no-cloning theorem and trapdoor one-way functions of the public-key, the eavesdropper cannot extract any private-information from the public-keys and the ciphertext. Introducing key-generation randomized logarithm to improve security of our proposed protocol, i.e., one private-key corresponds to an exponential number of public-keys. Using unitary operations and the single photon measurement, secret messages can be directly sent from the sender to the receiver. The security of the proposed protocol is proved that it is information-theoretically secure. Furthermore, compared the symmetrical Quantum key distribution, the proposed protocol is not only efficient to reduce additional communication, but also easier to carry out in practice, because no entangled photons and complex operations are required.

Data exchange has been rapidly increased recently by increasing the use of mobile networks. Sharing information (text, image, audio and video) over unsecured mobile network channels is liable for attacking and stealing. Encryption techniques are the most suitable methods to protect information from hackers. Hill cipher algorithm is one of symmetric techniques, it has a simple structure and fast computations, but weak security because sender and receiver need to use and share the same private key within a non-secure channel. Therefore, a novel hybrid encryption approach between elliptic curve cryptosystem and hill cipher (ECCHC) is proposed in this paper to convert Hill Cipher from symmetric technique (private key) to asymmetric one (public key) and increase its security and efficiency and resist the hackers. Thus, no need to share the secret key between sender and receiver and both can generate it from the private and public keys. Therefore, the proposed approach presents a new contribution by its ability to encrypt every character in the 128 ASCII table by using its ASCII value direct without needing to assign a numerical value for each character. The main advantages of the proposed method are represented in the computation simplicity, security efficiency and faster computation.

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.

Introduction: Development of practical post-quantum signature schemes is a current challenge in the applied cryptography. Recently, several different forms of the hidden discrete logarithm problem were proposed as primitive signature schemes resistant to quantum attacks. Purpose: Development of a new form of the hidden discrete logarithm problem set in finite commutative groups possessing multi-dimensional cyclicity, and a method for designing post-quantum signature schemes. Results: A new form of the hidden discrete logarithm problem is introduced as the base primitive of practical post-quantum digital signature algorithms. Two new four-dimensional finite commutative associative algebras have been proposed as algebraic support for the introduced computationally complex problem. A method for designing signature schemes on the base of the latter problem is developed. The method consists in using a doubled public key and two similar equations for the verification of the same signature. To generate a pair of public keys, two secret minimum generator systems <G, Q> and <H, V> of two different finite groups G<G, Q> and G<H, V> possessing two-dimensional cyclicity are selected at random. The first public key (Y, Z, U) is computed as follows: Y = Gy1Qy2a, Z = Gz1Qz2b, U = Gu1Qu2g, where the set of integers (y1, y2, a, z1, z2, b, u1, u2, g) is a private key. The second public key (Y¢, Z¢, U¢) is computed as follows: Y¢ = Hy1Vy2a, Z¢ = Hz1Vz2b, U¢ = Hu1Vu2g. Using the same parameters to calculate the corresponding elements belonging to different public keys makes it possible to calculate a single signature which satisfies two similar verification equations specified in different finite commutative associative algebras. Practical relevance: Due to a smaller size of the public key, private key and signature, as well as approximately equal performance as compared to the known analogues, the proposed digital signature scheme can be used in the development of post-quantum signature algorithms.

Several researchers have proposed the use of threshold cryptographic model to enable secure communication in ad hoc networks without the need of a trusted center. In this model, the system remains secure even in the presence of a certain threshold t of corrupted/malicious nodes.In this paper, we show how to perform necessary public key operations without node-specific certificates in ad hoc networks. These operations include pair-wise key establishment, signing, and encryption. We achieve this by using Feldman’s verifiable polynomial secret sharing (VSS) as a key distribution scheme and treating the secret shares as the private keys. Unlike in the standard public key cryptography, where entities have independent private/public key pairs, in the proposed scheme the private keys are related (they are points on a polynomial of degree t) and each public key can be computed from the public VSS information and node identifier. We show that such related keys can still be securely used for standard signature and encryption operations (using resp. Schnorr signatures and ElGamal encryption) and for pairwise key establishment, as long as there are no more that t collusions/corruptions in the system.The proposed usage of shares as private keys can also be viewed as a threshold-tolerant identity-based cryptosystem under standard (discrete logarithm based) assumptions.

Updatable encryption (UE) plays an important role in mitigating the impact of key compromise on ciphertext in the scenario of cloud storage. Nevertheless, most of the existing UE schemes focus on making symmetric encryption updatable. In this paper, to give play to advantages of symmetric and asymmetric encryption, we present an updatable hybrid encryption (UHE) scheme. By setting the REACT transform as the underlying encryption scheme and using the indistinguishable obfuscation to convert the private key into a public key encryption program, the synchronous update of public/private key pair and ciphertext can be realized. More importantly, the generation and update of private key are stored locally in hybrid encryption, the update token is not used to derive the private key, and thus the no-directional key update can be achieved. Furthermore, considering for the adversarial attack behaviors, we build a reasonable security model. Finally, since the decryption ability of the punctured keys is limited at the punctured points, the adversary can be allowed to access to all oracles at the full epochs, and then under the proposed security framework the confidentiality of the proposed scheme can be proven based on the indistinguishability between pseudorandom functions, where the confidentiality can capture forward and post-compromise security.KeywordsUpdatable encryptionHybrid encryptiont-puncturable pseudorandom functionForward securityPost-compromise security

Highly-Secure Backdoors: Internet of Traitorous Things (IoTT)

In this paper, we propose two authenticated key distribution protocols and one conference key protocol using identity-based, self-certified public keys. These proposed protocols have the following properties:(i) No extra public key certificates and computational efforts are required for verification of authenticity for public keys.(ii) Key establishment and validation of the desired public keys are integrated in a logically single step.(iii) Each registering user can use his derived private key to check the validity of his public key issued by the system authority.(iv) The system authority cannot access to users' private keys. Hence, all private keys cannot be compromised in case of disruption or corruption of the system authority.(v) The proposed protocols provide the security property of key authentication whereby one user is assured that no other user aside from specifically identified user (s) may gain access to the derived shared key/conference key.

Yamaguchi, Okayama, and Miyahara proposed a simple but efficient authentication sys- tem, SPLICE/AS. In this article, we show that their method is vulnerable to the guessing attack. An attacker can obtain the password, private-key, and public-key of the user. To overcome the vul- nerability of SPLICE/AS to the guessing attack, we propose an improvement of their system. In our scheme, we not only prevent the guessing attack to obtain secret messages but also enhance the security of the SPLICE/AS authentication system in WIDE.

Recently, the notion of the key-insulated public- key system has been suggested to protect the security of users' private keys. A general idea of this system is changing the user's private key along with the time, but the user's public key remains unchanged. In this paper, we propose a new identity (ID)-based key-insulated signature scheme from bilinear pairings. As compared with the recently proposed ID-based key-insulated signature schemes, our proposed scheme has better performance in the batch verifying phase. For security analysis, our scheme is a provably secure key-insulated signature scheme in the random oracle model and under the computational Diffie-Hellman assumption. Meanwhile, to demonstrate the additional advantage of a key-insulated signature, we present a novel application based on the proposed scheme, called full delegation ID-based proxy signature scheme with time restriction. To our best knowledge, no such a proxy signature scheme is proposed until now.

Steganography is the art and science of writing hidden messages or hiding messages in such a way that, apart from the sender and the recipient, no one knows or is aware that there is a secret message (it does not appear that there is a hidden message. Furthermore, public key cryptography is the type of cryptography that using two interrelated keys, namely the public and private keys. Cryptography and steganography techniques have an important role in securing information. Parallel Encryption with Digit Arithmetic of Covertext (PDAC) encryption model adopts cryptography and steganography for securing messages. The accuracy of the number of covertext in the PDAC affects whether the PDAC works. If the number of PDAC covertext does not match, then the encryption process will be imperfect. This study aims to close the PDAC gap. The proposed model adopts the repeated use of covertext. Covertext loops applied in PDAC can process information security. Another advantage obtained is that this modification makes it easier for users to use PDAC without having to meet the minimum covertext requirement.

Asynchronous Remote Key Generation (ARKG, introduced in ACM CCS 2020) allows for a party to create public keys for which corresponding private keys may be later computed by another intended party only. ARKG can be composed with standard public-key cryptosystems and has been used to construct a new class of privacy-preserving proxy signatures. The original construction of ARKG, however, generates discrete logarithm key pairs of the form $$(x, g^x)$$ . In this paper we define a generic approach for building ARKG schemes which can be applied to a wide range of pairing-based cryptosystems. This construction is based on a new building block which we introduce and call Asymmetric Key Generation (AKG) along with its extension $$\phi $$ -AKG where $$\phi $$ is a suitable mapping for capturing different key structures and types of pairings. We show that appropriate choice of $$\phi $$ allows us to create a secure ARKG scheme compatible with any key pair that is secure under the Uber assumption (EUROCRYPT 2004). To demonstrate the extensive range of our general approach, we construct ARKG schemes for a number of popular pairing-based primitives: Boneh-Lynn-Shacham (JoC 2004), Camenisch-Lysyanskaya (CRYPTO 2004), Pointcheval-Sanders (CT-RSA 2016), Waters (EUROCRYPT 2005) signatures and structure-preserving signatures on equivalence classes (ASIACRYPT 2014). For each scheme we give an implementation and provide benchmarks that show the feasibility of our techniques.

Identity-based cryptosystems were introduced to overcome one of the main problems in public key encryption, the generation of public and private keys. In the identity-based cryptosystem, an identifier such as an e-mail address of a user can be used to generate public and private keys by a trusted third party. The trusted third party uses a system-wide master secret to provide private keys to a user. Identity-based cryptosystems can be constructed using the idea of pairings. This article discusses four different identity-based cryptosystems: the Boneh-Franklin scheme, the Cock's scheme, the Authenticated IBE scheme and the Hierarchical IBE scheme. This article also discusses the security notions considered for the identity-based cryptosystem. The security notions considered are: one-wayness, indistinguishability, semantic security and non-malleability. An architecture consisting of a public parameter server and private key generator for the implementation of the identity-based cryptosystems is also discussed.

A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum algorithm that proves the superiority of quantum computing over classical computing. It has a quadratic reduction in the query complexity of a database search and is known to be optimal when no a priori information about the elements of the database is provided. In this work we consider a probabilistic Grover search algorithm allowing nonzero probability of failure for a database with a general a priori probability distribution of the elements and minimize the number of oracle calls by optimizing the initial state of the quantum system and the reflection axis of the diffusion operator. The initial state and the reflection axis are allowed to not coincide and thus the quantum search algorithm rotates the quantum system in a three-dimensional subspace spanned by the initial state, the reflection axis, and the search target state in general. The number of oracle calls is minimized by a variational method, and formal results are obtained with the assumption of low failure probability. The results show that for a nonuniform a priori distribution of the database elements, the number of oracle calls can be significantly reduced given a small decrease in the success probability of the quantum search algorithm, leading to a lower average query complexity to find the solution of the search problem. The results are applied to a simple but nontrivial database model with two-value a priori probabilities to show the power of the optimized quantum search algorithm. The paper concludes with a discussion about the generalization to higher-order results that allows for a larger failure probability for the quantum search algorithm.

This paper proposes a novel hybrid public/private key cryptography scheme based on perfect Gaussian integer sequences (PGISs) of period $N=pq$ . First, a review study of construction degree-4 PGIS is addressed. We show that circular convolution over PGISs is a trapdoor one-way permutation function that enables simultaneous cipher encryption and digital signatures. To implement the proposed cipher encryption scheme, a private PGIS is assigned as the encryption key sequence for circular convolution with the plaintext to generate the ciphertext. The reverse decryption key sequence involves the time reflection and complex conjugation of the encryption sequence, which can be regenerated using a pair of public and private keys. The security level of the proposed scheme is the same as that of the Rivest-Shamir-Adleman (RSA) system; however, the capacity of a cryptosystem based on PGISs may outperform that of based on RSA, because abundant PGISs are available. Simulation results show that the approximation error when finite digits are used to represent the irrational coefficients of a normalized PGIS can be relatively small compared with the noise. This contributes to the simplicity of this scheme’s implementation. With the fast development of IoT (internet of things), the adaptation and applicability of the proposed scheme to IoT platforms are also addressed, where lightweight cryptographic functions are preferable due to the limited resources of IoT devices.