Public key cryptography is extensively used for encryption, signing contracts and secure exchanges over the unreliable network.The findings of Shor in 1994, of a powerful algorithm which was based on quantum mechanics for computing discrete logarithms and factoring large integers sabotaged the security presumptions upon which the currently used public key cryptographic protocols are based, like ElGamal, RSA and ECC.However, few cryptosystems, known as post quantum cryptosystems, while not currently in wide use are considered to be resistant to such attacks.In this paper, a quantum version of ElGamal Cryptosystem is proposed whose security relies on the commutative rotation transformations and measurements in computational basis of qubits.An understanding of the new scheme over the quantum channels is provided.The proposed cryptosystem allows the party to send messages in the form of qubits over a quantum channel.Also the proposed protocol provides an opportunity for two parties to exchange keys which is considered as one of the major concerns while developing post quantum cryptosystems.
Public key cryptography is extensively used for encryption, signing contracts and secure exchanges over the unreliable network.The findings of Shor in 1994, of a powerful algorithm which was based on quantum mechanics for computing discrete logarithms and factoring large integers sabotaged the security presumptions upon which the currently used public key cryptographic protocols are based, like ElGamal, RSA and ECC.However, few cryptosystems, known as post quantum cryptosystems, while not currently in wide use are considered to be resistant to such attacks.In this paper, a quantum version of ElGamal Cryptosystem is proposed whose security relies on the commutative rotation transformations and measurements in computational basis of qubits.An understanding of the new scheme over the quantum channels is provided.The proposed cryptosystem allows the party to send messages in the form of qubits over a quantum channel.Also the proposed protocol provides an opportunity for two parties to exchange keys which is considered as one of the major concerns while developing post quantum cryptosystems.
Modern technologies like quantum and cloud computing have reshaped computing, offering immense power and scalability. While beneficial, they also challenge the security of traditional cryptographic systems. Quantum computing threatens RSA and ECC with algorithms like Shor’s algorithm, which can accelerate computations exponentially. This risks exposing these systems to attacks, necessitating quantum-resistant cryptography. Cloud computing poses data security concerns, requiring robust cryptographic mechanisms and access controls. Lattice-based cryptography, leveraging problems like the Short Integer Solution (SIS), emerges as a solution. This paper presents a novel quantum-resistant public key encryption scheme based on ElGamal and SIS, ensuring security against quantum and classical threats in modern cryptographic environments.
GenElGamal is an extension of the ElGamal public key encryption scheme, which modifies the key generation and encryption steps, proposed by Sow and Sow in [24]. With the rise of quantum computing, the security of public key cryptosystems based on the discrete logarithm problem, particularly GenElGamal, is threatened. In this paper, we propose a post-quantum version of the GenElGamal cryptosystem called PQ-GenElGamal using the difficult modulo 1 factoring problem (M1FP) that is resistant to post-quantum attacks. We describe our scheme and prove its security against both classical and post-quantum attacks.
It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational setting are longed for cryptology. In order to define the security notions of public-key cryptosystems, we have to model the power of the sender, receiver, adversary and channel. While we may consider a setting where quantum computers are available only to adversaries, we generally discuss what are the right security notions for (quantum) public-key cryptosystems in the quantum computational setting. Moreover, we consider the security of quantum public-key cryptosystems known so far.
The boom of quantum computing has brought both benefits and threats to cyber-physical systems. The primary purpose of the paper is to highlight the possible threats by quantum computers, and to provide a comparative study of the on-going quantum-resistant post-quantum cryptography suitable for current network infrastructure. Asymmetric key cryptography, mainly the widely adopted RSA and ECC algorithms, has been compromised by quantum algorithms such as the Shor’s algorithm. Moreover, symmetric algorithms such as AES are weakened by brute force attacks using Grover’s algorithm. Thus, researchers are developing public key algorithms based on hard mathematical models that provide resistance against quantum attacks and can be deployed in classical hardware. We categorize the well-known post-quantum schemes based on (1) their security goals: confidentiality and integrity, and (2) their mathematical problems: code-based, lattice-based, super-singular elliptic curve isogeny based, multivariate and hash-based algorithm. Hash-based post- quantum cryptography is further categorized into two: stateless and stateful signature scheme. Furthermore, the chapter compares the algorithms based on the key sizes, ciphertext sizes, signature sizes, computation, and time cost. The paper also presents the challenges faced by the post-quantum algorithms, and it outlines directions for further research to improve the algorithms. Moreover, various cyber-physical fields, including industrial control systems, mainly nuclear power plants, water management plants, and even space stations and their infrastructure, rely on classical cryptography. Thus, the paper presents a generic hybrid cryptosystem based on classical and post-quantum cryptography to enhance resistance against classical and quantum attacks.
Contemporary cryptographic algorithms are resistant to the strongest threats to cybersecurity and high-profile cyber-attacks. In recent times, information security scientists and researchers had developed various cryptographic schemes that defeated attacks using the most sophisticated (in terms of processor speed) classical computer. However, this resistance will soon erode with the arrival of quantum computers. In this paper, we profiled quantum computers and quantum algorithms based on their widely believed threat against currently secure cryptographic primitives. We found that Grover’s and Shor’s quantum-based algorithms actually pose a threat to the continued security of symmetric cryptosystems (e.g. 128-bit AES) and asymmetric (public key) cryptosystems (e.g. RSA, Elgamal, elliptic curve Diffie Hellman (ECDH), etc.) respectively.We discovered that the source of the algorithms’ cryptanalytic power against the current systems, stems from the fact that they (Grover and Shor) both equipped their respective algorithms with a quantum circuit component that can execute the oracle in parallel by applying a single circuit to all possible states of an n-qubit input. With this exponential level of processing characteristic of quantum computers and quantum-based algorithms, it is easy for the current cryptosystems to be broken since the algorithms can existentially solve the underlying mathematical problems such as integer factorization, discrete logarithm problem and elliptic curve problem, which formed the basis of the security of the affected cryptosystems. Based on this realization and as part of our readiness for a post quantum era, we explored other mathematical structures (lattices, hashes, codes, isogenies, high entropy-based symmetric key resistance, and multivariate quadratic problems) whose hardness could surpass the cryptanalytic nightmare posed by quantum computers and quantum-based algorithms. Our contribution is that, based on the findings of this research work, we can confidently assert that all hope is not lost for organizations heavily relying on protocols and applications like HTTPS, TLS, PGP, Bitcoin, etc., which derived their security from the endangered cryptosystems.
Not only is quantum computing a game changer but it is also an unprecedented threat to world security in cyberspace. Although quantum systems are expected to transform scientific computing, they are also endangering the very notion of classical cryptography, specifically, the public key system of RSA and elliptic curve cryptography (ECC). The problems in computation that such schemes are built on, including integer factorization and discrete logarithms, can be efficiently solved using quantum algorithms, including Shor. This makes the secured communication network by classical encryption susceptible to quantum attacks in the future. In turn, current quantum-resistant or post-quantum cryptographic algorithms (PQC) are resistant to classical and quantum adversaries. The article provides a general overview of significant families of PQC, such as lattice-based, code-based, multivariate polynomial, hash-based and isogeny-based, and discusses their relevance to the provisioning of communication networks. The work illuminates to some degree the advances toward standardization already being undertaken by the National Institute of Standards and Technology (NIST) by analysing its security underpinnings, trade-offs in its operation and its readiness to deploy. Experiments show that lattice based (CRYSTALS-Kyber, Dilithium) and code based (McEliece) are both well-theoretically secure as well as high performance, and that systems based on code (McEliece) have a long track record of reliability at the cost of large key-sizes. Other issues which have been talked about in the paper are interoperability issues, migration policies and side-channel attack defence. It finds conclusively that quantum-resistant cryptography is the next step that must be regarded as the most important to secure the secrecy and integrity of communication networks in the future.