Threats to Modern Cryptography: Grover’s Algorithm

David Yang

The emergence of a new era of quantum computing is on the horizon, presenting modern cryptography with a cluster of unprecedented threats.This review delves into the cryptographic techniques that risk being challenged in a postquantum environment and the algorithms that challenge these techniques.We first investigate aspects of traditional cryptography, covering both asymmetric and symmetric cryptography.Then, we analyze quantum computing and its impact on cryptographic techniques, notably Shor's and Grover's algorithms.Finally, we will research quantum-resistant solutions and explore our current status in post-quantum cryptography.This review aims to provide a comprehensive understanding of the threats posed by quantum computing from a cryptographic standpoint and the approaches available to mitigate these risks for a more secure future.

Gina Bari Kolata

Danya Al-Jubouri, Qasem S. Abu Al-Haija

With the fast advancement in quantum computing, conventional cryptography is facing great challenges, with quantum algorithms like Shor’s algorithm and Grover’s algorithm threatening to break most widely used cryptosystems and hashing algorithms. Cryptosystems that use public-key cryptography, such as RSA, have proven vulnerable to quantum attacks. This presents a high threat to digital communication, as it can compromise modern communication systems’ confidentiality, authenticity, and integrity. On the other hand, modern cryptosystems treat digital signatures and encryption as two separate operations, adopting the sign-then-encrypt method for securing communication, which results in significant computational cost and overhead. This paper proposes a Quantum Signcryption tool to solve these problems, offering a system enhanced by quantum technology and secured against quantum threats. This system combines the functions of encryption and digital signatures into a single process to function as an efficient and secure tool for future quantum communication, with an average end-to-end execution time of 20.615s, consuming 11092 KBs of memory.

Rudolf Sinaga, Uswatun Kasanah

Quantum computing has emerged as a revolutionary paradigm, holding immense potential to solve complex problems that classical computing struggles to address. This study explores the application of quantum computing in cryptography, with a specific focus on two major quantum algorithms: Shor’s algorithm for large number factorization and Grover’s algorithm for unstructured database searching. The main objective of this research is to compare the performance of these quantum algorithms with classical cryptographic methods in terms of computational efficiency and time. Shor’s algorithm, which can factorize large numbers in polynomial time, presents a significant threat to the security of public-key cryptosystems such as RSA, which rely on the difficulty of factoring large numbers. On the other hand, Grover’s algorithm offers a quadratic speedup for searching unstructured databases, making it highly relevant for symmetric key cryptography systems like AES. In this study, simulations of both algorithms were conducted using quantum simulators to assess their speed and effectiveness in solving cryptographic challenges. The results demonstrate that quantum algorithms significantly reduce the computation time compared to classical methods, with Shor’s algorithm efficiently solving factorization problems and Grover’s algorithm accelerating key searching processes. However, while these quantum algorithms show promise in improving cryptographic systems, the implementation of large-scale quantum computers remains a challenge. This research highlights the potential of quantum computing to revolutionize data security and underscores the need for further development in quantum algorithms and the transition to quantum-resistant cryptographic systems to safeguard against the threat posed by quantum computers.