This paper proposes RSA parameters for which (1) key generation, encryption, decryption, signing, and verification are feasible on today’s computers while (2) all known attacks are infeasible, even assuming highly scalable quantum computers. As part of the performance analysis, this paper introduces a new algorithm to generate a batch of primes. As part of the attack analysis, this paper introduces a new quantum factorization algorithm that is often much faster than Shor’s algorithm and much faster than pre-quantum factorization algorithms. Initial pqRSA implementation results are provided.
This paper proposes RSA parameters for which (1) key generation, encryption, decryption, signing, and verification are feasible on today’s computers while (2) all known attacks are infeasible, even assuming highly scalable quantum computers. As part of the performance analysis, this paper introduces a new algorithm to generate a batch of primes. As part of the attack analysis, this paper introduces a new quantum factorization algorithm that is often much faster than Shor’s algorithm and much faster than pre-quantum factorization algorithms. Initial pqRSA implementation results are provided.
The present study explores the groundbreaking possibilities of Shor's algorithm in cracking RSA encryption, hence enhancing the security consequences of this extensively employed cryptographic protocol. Due to Shor's algorithm's exponential speed advantage over classical algorithms, RSA encryption—a popular public key cryptosystem—is vulnerable to quantum attacks. To keep its security, RSA depends on the difficulty of factoring huge semi-primes. RSA's security presumptions are called into question by Shor's algorithm's quick factorization on a quantum computer, which has prompted research into post-quantum cryptography solutions to guarantee secure communication in the quantum age. Even with parallel computation, the speed and storage capacity of classical computing are constrained. A key idea in quantum computing is quantum parallelism, which allows quantum systems to carry out several computations at once. In contrast to classical portions. The scope of this paper is to understand the fundamentals of Quantum Computing, the current state of Shor’s algorithm implementation, and efficiency, particularly its application in compromising public key cryptosystems like RSA. The project aims to achieve how factorization is done through classical methods and further, how is this done through Shor’s algorithm and QFT techniques.
The growing threat of quantum computing to classical cryptographic systems such as RSA and ECC has led to an urgent need for post-quantum cryptographic (PQC) research and implementation. The base paper, “Quantum Computing in Cryptography”, identified a major research gap - the lack of practical implementation of post-quantum algorithms, emphasizing that most existing works remain at a theoretical level. Addressing this gap, we develop and execute a practical benchmarking framework that compares classical RSA and simulated post-quantum cryptographic algorithms. The implementation integrates automatic setup, execution, and visualization of key generation, encryption, and decryption operations for both classical and PQC schemes. Experimental results demonstrate that while RSA achieves faster computational performance, it becomes vulnerable to quantum computational attacks. Conversely, post-quantum algorithms, though more computationally demanding, exhibit strong resistance against such attacks. The performance analysis highlights the trade-off between speed and quantum resilience, confirming the practical viability of PQC for future-proof cryptographic systems. This work effectively bridges the theoretical–practical divide noted in the base paper by providing a concrete, implementable model for evaluating post-quantum cryptography under realistic computational conditions.
The ongoing development of Quantum Computing (QC) is a breakthrough paradigm that holds the power to revolutionize the way we process information and solve complex problems today. Quantum Computation works on the fundamental principles of Superposition and Entanglement, enabling Quantum Computers to Leverage the power of Physics in Computing. QC has the potential to revolutionize fields such as Drug Development, Financial Modeling, Optimization, and Cryptography. Shor’s algorithm, a quantum algorithm used to factorize large numbers, poses significant threats to RSA, a widely used public key cryptosystem. RSA relies on the difficulty of factoring large semi-primes to keep its security. Shor's algorithm's ability to factorize quickly on a quantum computer undermines RSA's security assumptions, necessitating the exploration of post-quantum cryptographic solutions to ensure secure communication in the quantum era. The goal of this paper is to assess the present state of Shor's algorithm implementation and efficiency, specifically its application in the context of compromising public key cryptosystems like RSA.
The ongoing development of Quantum Computing (QC) is a breakthrough paradigm that holds the power to revolutionize the way we process information and solve complex problems today. Quantum Computation works on the fundamental principles of Superposition and Entanglement, enabling Quantum Computers to Leverage the power of Physics in Computing. QC has the potential to revolutionize fields such as Drug Development, Financial Modeling, Optimization, and Cryptography. Shor’s algorithm, a quantum algorithm used to factorize large numbers, poses significant threats to RSA, a widely used public key cryptosystem. RSA relies on the difficulty of factoring large semi-primes to keep its security. Shor's algorithm's ability to factorize quickly on a quantum computer undermines RSA's security assumptions, necessitating the exploration of post-quantum cryptographic solutions to ensure secure communication in the quantum era. The goal of this paper is to assess the present state of Shor's algorithm implementation and efficiency, specifically its application in the context of compromising public key cryptosystems like RSA.
The advent of quantum computers introduces new challenges to the fields of encryption and authentication. Traditional cryptographic systems, such as RSA and ECC, rely on mathematical problems that are computationally hard for classical computers to solve. However, quantum computers have the potential to render these algorithms ineffective by leveraging Shor's algorithm, which can efficiently factor large numbers and solve the discrete logarithm problem. This capability threatens the security of many widely deployed encryption and authentication schemes. There have been a number of post-quantum cryptography methods proposed in the past. However, they are either relatively difficult to implement in current small-scale quantum computers or they do not take noise and error mitigation into account. In this paper, we propose a new framework of post-quantum key generation and identity verification mechanisms which are relatively easy to implement and adapt. Our approaches take the noisy nature of current quantum devices into consideration. As a result, our proposed approach can resist attacks from malicious quantum computers and the successful attack rate could quickly decay to zero as the number of qubits increases.
Security analysis of public-key cryptosystems is of fundamental significance for both theoretical research and applications in cryptography. In particular, the security of widely used public-key cryptosystems merits deep research to protect against new types of attacks. It is therefore highly meaningful to research cryptanalysis in the quantum computing environment. Shor proposed a well-known factoring algorithm by finding the prime factors of a number n = pq, which is exponentially faster than the best known classical algorithm. The idea behind Shor's quantum factoring algorithm is a straightforward programming consequence of the following proposition: to factor n, it suffices to find the order r; once such an r is found, one can compute gcd(ar/2± 1, n) = p or q. For odd values of r it is assumed that the factors of n cannot be found (since ar/2is not generally an integer). That is, the order r must be even. This restriction can be removed, however, by working from another angle. Based on the quantum inverse Fourier transform and phase estimation, this paper presents a new polynomial-time quantum algorithm for breaking RSA, without explicitly factoring the modulus n. The probability of success of the new algorithm is greater than 4φ(r)/π2r, exceeding that of the existing quantum algorithm for attacking RSA based on factorization. In constrast to the existing quantum algorithm for attacking RSA, the order r of the fixed point C for RSA does not need to be even. It changed the practices that cryptanalysts try to recover the private-key, directly from recovering the plaintext M to start, a ciphertext-only attack attacking RSA is proposed.