Many cryptographic algorithms depend on computational complexity assumptions. Notorious cases are the RSA algorithm for public key criptography or the Diffie-Hellman key exchange protocol, to publicly agree on a common secret key. Both algorithms are known to be broken by quantum computing as well as those that can be reduced to a discrete logarithm problem. These are key algorithms in our digital society and are at the basis of everyday tasks, specially those that rely on digital signatures. The RSA algorithm, in particular, is probably the most used algorithm and is its assumed security the one that guards most of the e-commerce nowadays. In this case, it is the time complexity of finding the prime factors of a large number, that grows worse than polinomially with the size of the number, the main guardian of our cyberinfrastructure. The fact that a quantum computer can solve this problem in polynomial time using Shor's algorithm is seen as a potentially major disruption and has prompted security agencies to advice the progressive deprecation of these algorithms.
Many cryptographic algorithms depend on computational complexity assumptions. Notorious cases are the RSA algorithm for public key criptography or the Diffie-Hellman key exchange protocol, to publicly agree on a common secret key. Both algorithms are known to be broken by quantum computing as well as those that can be reduced to a discrete logarithm problem. These are key algorithms in our digital society and are at the basis of everyday tasks, specially those that rely on digital signatures. The RSA algorithm, in particular, is probably the most used algorithm and is its assumed security the one that guards most of the e-commerce nowadays. In this case, it is the time complexity of finding the prime factors of a large number, that grows worse than polinomially with the size of the number, the main guardian of our cyberinfrastructure. The fact that a quantum computer can solve this problem in polynomial time using Shor's algorithm is seen as a potentially major disruption and has prompted security agencies to advice the progressive deprecation of these algorithms.
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.
In this world of massive communication networks, data security and confidentiality are of crucial importance for maintaining secured private communication and protecting information against eavesdropping attacks. Existing cryptosystems provide data security and confidentiality by the use of encryption and signature algorithms for secured communication. Classical computers use cryptographic algorithms that use the product of two large prime numbers for generating public and private keys. These classical algorithms are based on the fact that integer factorization is a non-deterministic polynomial-time (NP) problem and requires super-polynomial time making it impossible for large enough integers. Shor’s algorithm is a well-known algorithm for factoring large integers in polynomial time and takes only O(b3) time and O(b) space on b-bit number inputs. Shor’s algorithm poses a potential threat to the current security system with the ongoing advancements of Quantum computers. This paper discusses how Shor’s algorithm will be able to break integer factorization-based cryptographic algorithms, for example, Rivest–Shamir–Adleman (RSA) and Rabin Algorithms. As a proof of concept, experimental analysis of Quantum Shor’s algorithm on existing public-key cryptosystems using IBM Quantum Experience is performed for factorizing integers of moderate length (seven bits) due to limitations of thirty-two qubits in present IBM quantum computers. In a nutshell, this work will demonstrate how Shor’s algorithm poses threat to confidentiality and authentication services.
The complexity of public key algorithms like RSA and variants of Elgamal is based on the involvement of exponentiation in encryption and decryption. RSA is based on integer factorization and variants of Elgamal or based on discrete logarithms and are formed as hard problems. To achieve the perceived level of security, the required key length for public key cryptosystem needs to be determined. Quantum computers are capable of conducting an exponential number of simultaneous computations because of which they can find factors in polynomial time. Shor’s algorithm is popular algorithm for factoring huge integers in polynomial time on quantum computers. This paper presents RSA algorithm followed by various possible attacks for factoring and demonstrates Shor’s algorithm for factoring and discuss results for interpretations.
Today we witness an explosive growth in attention to Q-computing. Q-computing technologies, along with artificial intelligence (AI) and machine learning (ML) technologies, cloud and foggy computing, as well as technologies for collecting and streaming processing of Big Data and ETL, are constantly leading the lists of ""end-to-end"" information technologies for the digital economy of technologically developed countries of the world. One of the main reasons for this is the potential ability of quantum computers to solve some computational problems more efficiently than any of the most modern classical computers of the von Neumann architecture (supercomputers). The most expressive and interesting, from an applied point of view, examples of such problems are integer factorization, effectively performed by Shor's quantum algorithm, as well as record search in an unordered database, effectively solved by Grover's algorithm. This monograph contains the best practice for solving problems of quantum cryptanalysis to improve cyber security and resilience of the digital economy. The book discusses well-known and author's software implementations of promising quantum Shor algorithms, Grover, Simon et al. Shor's algorithm provides exponential acceleration of solving factorization problems, discrete logarithm problems (DLPs) and elliptic curve discrete logarithm problems (ECDLPs). The mentioned tasks are widely used in TLS, SSH or IPsec cryptographic applications of Internet/Intranet and IIoT/IoT networks, communication protocols based on Diffie–Hellman key agreements (dependent on the strength of the DLP or ECDLP), digital signature algorithms (DSA, ECDSA, RSA-PSS), public key encryption algorithms (El Gamal, RSA-OAEP), etc. In other words, Shor's quantum algorithm is potentially capable of violating these algorithms, and with them all the mechanisms of public-key cryptography deployed in cyberspace.
The defense of public key cryptography (PKC) lies in computational issues like the difficulty of factorizing enormous prime numbers and the discrete logarithm calculations. Such kinds of algorithms are called one-way functions because although it is straightforward to compute output given input, it is difficult to compute input if output is given. It is expected that such numerical or computational issues which are utilized in current cryptographic plans are difficult to address for an adversary utilizing present PCs. Yet, many organizations are attempting to assemble a high-powered quantum PC and in the future quantum PCs will be available for business use. Traditional asymmetric cryptographic algorithms are not secure against strong quantum machines. Shor’s algorithm running on a powerful quantum PC is able to solve integer factorization problems and discrete logarithm problems in polynomial time. So, asymmetric algorithms that are used today, like RSA, DSA and Diffie-Hellman will become insecure. Similarly, Grover’s algorithm running on a powerful quantum computer poses a serious threat to symmetric key algorithms which uses small key size. There is a need to work on alternate algorithms to resist quantum threat. NIST has already started with a process for the standardization of algorithms which are known as post-quantum cryptography (PQC) algorithms. Specialists globally are exploring progress toward post-quantum cryptography.