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Quantum Computing India #Quantum30 Day20: Quantum Cryptanalysis ------------------------------------------------------------------------------------ Quantum cryptanalysis refers to the use of quantum computing and quantum algorithms to break classical cryptographic schemes. Quantum computers have the potential to significantly impact the field of cryptography because they can solve certain mathematical problems much faster than classical computers. Some of the most well-known quantum algorithms that could threaten classical cryptography include Shor's algorithm and Grover's algorithm. The advent of practical quantum computers poses a significant challenge to the security of classical cryptographic protocols. To mitigate the risks associated with quantum cryptanalysis, researchers are exploring various post-quantum cryptography approaches. These are cryptographic schemes that are believed to be secure against attacks by quantum computers. Some post-quantum cryptographic methods include: 1. Lattice-based cryptography 2. Hash-based cryptography 3. Code-based cryptography 4. Multivariate polynomial cryptography 5. Isogeny-based cryptography The transition to post-quantum cryptography is essential to ensure the long-term security of sensitive data in a world where quantum computers become practical for cryptanalysis. It's important for organizations to stay informed about developments in quantum computing and the ongoing efforts to create quantum-resistant cryptographic protocols.

A recent article in Quanta Magazine highlights the algorithmic progress in quantum factoring, a field that has excited (and scared) many since Peter Shor's 1994 period-finding algorithm that runs exponentially faster than classical alternatives. Key points include: Challenges in Implementing Shor's Algorithm: Implementing Shor's algorithm is difficult due to the susceptibility of quantum computers to errors. A recent paper estimated that factoring a standard 2,048-bit number would require a quantum computer with 20 million qubits, far beyond the capability of current quantum computers. Oded Regev's Contribution: Oded Regev, a cryptographer, has been exploring the connection between factoring and lattice-based cryptography. He has developed a new approach to quantum factoring by generalizing the periodic function in Shor's algorithm from one dimension to multiple dimensions, leading to a more efficient factoring process. Regev's Algorithm and Its Efficiency: Regev's algorithm reduces the number of logical steps required in the quantum part of the factoring process. This improvement could make the algorithm easier to implement in practice despite the increased number of qubits required. Recent Developments: Following Regev's work, researchers Vaikuntanathan and Ragavan found a way to reduce the memory use of Regev's algorithm, bringing it closer to practical implementation. Regev's work underscores that quantum computing is still open to significant discoveries, even in well-studied areas. It suggests that there may be more efficient quantum algorithms yet to be discovered. https://lnkd.in/gCahZP3C

Whether it is an attack on RSA or even potentially on AES, the threat will come from a cryptographically relevant quantum computer (CRQC). The date when such a computer will be available is unknown, making it critical to track the pace of progress in quantum computing. IBM recently unveiled new strides they've made in quantum error correction, a critical component in making quantum computing more reliable and viable. The takeaway for those outside the quantum physics domain is clear: quantum computing is advancing at an accelerating pace. https://lnkd.in/gukSbNq8

In the mid-1990s, Peter Shor's groundbreaking algorithm opened the door to quantum computing's immense potential. It demonstrated how a hypothetical quantum computer could factor large numbers into their prime components far more efficiently than classical machines, challenging the foundations of internet security relying on public-key cryptography. Fast forward to today, Oded Regev, a computer scientist at New York University, has unveiled a groundbreaking variant of Shor's algorithm, altering the relationship between the size of the number being factored and the required quantum operations. This development marks a significant leap forward in quantum computing and cryptography. It's an exciting breakthrough that has the potential to revolutionize the industry and reshape our understanding of computational complexity. While further optimization is needed to apply this algorithm practically, it represents a remarkable advancement in the field. The broader message here is clear: quantum computing researchers must remain open to unexpected surprises and continue exploring new frontiers in this ever-evolving landscape. Don't miss this enlightening article that delves into the future of quantum computing and its potential impacts on our digital world. https://lnkd.in/gKthh8We #QuantumComputing #Cryptography #Innovation #Tech #IP #VC #Patents #DeepTech #Quantum

Y2Q, or Years to Quantum, is a funny way to refer to the years leading up to the day when a sufficiently powerful quantum computer executes Shor's algorithm, thus compromising the public cryptography algorithms currently in use. We have good reason to believe that this 'Quantum apocalypse' could occur sometime in the 2030s (It will only be an apocalypse if we fail to update the algorithms; otherwise, it will be a remarkable scientific and technological achievement). Naturally, the estimation for the Y2Q value fluctuates as our knowledge expands. It can go in either direction. A paper published last August, also covered in a great article by Quanta Magazine, has reduced estimations on Y2Q. Let's consider the minimum necessary set of quantum computer resources and performance metrics required to successfully run Shor's algorithm within a predefined time for, let's say, a 2048-bit number. Let's designate it with Q_shor. Q_shor encompasses more than just the minimum number of qubits; it also includes error rates, coherence times, connectivity, and more. Now, let's assume the 'best' current quantum computer is characterized by the parameter set Q. The Quantum apocalypse occurs when the two variables meet: Q = Q_shor. The paper demonstrated that both variables are dynamic over time. Q naturally grows over time, similar to the exponential growth of processor power (Moore's law) over the past several decades. This paper also established that Q_shor is not static and can be reduced. In particular, the number of logical qubits necessary to break an n-bit integer, scales as n^1.5, compared to the original n^2. This is a huge difference for large n. There is however a potential difficulty with the new implementation, as it might require more memory qubits to store intermediate results. In conclusion, without succumbing to inflated hype, the key takeaway is that organizations should start contemplating a migration to quantum-safe cybersecurity. The risks are simply too high not to do so. Disclaimer: The paper is published on ArXiv and it seems it still hasn't gone through a peer review process. #deloitteriskadvisory #deloitte #shors #quantumsafe #postquantum #y2q https://lnkd.in/dCHrjtHF https://lnkd.in/d5ubv44w

Quantum computing has a hype problem   "Established applications for quantum computers do exist. The best known is Peter Shor’s 1994 theoretical demonstration that a quantum computer can solve the hard problem of finding the prime factors of large numbers exponentially faster than all classical schemes. Prime factorization is at the heart of breaking the universally used RSA-based cryptography, so Shor’s factorization scheme immediately attracted the attention of national governments everywhere, leading to considerable quantum-computing research funding.  "   "There are proposals to use small-scale quantum computers for drug design, as a way to quickly calculate molecular structure, which is a baffling application given that quantum chemistry is a minuscule part of the whole process. Equally perplexing are claims that near-term quantum computers will help in finance. No technical papers convincingly demonstrate that small quantum computers, let alone NISQ machines, can lead to significant optimization in algorithmic trading or risk evaluation or arbitrage or hedging or targeting and prediction or asset trading or risk profiling. This however has not prevented several investment banks from jumping on the quantum-computing bandwagon."   By Sankar Das Sarma at MIT Technology Review   Link https://lnkd.in/ddjbKVws

A Quantum Leap in Factoring – Communications of the ACM: In the mid-1990s, Peter Shor developed the first quantum computing algorithms, demonstrating their potential to vastly outperform classical computers in factoring large numbers, a task crucial for public-key cryptography. Oded Regev of New York University has recently proposed a new scheme that shows promise for significantly reducing the resources required for factoring. However, while Regev's innovation represents an asymptotic improvement, its practical consequences are yet to be determined. Regev's approach involves looking for periodicity in a higher-dimensional space, leading to a more efficient computation process. It also requires more qubits but can be optimized for space. The introduction of new quantum algorithms has sparked optimism for future improvements, but the practical implications and implementation of these advancements remain uncertain.

Computer scientist Oded Regev from New York University has unveiled a faster quantum factoring algorithm, taking #QuantumComputing another step forward. This achievement builds upon Peter Shor's groundbreaking work in the mid-1990s, which had raised questions about the security of classical encryption systems. Regev's algorithm is the first to enhance the relationship between the size of the number being factored and the number of quantum operations needed to factor it. This development holds immense promise for quantum computing's impact on #cryptography and #security. The field of quantum computing never ceases to amaze with its potential for groundbreaking discoveries. The journey towards unlocking the full potential of quantum technology continues. #QuantumTechnology #QuantumAlgorithm #Innovation

The Rise of Quantum Computing: Potential and Challenges Quantum computing represents a paradigm shift in computational power, offering capabilities that surpass traditional computing systems. This emerging technology holds promise for solving complex problems across scientific research, cryptography, optimization, and machine learning. Understanding Quantum Computing Quantum computers operate on principles of quantum mechanics, using quantum ... [...] #QuantumComputing Read more... https://lnkd.in/dJKzDhvx

Quantum computing (QC) is gaining momentum in the market. As the number of QC use cases has grown, so has the size of QC companies. Most QC use cases focus on solving complex scientific and mathematical problems, including cryptography, optimization, and simulations. Given the growth of QC in company size and use cases, it is imperative for companies to take proactive steps to evaluate how QC breakthroughs could revolutionize their operations. This is particularly important because of the time gap that often exists between formulating strategic visions and implementing them, particularly in the realm of IT systems. In this rapidly evolving landscape, embracing QC or preparing for its impact is not a strategic choice but a necessity for companies looking to secure their future competitiveness.