Comment l’informatique quantique peut-elle casser le cryptage RSA avec l’algorithme de Shor ?

- Understanding that Shor's algorithm, is a key algorithm in quantum computing, can efficiently factor large numbers into their prime factors.🛡️🔓 - Shor's algorithm can break RSA encryption by efficiently factoring the large composite numbers used as RSA public keys. 🕵️♂️🔍 - While Shor's algorithm is theoretically capable of breaking RSA encryption, the current practical implementation of quantum computers is not yet at a level where they can factor large numbers efficiently enough to pose an immediate threat to RSA encryption. ⏳🔬 - It's important to explore and develop post-quantum cryptographic algorithms that are resistant to attacks from quantum computers. 💻🔒

Quantum computing is a new paradigm that harnesses quantum mechanical phenomena to process information. Unlike classical computers that use bits (0 or 1), quantum computers use qubits which can be in a superposition of both states simultaneously. This allows quantum computers to perform certain computations exponentially faster than classical computers by exploiting quantum parallelism and entanglement. Quantum algorithms, like Shor's, are designed to take advantage of these quantum properties to solve problems that are intractable for classical computers. While still in its early stages, quantum computing has the potential to revolutionize fields like cryptography, chemistry, and optimization.

Quantum computers are non-deterministic Turing machines as opposed to classical computers which are deterministic. A non deterministic Turing machine is capable of evaluating multiple logical paths simultaneously and then returning the result that satisfies some criteria first. A deterministic machine can do the same thing but it must evaluate each path one at a time. The word determinism tells us that one input effectively maps to one correct path meanwhile a non-deterministic machine's state maybe evaluating multiple paths simultaneously in search of a single correct path. For certain classes of problems this quasi-parallelism can obtain an exponential speedup in time the deterministic alternative. This is quantum advantage.

Think of regular computers as light switches that are either on (1) or off (0). Quantum computers use something called qubits, which can be both on and off at the same time, thanks to a strange property called superposition. It’s like having a spinning coin that’s both heads and tails until you look at it. This allows quantum computers to explore many possibilities at once, making them potentially super-fast at solving certain problems, like cracking codes or simulating molecules for drug discovery.

Quantum computing still needs to prove itself but one thing that we know that quantum will work is to break cryptography. We don't know when but will know that will happen. This is mainly because we know that Shor and Grover's algorithm will work in large quantum computers. So collecting now and decrypting later with data is the problem.

RSA encryption is a widely used asymmetric cryptographic algorithm named after its inventors, Ron Rivest, Adi Shamir, and Leonard Adleman. It is based on the practical difficulty of factoring the product of two large prime numbers, the "factoring problem". RSA involves a public key and a private key. The public key is used for encryption, while the private key is used for decryption. The method is widely used in secure communication protocols, digital signatures, and other cryptographic applications due to its security properties and practicality. However, its security relies on the difficulty of factoring large integers, which could be compromised by quantum algorithms if large enough quantum computers are developed in the future.

RSA (Rivest–Shamir–Adleman) is a widely-used public-key cryptosystem for secure data transmission. It is an asymmetric algorithm, meaning it uses a pair of keys - a public key for encryption and a private key for decryption. The security of RSA relies on the difficulty of factoring the product of two large prime numbers. The public key consists of this product (called the modulus) and an encryption exponent. The private key is derived from the prime factors and a decryption exponent. To encrypt a message, it is raised to the power of the encryption exponent modulo the modulus. Decryption involves raising the ciphertext to the power of the decryption exponent modulo the modulus.

RSA is an asymmetric encryption model, which means it has two different keys (a public one and a private one). In classical computing, this makes it more secure than symmetric encryption, where both sender and receiver share the same key. Quantum computing changes this conventional wisdom because Shor’s algorithm only works against asymmetric encryption. Symmetric encryption models -- such as AES – are believed to be quantum resistant already so long as the key size is larger enough.

RSA has been here for many and many years and will be broken when it is possible to run Shor's algorithm in large quantum computers, the main point is that it can factor large prime numbers in a fast way. The point is that the problem that RSA solves is easy for quantum computers and hard for classical ones.

In simpler terms, think of RSA encryption as like sending secret messages in a locked box. There are two keys: a public key and a private key. You share your public key with everyone, like a mailbox where anyone can drop a message. Only you have the private key, which is like the special key to open the mailbox. When someone wants to send you a secret message, they use your public key to lock the message in the box. Even though anyone can see the locked box, only you can open it with your private key to read the hidden message.

Imagine you have a huge box of Lego blocks that are all stuck together, and your job is to find the exact way they were combined, but there are millions of possibilities, and it could take forever to do it by trying one piece at a time. Shor's algorithm is like having an Apple Vision Pro that lets you see inside the big Lego block through augmented reality, showing you precisely where to split the big block into smaller, exact pieces without trying every single option. In the world of computers, this "Apple Vision Pro" helps a quantum computer break down really big numbers into smaller pieces (factors) super fast, something that regular computers take a really long time to do. Follow to learn more.

it developed by Peter Shor in 94,is a quantum algorithm for integer factorization.It finds the prime factors of a large composite number exponentially faster than the best known classical algorithms.The algorithm has two main parts: a quantum subroutine and a classical post-processing step.The quantum subroutine uses the Quantum Fourier Transform to find the period of a modular exponential function.This period,with high probability,allows the factors to be derived using a classical method like the continued fractions algorithm.Shor's algorithm achieves an exponential speedup over classical factoring algorithms by exploiting quantum superposition and interference.If implemented on a large-scale quantum computer,it could break RSA encryption.

Owing to quantum parallelism and and quantum interference, the Quantum Fourier Transform can be implemented with only n^2 gates, exponentially faster than classical Discrete Time Fourier Transform which needs O(n(2^n)) gates.

Shor's algorithm, designed for quantum computers, exploits the phenomenal processing power of quantum mechanics. It's capable of efficiently solving the prime factorization problem that RSA relies on for its security. Threat to RSA: Unlike classical computers, quantum computers can rapidly factorize large numbers, undermining the security of RSA encryption.

Shor's algorithm can break public-key encryption through its ability to factor prime numbers exponentially faster than the best classical super computers. While we are many years away from powerful enough quantum computers to pose a real threat to current PK cryptography, they key point is Shor's algorithm has been shown to successfully find the prime factors of a small number. The algorithm is proven, it's just a matter of time before the technology catches up. How long? That's the million dollar question. Key message: organisations will need to devise plans to modernise their cryptography to become quantum resistant over the next decade.

Peter Shor, who was one of my professors during my Quantum course at MIT, developed Shor's algorithm. This algorithm has the capability to compromise RSA encryption by effectively factoring large integers, a foundational aspect of RSA's security mechanism. The catch is that a sufficiently powerful quantum computer is required. Without a fault-tolerant quantum computer, we only possess part of the solution. Therefore, there's still some time before this becomes a practical concern. Check out my latest Linkedin Live on this topic.

which is the product of two secret prime factors. If these prime factors can be determined, the private key can be easily calculated, breaking the encryption. Shor's quantum algorithm provides a way to find these prime factors efficiently. By running the quantum subroutine on the RSA modulus, a quantum computer can determine its period, which then allows the prime factors to be derived using classical post-processing. With the prime factors, the private key can be computed, enabling the decryption of RSA-encrypted messages. While current quantum computers are not yet advanced enough to factor typical RSA key sizes, Shor's algorithm demonstrates that RSA is theoretically vulnerable to a quantum attack.

There is a short equation with 3 variables. We start off knowing 1 variable, the integer we want to factor. We normally have to guess the other 2 variables, which is what makes factorization so challenging. But Shor's gives us 1 of the unknown values, so now we know 2 and have to guess 1. It's much easier to guess 1 unknown, and we soon have all 3 values. With these 3 values, we can calculate the factors of the target integer. And with these factors, if we're talking about RSA, the message is compromised.

It leverages quantum parallelism and the periodicity of modular exponentiation to find the prime factors of a composite number, which forms the basis of RSA encryption. Traditional RSA relies on the difficulty of factoring large numbers to secure communication, but Shor's algorithm undermines this assumption by offering a polynomial-time solution on quantum computers. As quantum computing advances, Shor's algorithm poses a significant threat to classical cryptographic systems like RSA, emphasizing the urgency for quantum-resistant encryption schemes.

The potential of quantum computers to break widely-used public-key cryptography like RSA has significant implications for digital security. If large-scale quantum computers become a reality, they could retroactively decrypt vast amounts of RSA-encrypted data, compromising privacy and security. This has led to the development of post-quantum cryptography - cryptographic algorithms believed to be secure against both classical and quantum attacks. These include lattice-based, code-based, and multivariate cryptography. Standardization efforts, like NIST's post-quantum cryptography competition, aim to establish new quantum-resistant standards.

The US government and many tech companies like Qualcomm are already taking steps to convert to post quantum cryptography which would be resistant against Shor's algorithm. Unlike RSA, post-quantum cryptography uses mathematical problems believed to be hard even for quantum computers, such as lattice-based, hash-based, or code-based problems. These methods don't depend on prime factorization or discrete logarithms, making them resistant to quantum attacks while still enabling secure communication and data protection in a quantum future. NIST has spearheaded the effort to create standards and there are currently 4 algorithms. It's expected that these algorithms will be "production ready" sometime in 2024.

Quantum computing is reshaping cryptography in major ways: 1. Encryption Threat: Quantum computers can solve problems like factoring large numbers much faster than classical ones, potentially breaking current encryption methods like RSA and ECC. Shor’s algorithm could crack RSA encryption in record time. 2. Post-Quantum Cryptography: To counter this, researchers are developing post-quantum cryptography—new methods based on complex problems that are resistant to quantum attacks. 3. New Security Frontiers: Quantum tech also offers Quantum Key Distribution (QKD), which could establish secure communication channels immune to eavesdropping. Updating our cryptographic strategies is crucial as we enter the quantum era.

Although, Quantum Computing and Shor’s algorithm pose a significant threat to cryptography and encryption in general, it also depends on how good a quantum computer we have, which is still a fair bit away. There is intensive active research going on in quantum cryptography to have an algorithm which is secure and cannot be broken even by perfect quantum computer.

While the threat of quantum computers breaking RSA is not immediate, the potential consequences are severe enough to warrant serious attention and preparation. Sensitive data encrypted today with RSA could be stored and decrypted in the future once quantum computers become powerful enough. A proactive approach to post-quantum transition is crucial. This involves increasing awareness, assessing quantum risks, creating transition roadmaps, and testing and implementing post-quantum solutions. Hybrid schemes that combine classical and post-quantum algorithms can offer a gradual transition. Ongoing research in quantum cryptanalysis is essential to assess the long-term security of post-quantum candidates.

Shor's algorithm leverages the inherent parallelism of qubits to factorize large numbers exponentially faster than classical algorithms. In the context of RSA, which relies on the difficulty of factoring the product of two large prime numbers, Shor's algorithm becomes a game changer. The quantum parallelism enables it to efficiently determine the prime factors, compromising the security of RSA encryption. To safeguard against such quantum threats, the field is actively exploring post-quantum cryptographic algorithms resistant to quantum attacks.

Currently, due to limitations in quantum hardware - NISQ - we are quite far from decryption of messages encrypted with RSA with for example 2048bits. Now - until quantum hardware has evolved enough - we have the chance to think about ways out of the dilemma, either by applying Post-Quantum-Cryptography algorithms or enlarging bit depth used in current cryptography algorithms. Nevertheless, we need to think about a stable interface and API that allows to seamless change the underlying cryptography algorithms if need be.

Post-Quantum Cryptography (PQC), which is often overlooked, requires immediate attention from large organizations with complex digital infrastructures. Quantum threats are on the horizon, and implementing PQC takes time. Sectors like finance, healthcare, and government, dealing with sensitive data, must act swiftly to ensure long-term security. The clock is ticking; the journey to PQC readiness is essential to protect critical infrastructure and data. In this quantum era, PQC is the shield organizations need to safeguard their digital assets.