Quantum computers and classical computers are fundamentally different
Introduction: Decoding Quantum Mechanics
The curious world of quantum mechanics plays host to quantum computers. Unlike traditional computers, quantum computers operate with qubits, the quantum version of classical bits. In a fascinating twist of quantum physics, qubits can be both a 0 and a 1 simultaneously due to a quantum property known as superposition. Furthermore, qubits can become entangled, a state where the information of one qubit is inextricably linked to another, no matter the distance between them. Apart from the number of qubits, quantum computers’ efficiency is influenced by a range of factors including qubit quality (measured by coherence time), error rates, connectivity (how qubits can interact with each other) and control precision. These nuances mean that quantum computing is as much an engineering challenge as a scientific one.
Quantum Computers vs. Classical Computers: More than Just a Numbers Game
Quantum computers and classical computers are fundamentally different. They are not competitors, but rather complementary tools optimized for different types of problems. Classical computers excel at tasks like running operating systems, managing databases and performing complex arithmetic operations, whereas quantum computers could be capable of transforming fields that involve combinatorial optimization, quantum system simulations and prime factorization of large numbers used in cryptography.
Central to these differences are the algorithms employed by each system. Take Shor’s
algorithm, for example. This quantum algorithm enables quantum computers to factorize large numbers exponentially faster than classical computers can, posing a potential risk to RSA encryption, the backbone of today’s internet security. However, it’s crucial to understand that not all computational tasks will enjoy this quantum speedup—many will see only modest improvement, while some tasks might not benefit at all from quantum processing.
Modern Encryption Schemes: The Security Backbone of the Digital World
The secure communication that underpins today’s internet infrastructure relies on several encryption schemes. RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography) are vital for public-key cryptography, while AES (Advanced Encryption Standard) is a common choice for symmetric-key encryption. These cryptographic systems protect a vast range of digital interactions — from your personal emails and credit card transactions to the blockchain networks that enable cryptocurrencies like Bitcoin.
Quantum Threat to Encryption: A Future Concern?
The potential for quantum computers to efficiently solve the hard mathematical problems that underpin RSA and ECC encryption makes these systems vulnerable. In theory, Shor’s algorithm could break RSA-256 bit encryption with about 4098 logical qubits and ECC-256 with around 2330 logical qubits. However, these numbers don’t account for the error correction overhead, which could multiply the required number of qubits by several orders of magnitude.
AES encryption, meanwhile, faces less risk. Grover’s algorithm—a quantum algorithm — could be used to halve the key length. This would make AES-256 effectively equivalent to AES-128 in a quantum era. But even this scaled-down threat would require an impractical number of about 6.7 million physical qubits, once we consider error correction needs.
Breaking 256-bit Elliptic Curve Encryption with a Quantum Computer
Bitcoin uses the Elliptic Curve Digital Signature Algorithm (ECDSA), which relies on the hardness of the Elliptic Curve Discrete Log Problem (ECDLP), and a modified version of Shor’s algorithm can provide an exponential speedup using a quantum computer for solving this problem. The encryption of keys in the Bitcoin network is only vulnerable for a short window of time, around 10 min to an hour, depending on the fee paid.
The number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would pose a threat to do so. It would require 317 million physical qubits to break the encryption within one hour using the surface code, a code cycle time of 1 μ_s, a reaction time of 10 μ_s, and a physical gate error of (10)^(-3). To instead break the encryption within one day, it would require at least 13 million physical qubits.
The Future of Encryption: Navigating a Quantum World
Despite the theoretical threats, the actual breaking of modern 256-bit encryption by quantum computers remains a distant prospect. As of 2023, the most advanced quantum computers have a few hundred physical qubits, and logical qubits are still in the experimental stage. We are likely several decades away from having the required number of high-quality, error-corrected qubits to break modern encryption.
Director General, COAI
However, the clock is ticking. The field of post-quantum cryptography is already developing new cryptographic systems believed to be secure against quantum attacks. Transitioning to these systems will present its own challenges, but it’s a necessary move to ensure data security in a future quantum world.
The journey to practical quantum computing is long ahead as we are still at the early stages of this technology, and challenging—not just in terms of hardware development, but also towards devising efficient quantum algorithms. Although the impact on our current encryption systems is a concern, it is one that researchers around the globe are actively working to address, ensuring that our digital world remains secure even as we venture further into the quantum space.
