In the realm of data security, a significant concern arises from the interception and storage of encrypted information by nation-states and individual actors. However, the landscape is expected to witness a paradigm shift within the next 10 to 20 years over Encryption. It is believed that the emergence of quantum computers will enable the decryption of encoded data in a matter of minutes. Referred to as “store now or decrypt later” (SNDL), this process poses a considerable challenge to the existing security infrastructure. The National Security Administration warns that a large-scale quantum computer if realized, could potentially undermine all widely deployed public key algorithms.
The Power of Quantum Computers:
Unlike traditional computers, quantum computers harness the principles of quantum mechanics to operate on quantum bits or qubits. These qubits possess two states, zero or one, allowing for an exponential increase in computational power. With a mere 300 qubits, a quantum computer can represent more states than there are particles in the observable universe. However, it is important to note that the practical application of quantum computers remains limited, as their potential is largely confined to specific complex computations.
Unraveling the Encryption Challenge:
To comprehend how quantum computers can efficiently factorize the product of two primes, it is crucial to examine a simplified example that does not require the utilization of a quantum computer.
The Role of Divisors:
The “divisor” concept refers to the greatest common divisor of two numbers. Let us consider the example of finding the greatest common divisor of 32,769 and 77, which is denoted as the divisor. In this scenario, Euclid’s algorithm is employed to determine the factors of n.
Accelerating the Process:
In the absence of quantum computing, the steps involved in factoring a product can be expedited through alternative methods. Initially, the qubits are divided into two sets. The first set is prepared in a superposition state, encompassing zero, one, and one.
The second set comprises an equal number of qubits, all in the zero state initially. Subsequently, an educated guess, denoted as g, is made, assuming it does not share factors with n. The first set is then raised to the power of g and divided by n, with the remainder being stored in the second set. This process is repeated, ensuring the same state for all remainders. Additionally, each term is separated from its neighbors by an amount denoted as r.
The Impact of Quantum Computing on Encryption:
The implications of quantum computing for encryption are significant. As the computational power of quantum computers advances, the secure nature of modern cryptography, which relies on prime numbers with approximately 313 digits, is at stake. Factoring such large prime numbers conventionally would require an estimated 16 million years. However, with the advent of quantum computers, this daunting task can be accomplished much more swiftly. Quantum computing enables a quantum Fourier transform, facilitating the extraction of frequency information from a periodic superposition. Nevertheless, it is essential to note that for most practical applications, quantum computers currently offer limited utility.
In conclusion, the rise of quantum computing introduces both promises and challenges in the field of data security. The ability to decrypt encrypted information within minutes poses a significant concern for the future of encryption algorithms. While quantum computers exhibit immense potential, their practical application is currently constrained. As technological advancements continue, it is imperative for researchers and security experts to develop robust encryption methods capable of withstanding the computing power of quantum systems.