Over the past 25 years, the world’s ability to exchange information at the speed of light through the Internet has changed everything. One of the basic functions of this Internet grid is the secure exchange of information between systems and people. As we discussed in our Ethical Hacking and Cybersecurity course, this secure exchange of information relies on a set of cipher suites for symmetric encryption, asymmetric encryption, and hashing, and there has always been an assumption that a brute force approach will also be adopted because trying all possible permutations and combinations requires a lot of processing time. As we saw in the course, all public-key and private-key encryption today rely on a large number of combinations of prime factors, integer factors, and discrete logarithms. Cracking with brute force is impossible as the time required increases exponentially.

However, with the advent of quantum computing, that may change in the future. If quantum computing can realize its potential, it could enable successful brute force attacks. Using quantum computing, a hacker can crack a password or private key by trying many possibilities in a short period of time, which is almost impossible in the traditional non-quantum computing world.

Computer engineers classify problems into three categories: P, NP, and NP-complete.

• P problem – which computers can solve efficiently in polynomial time
• NP problem – whose solution can be verified in polynomial time, but whose solution itself is an exponential time problem
• NP-Complete – An efficient solution to any of these problems will provide solutions to all NP problems

If we want to solve NP problems in polynomial time, our last hope is to expand what we mean by “computer.” Moreover, quantum computers may be a far-sighted hope for solving this problem.

How is quantum computing different?

Quantum computers do calculations differently than the classical computers we know. Our classic computers relied on a bunch of scratchpad registers and performed AND/OR and conditional operations in an intuitive and easy-to-understand way. However, quantum computers perform a different set of operations in addition to traditional logical and conditional operations. That’s the difference.

Imagine we have 1000 particles to measure. At any time, when we measure these 1,000 particles, they are either spinning up or down. If an electron spins clockwise around its axis, it is said to be spin-up; if it spins counterclockwise, it is spin-down.

Now, each particle can be rotated up or down, so the possible permutations are 2^1000. So, in the world of quantum computing, we assign what’s called an “amplitude” (a value expressed as a complex number) to each permutation.

P1, P2, P3, P4,…, P1000

U, D, D, D,…………., D —> Specify amplitude A1

U, U, D, D,…………., D —> allocated amplitude A2

Wait…you know what to do.

But the problem is with the amplitude value. They can be both positive and negative.

Now, we perform physical manipulations on these particles, such as hitting these 1,000 particles with radio waves or laser pulses. After doing this, we examine the final quantum states of these particles. Note that when we examine at any point in time, we still only capture one of the physical states.

So, how is this different from classical computing? It still feels the same. The difference lies in the interference or superposition of the amplitudes of these particles.

This intuition comes from particle physics, where good equilibrium solutions usually place particles in certain positions. This means that, while there are many possibilities in theory, particles naturally tend toward equilibrium positions that provide equilibrium solutions.

Therefore, in a quantum computer algorithm, the possibility of not leading to an equilibrium solution will cause the particle amplitudes to cancel each other out. This would lead to situations where the permutations leading to solutions would have a certain type of magnitude, leading to the cancellation or exclusion of many possibilities that would not lead to solutions.

When the amplitudes cancel, the interference is called destructive interference. When amplitudes with the same sign are added, it is called constructive interference.

We cannot solve all problems this way. There are actually only a few problems designed to test this solution, but even these don’t have much practical application.

However, one of the problems where this quantum solution framework might be applicable is factorization. Furthermore, we know that public-private key encryption relies heavily on factorization. Quantum computing could therefore lead to a fundamental disruption of public-private key encryption, in which case all communication systems would be made public.

What kind of problems (P, NP,…) can be solved by quantum computing?

There is a new problem called bounded error, quantum polynomial time (BQP). These problems are not NP-hard, but a set of NP-complete problems that can be solved by a quantum computer in polynomial time. Currently, it has been found that exponential time problems involving factorization can be solved in polynomial time using quantum computers, but the evidence is not yet fully established due to the large number of errors in quantum computing.

in conclusion

We’ll never know if quantum computing will ever see the light of day in practical applications. A major problem with quantum computing is the lack of fundamental principles for solving the problem. But, never say never! It has the potential to be used for a specific set of applications involving factorization, but the current effort and error are still too high to be practical on a large scale.

Quantum-safe cryptography or post-quantum cryptography (PQC) is the emergence of a set of cryptographic algorithms that will be resistant and safe from quantum decryption, preparing for a post-quantum world in case such risks arise in the future.

Hope this helps, thanks.

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