Quantum Computing and Encryption Breaking

Question

I read a while back that Quantum Computers can break most types of hashing and encryption in use today in a very short amount of time(I believe it was mere minutes). How is it possible? I've tried reading articles about it but I get lost at the a quantum bit can be 1, 0, or something else. Can someone explain how this relates to cracking such algorithms in plain English without all the fancy maths?

Answer 1

The Wikipedia article does a very good job of explaining this.

In short, if you have N bits, your quantum computer can be in 2^N states at the same time. Similar conceptually to having 2^N CPU's processing with traditional bits (though not exactly the same).

Answer 2

A quantum computer can implement Shor's algorithm which can quickly perform prime factorization. Encryption systems are build on the assumption that large primes can not be factored in a reasonable amount of time on a classical computer.

Answer 3

Quantum computing is inherently a very mathematical subject, and explaining how quantum computers can be more efficient than classical computers in breaking encryption algorithms is not a simple task. You'll have to have at least an undergraduate understanding of linear algebra and quantum mechanics to understand half of the details. I'll try to break it down, though.

The basic premise of quantum computation is quantum superposition. The idea is that a quantum system (such as a quantum bit, or qubit, which is the quantum analogue of a normal bit) can, as you say, exist not only in the 0 and 1 states (called the computational basis states of the system), but also in any combination of the two (so that each has an amplitude associated with it). When the system is observed by someone, the qubit's state collapses into one of its basis states (you may have heard of the Schroedinger's cat thought experiment, which is related to this).

Because of this, a register of n qubits has 2^n basis states of its own (these are the states that you could observe the register being in; imagine a classical n-bit integer). Since the register can exist in a superposition of all these states at once, it is possible to apply a computation to all 2^n register states rather than just one of them. This is called quantum parallelism.

Because of this property of quantum computers, it may seem like they're a silver bullet that can solve any problem exponentially faster than a classical computer, but the problem is that once you observe the result of your computation, it collapses (as I mentioned above) into the result of just one of the computations and you lose all of the others.

The field of quantum computation/algorithms is all about trying work around this problem by manipulating quantum phenomena to extract information in fewer operations than would be possible on a classical computer. It turns out that it's very difficult to contrive a "quantum algorithm" that is faster than any possible classical counterpart.

The example you ask about is that of quantum cryptanalysis. It's thought that quantum computers might be able to "break" certain encryption algorithms: specifically, the RSA algorithm, which relies on the difficulty of finding the prime factors of very large integers. The algorithm which allows for this is called Shor's algorithm, which can factor integers with polynomial time complexity. By contrast the best classical algorithm for the problem has sub-exponential time complexity, and the problem is hence generally considered "intractable".

If you want further insight into this, I suggest you get a few books on linear algebra and quantum mechanics and sit down somewhere comfortable with a lot of coffee. If you want some clarification, I'll see what I can do!

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Aside: to better understand the idea of quantum superposition, think in terms of probabilities. Imagine you flip a coin and catch it on your hand, covered so that you can't see it. As a very tenuous analogy, the coin can be considered to be in a superposition of the heads and tails "states": each one has a probability of 0.5 (and since there are two states, these probabilities add up to 1). When you take your hand away and observe the coin directly, it collapses into either the heads state or the tails state, and so the probability of this state becomes 1, while the other becomes 0. One way to think about it, I suppose, is a set of scales that is balanced until observation, at which point it tips to one side as our knowledge of the system increases and one state becomes the "real" state.

Of course, we don't think of the coin as a quantum system: for all practical purposes, the coin has a definite state, even if we can't see it. For genuine quantum systems, however (such as an individual particle trapped in a box), we can't think about it in this way. Under quantum mechanics, the particle fundamentally has no definite position, but exists in all possible positions at once. Only upon observation does it take a specific position (though this opens up another can of worms), and even this is purely random and determined only by probability.

By the way, quantum systems are not restricted to having just two observable states (those that do are called two-level systems). Some have a large but finite number, some have a countably infinite number (such as the electron in a hydrogen atom), and some even have an uncountably infinite number (such as a particle's position, which isn't constrained to individual points in space).

Answer 4

In the most basic terms, a normal no quantum computer works by operating on bits (sates of on or off) uesing boolean logic. You do this very fast for lots and lots of bits and you can solve any problem in a class of problems that are computable.

However they are "speed limits" namely something called computational complexity.This in lay mans terms means that for a given algorithm you know that the time it takes to run an algorithm (and the memory space required to run the algorithm) has a minimum bound. For example a algorithm that is O(n^2) means that for a data size of n it will require n^2 time to run.

However this kind of goes out the window when we have qbits (quantum bits) when you are doing operations on qbits that can have "in between" values. algorithms that would have very high computational complexity (like factoring huge numbers, the key to cracking many encryption algorithms) can be done in much much lower computational complexity. This is the reason that quantum computing will be able to crack encrypted streams orders of magnitude quicker then normal computers.

Answer 5

It's highly theoretical at this point. Quantum Bits might offer the capability to break encryption, but clearly it's not at that point yet.

At the Quantum Level, the laws that govern behavior are different than in the macro level.

To answer your question, you first need to understand how encryption works.

At a basic level, encryption is the result of multiplying two extremely large prime numbers together. This super large result is divisible by 1, itself, and these two prime numbers.

One way to break encryption is to brute force guess the two prime numbers, by doing prime number factorization.

This attack is slow, and is thwarted by picking larger and larger prime numbers. YOu hear of key sizes of 40bits,56bits,128bits and now 256,512bits and beyond. Those sizes correspond to the size of the number.

The brute force algorithm (in simplified terms) might look like

for(int i = 3; i < int64.max; i++)
{
  if( key / i is integral)
  {
    //we have a prime factor
  }
}

So you want to brute force try prime numbers; well that is going to take awhile with a single computer. So you might try grouping a bunch of computers together to divide and conquer. That works, but is still slow for very large keysizes.

How a quantum bit address this is that they are both 0 and 1 at the same time. So say you have 3 quantum bits (no small feat mind you).

With 3 qbits, your program can have the values of 0-7 simulatanously

(000,001,010,011 etc)

, which includes prime numbers 3,5,7 at the same time.

so using the simple algorithm above, instead of increasing i by 1 each time, you can just divide once, and check

0,1,2,3,4,5,6,7

all at the same time.

Of course quantum bits aren't to that point yet; there is still lots of work to be done in the field; but this should give you an idea that if we could program using quanta, how we might go about cracking encryption.

Answer 6

Almost all our public-key encryptions (ex. RSA) are based solely on math, relying on the difficulty of factorization or discrete-logarithms. Both of these will be efficiently broken using quantum computers (though even after a bachelors in CS and Math, and having taken several classes on quantum mechanics, I still don't understand the algorithm).

However, hashing algorithms (Ex. SHA2) and symmetric-key encryptions (ex. AES), which are based mostly on diffusion and confusion, are still secure.

Answer 7

First of all, quantum computing is still barely out of the theoretical stage. Lots of research is going on and a few experimental quantum cells and circuits, but a "quantum computer" does not yet exist.

Second, read the wikipedia article: http://en.wikipedia.org/wiki/Quantum_computer

In particular, "In general a quantum computer with n qubits can be in an arbitrary superposition of up to 2^n different states simultaneously (this compares to a normal computer that can only be in one of these 2^n states at any one time). "

What makes cryptography secure is the use of encryption keys that are very long numbers that would take a very, very long time to factor into their constituent primes, and the keys are sufficiently long enough that brute-force attempts to try every possible key value would also take too long to complete.

Since quantum computing can (theoretically) represent a lot of states in a small number of qubit cells, and operate on all of those states simultaneously, it seems there is the potential to use quantum computing to perform brute-force try-all-possible-key-values in a very short amount of time.

If such a thing is possible, it could be the end of cryptography as we know it.