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The Threat of Quantum Computers – A Curated List

Managed Web Services & Security On Demand The Threat of Quantum Computers – A Curated List

This isn’t mean to be alarmist, as we have other blog posts for that. This is a curated list of supporting articles by Professors, Scientists & Journalists all heralding the same words of warning that have so far been grossly ignored. But first, let us begin with a short Q&A sessions.

So what is a Quantum Computer anyway?

quan·tum com·put·er

noun
a computer that makes use of the quantum states of subatomic particles to store information.
Quantum computing refers to the use of quantum mechanical phenomena like superposition, entanglement etc, to perform computing. Traditional computing works with bits. That is all information is processed and exchanged in 1, 0 /true-false signal which comprises a bit. That is bit is the unit of information in traditional computing. In quantum computer qubits are used instead.1
What is a qubit?
qubits are the basic unit of quantum information, a qubit is a two state quantum mechanical system. (what this means? A quantum mechanical two state system can be like electronic spin (or any fermion) with states of +1/2 and -1/2, or photons with two states of polarization, nuclear spins, etc).  We represent this by vectors (kets) |0and|1|0⟩and|1⟩, Think of this as down and up vectors.2

Now for the fun stuff, lets look at the classic  examples – then go into classic answers.
1. How many qubits are required for breaking RSA 2048 and RSA 4096 in real-time with a quantum computer?

Like the answer linked shows, about log2(N2)=2log2(N)log2⁡(N2)=2log2⁡(N) or just 2n2n where nn is the number of bits of the modulus NN, i.e. the key size of RSA. So 4096 for 2048-bit RSA, double that for 4096-bit.

This paper (PDF) has an algorithm using 2n+32n+3 qubits, where n=log2(N)n=log2⁡(N), where log2(N)log2⁡(N)is the way to calculate the number of bits in NN.

1. How many qubits are required to break Curve25519?

Breaking elliptic curves requires (pdf, see 6.2) roughly 6n6n qubits where nn is the order or key size of the curve, which for Curve25519 would be 6255=15306∗255=1530. Less than secure RSA sizes require, but much more than has been accomplished.

1. I want to work out the relationship between the key length and number of qubits required to break that key length.

See above.

Source – https://www.quora.com/What-is-quantum-computing-and-what-is-its-scope-in-future

Source – https://crypto.stackexchange.com/questions/35137/how-many-qubits-are-required-to-break-rsa-2048-or-4096-with-a-universal-quantum