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# Calculating RSA public keys

### Question

Quantum computers are getting better every year and big companies like Microsoft and Google want to add them to their cloud offerings.

One task that quantum computers can do better than regular computers is factoring numbers. This is crucial because a common public-key encryption (and signature) scheme, RSA, relies on the difficulty of factoring the product of two large primes (this product is known as a semiprime). Besides RSA, the two other public-key schemes used in securing internet traffic, DSA signatures and Diffie–Hellman key exchange, are also breakable by quantum computers. The timescale for this happening, however, is unclear (and some still doubt whether it is even in principle possible.)

For a precise question we'll ask:

When will it cost less than $1000 to factor any given 2048-bit semiprime? There's a previous question which makes a prediction for 2030. When will it cost less than$1000 to calculate the private key of a 2048-bit RSA public key?

Resolution is positive if there is compelling evidence that a computing system is employed to perform this task for < $1000. (Thus the system must cost less than this or – far more likely – it must be possible to purchase use of such a computer for the task for <$1000 USD. We'll assume 2020 dollars for this.)

### Prediction

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