Tools

Time and odds calculator

Work out for yourself how much hardware it takes before any of this means anything. Move the sliders and two things come into focus — that one bit is a factor of two, and that whether the public key is exposed matters more than ten thousand machines.

Puzzle number (= bit width)#71 · interval 2^70

#71 runs from 2⁷⁰ to 2⁷¹−1, so it holds 2⁷⁰ keys.

The public key is known — Kangaroo, square root of the intervalSome of the puzzles numbered in multiples of five qualify. Tick this and the work needed drops to a square root.

Rate per machine2.5×10^9 keys/s

Number of machines1

Combined rate

2.5×10^9

keys / sec

Work required

1.2×10^21

2^70

Time to sweep it all

14,964 years

whole interval

Chance of success in a year

1 in 14,964

a day is not a meaningful unit here

Not realistic

This setup does not finish inside a human lifetime. Lower the bits (an easier puzzle), pick one whose public key is exposed, or add hardware by orders of magnitude.

How this is calculated

· No public key: based on sweeping the whole interval, 2^n-1 keys. With luck it turns up around halfway.
· Public key exposed: expected work for Pollard's Kangaroo ≈ √(interval) = 2^(n-1)/2.
· The probabilities assume a uniform distribution. There is no “it's been a while, so it's due”.