That's not correct. Consider, for example, a processor that can handle 2^31 computations per second. 2^32 operations can be computed in 2 time units, whereas 2^64 operations will take 2^33 time units.
search_space(n: number_of_bits) = 2^n * k
so search_space(1024)/search_space(512)=2^512, not 2^2.
Asymptotics in GNFS are better[0], but only on the order of e^(cbrt(512 * 64/9)) times more work, not 2^2.
This would give an approximation of math.exp(math.cbrt(512 * 64/9))*$8 = $40 million for 1024 bits.
Pretty sure the search cost of GNFS is (bits)^2, the search cost of brute force is 2^(bits), if it was 2^(bits) GNFS would be no better than brute force.
search_space(n: number_of_bits) = 2^n * k
so search_space(1024)/search_space(512)=2^512, not 2^2.
Asymptotics in GNFS are better[0], but only on the order of e^(cbrt(512 * 64/9)) times more work, not 2^2.
This would give an approximation of math.exp(math.cbrt(512 * 64/9))*$8 = $40 million for 1024 bits.
[0] https://en.wikipedia.org/wiki/General_number_field_sieve