That's what raising to d is, taking root of power e.
D is not chosen, it is computed as e^-1 mod (p-1)(q-1). Which makes m^d the root of degree e of m. No one can compute d, because they don't know (p-1)(q-1), because they can't factor pq.
Now, p and q are random, so d is also random, even if e isn't. E is small, so signature verification is faster. Because you can afford to choose e to make someone's life easier.
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timeasmymeasure
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Date: 2020-02-22 08:21 am (UTC)D is not chosen, it is computed as e^-1 mod (p-1)(q-1). Which makes m^d the root of degree e of m. No one can compute d, because they don't know (p-1)(q-1), because they can't factor pq.
Now, p and q are random, so d is also random, even if e isn't. E is small, so signature verification is faster. Because you can afford to choose e to make someone's life easier.