For the record, how does RSA work?

Question

RSA

Help to understand some points of the RSA crypto algorithm.
How is the secret exponent calculated here, above in the theory it is written that this is the multiplicatively inverse of the mod operation , could you give an example, and where did the coefficient k come from , above in the theory it is not mentioned.

Answer 1

where did the coefficient come from

I picked up the method of scientific poke.
The multiplicatively inverse element d modulo phi(n) means e*d = 1 mod phi(n), i.e. e*d = k*phi(n) + 1, for some integer k. You need to choose k so that the right side of the last equality is divisible by e without a remainder