Timeline for Breaking the RSA encryption based on a $(e,N)$ given an integer $w \neq 0$ such that $e^w = 1 \mod(N)$?

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May 31, 2016 at 16:40	comment	added	Emil Jeřábek		Yes, I believe the assumptions are mistaken.
May 31, 2016 at 16:24	comment	added	Jan Maly		I am still a bit confused by the line above the definition of the RSA function that you cited. There it is assumed that $g$ is coprime to $\phi(N)$. It seems to me, that this is a rather strange assumption if $g$ is the cyphertext and not the public key. In the paper, this assumption is not made (It is assumed that $g$ is coprime to $N$, which seems a lot more sensible). May I assume that this assumption is there by mistake? Or am I overlooking something?
May 31, 2016 at 16:14	comment	added	Jan Maly		You are right. I got confused by the notation. The paper you mentioned was very helpful. If I am correct, $g$ is not the plaintext but the cyphertext. Otherwise the algorithm for braking RSA attained on p. 155 would be rather strange as it gets $g$ as an input. However, as described in the paper, finding a $w$ such that $g^w = 1 \mod{N}$ suffices to break the encryption because we can compute the inverse $d$ of the encryption key $e$ modulo $w$. Then $g^d \mod{N}$ is the plaintext.
May 31, 2016 at 16:05	vote	accept	Jan Maly
May 31, 2016 at 14:48	history	edited	Emil Jeřábek	CC BY-SA 3.0	added 2 characters in body
May 31, 2016 at 14:15	history	answered	Emil Jeřábek	CC BY-SA 3.0