I am a bit confused. I just calculated manually the single steps of RSA for an implementation with small numbers and suddenly $d$ was equal $e$. Please help me understand what I am doing wrong.
Here’s my example:
- I chose: $q = 7$ and $p = 11$
- $N = 77$
- $phi(N) = 60$
- I chose: $e = 29$
- $e \times d + k \times phi(N) = 1 \rightarrow$ Extended Euclidean algorithm
$$k = -14\\ d = 29$$
Test: $29 \times 29 + (-14) \times 60 = 1$
Where is the mistake?