What data is saved in RSA private key?

Question

What data is saved in RSA private key in openssl? How to view it?

Wikpedia says these variables are saved.

Answer 1

You can print the data with (change PEM to DER if required):

openssl rsa -in Alice.key -text -inform PEM -noout

The following data is stored:

• Modulus ($n = pq$)
• Public exponent ($e$)
• Private exponent ($d = e^{-1} \pmod{\phi{(n)}}$)
• First prime ($p$)
• Second prime ($q$)
• First exponent, used for Chinese remainder theorem ($d_P = d \pmod{p - 1}$)
• Second exponent, used for CRT ($d_Q = d \pmod{q - 1}$)
• Coefficient, used for CRT ($q_{\mathrm{inv}} = q^{-1} \pmod{p}$)