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 ($q_{\mathrm{inv}} = q^{-1} \pmod{p}$)

Answer 2

e ∈ {1,2, . . . ,Φ(n)−1} and gcd(e,Φ(n)) = 1.

in addition Φ(n) = (p−1)(q−1) and n = p * q

and then compute: d*e ≡ 1 modΦ(n)

For Instance that might me this value:

p=0DFD2C2A288ACEBC705EFAB30E4447541A8C5A47A37185C5A9CB98389CE4DE19199AA3069B404FD98C801568CB9170EB712BF10B4955CE9C9DC8CE6855C6123h Q=EBE0FCF21866FD9A9F0D72F7994875A8D92E67AEE4B515136B2A778A8048B149828AEA30BD0BA34B977982A3D42168F594CA99F3981DDABFAB2369F229640115h n=F33188211FDF6052BDBB1A37235E0ABB5978A45C71FD381A91AD12FC76DA0544C47568AC83D855D47CA8D8A779579AB72E635D0B0AAAC22D28341E998E90F82122A2C06090F43A37E0203C2B72E401FD06890EC8EAD4F07E686E906F01B2468AE7B30CBD670255C1FEDE1A2762CF4392C0759499CC0ABECFF008728D9A11ADFh e=40B028E1E4CCF07537643101FF72444A0BE1D7682F1EDB553E3AB4F6DD8293CA1945DB12D796AE9244D60565C2EB692A89B8881D58D278562ED60066DD8211E67315CF89857167206120405B08B54D10D4EC4ED4253C75FA74098FE3F7FB751FF5121353C554391E114C85B56A9725E9BD5685D6C9C7EED8EE442366353DC39h d=C21A93EE751A8D4FBFD77285D79D6768C58EBF283743D2889A395F266C78F4A28E86F545960C2CE01EB8AD5246905163B28D0B8BAABB959CC03F4EC499186168AE9ED6D88058898907E61C7CCCC584D65D801CFE32DFC983707F87F5AA6AE4B9E77B9CE630E2C0DF05841B5E4984D059A35D7270D500514891F7B77B804BED81h