This might be a stupid question but: When RSA key pairs are generated, there is a pubkey and a private key file. Where is the modulus? Is it appended to the keys? I can't find any information about that.

  • $\begingroup$ Suppose that your folder to receive Key pair is "MyLoc" $ ssh-keygen Generating public/private rsa key pair. Enter file in which to save the key (/Users/MyLoc/.ssh/id_rsa): Enter passphrase (empty for no passphrase): Enter same passphrase again: Your identification has been saved in /Users/MyLoc/.ssh/id_rsa. Your public key has been saved in /Users/MyLoc/.ssh/id_rsa.pub. ... You can't edit the key pair.The data is encrypted with the passphrase you entered. Take a look here: git-scm.com/book/fr/v1/… $\endgroup$ Nov 5, 2016 at 16:51

1 Answer 1


The modulus is part of the public key. For RSA, the public key consists of the pair $(n,e)$ where $n$ is the modulus and $e$ is the public exponent.

The SSH public key file contains both, typically one after the other. There's a number of ways to encode this information. The gory details of these encodings I leave to this in-depth answer (it includes a section on SSH).

The SSH private key file contains pretty much all numbers associated with the key generation process. If you want to take a look yourself, try running the following command

openssl rsa -in test.key -text

where test.key is your private key file.

  • $\begingroup$ Ah I see. The private key just stores the primes so the chinese remainder theorem can be applied. The layout is indeed gory. I wonder why they didn't just concatenate the values. Btw, what is the coefficient used for? $\endgroup$
    – AdHominem
    Nov 5, 2016 at 23:31
  • $\begingroup$ @AdHominem: 'coefficient' is $q^{-1} \mod p$ and used in the CRT calcuation; see en.wikipedia.org/wiki/RSA_%28cryptosystem%29#Example . Note this answer is about (locally) stored keys, as the body of your Q seems to be (but only for OpenSSH, other implementations are different); for keys sent in the (current) protocol as in the title of your Q, see tools.ietf.org/html/rfc4253#section-6.6 . $\endgroup$ Nov 6, 2016 at 4:42
  • $\begingroup$ You could of course recalculate it, but I would say that the modulus is part of the private key as well. $\endgroup$
    – Maarten Bodewes
    Nov 6, 2016 at 12:44

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