Reviewing the SSH keys of hosts that I connect to (as gathered by PuTTY in registry key HKEY_CURRENT_USER\SoftWare\SimonTatham\PuTTY\SshHostKeys), I find that they all start with 0x10001 (65537) or 0x23 (35), most often followed by 2048-bit composite values with no small factor. I conclude they are RSA keys, and that 0x23 (35) is the second most common public exponent in my sampling.

What software commonly generates RSA keys with that public exponent 0x23 (35)? Why that value, which is not prime, and thus slightly complicates the selection of the factors of the public modulus?

  • is there anything common between the hosts that have that?
    – ilkkachu
    Oct 20 '16 at 21:37
  • 2
    @grochmal: this Q is about (pub)keys from servers received by putty. The RSA keys putty generates use 37, with a not-very-explanatory comment in sshrsag.c: #define RSA_EXPONENT 37 /* we like this prime */ Oct 21 '16 at 3:17

Versions of OpenSSH up to 5.3 AFAICT then they switched to F4=65537. I don't recall seeing an explanation for why they used 35, but I haven't read every line of everything.

  • Good one (+1). I always thought they generated the exponent too. But then again, that's part of the pubkey, so it is public anyway.
    – grochmal
    Oct 21 '16 at 10:02

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