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I have read that GnuPG limits the size of RSA keys to 4096-bits because this could lead
to problems with running out of secure memory. But in which operation is this the case?
Generating the keys? Encryption? Decryption? Signing? Verifying? All of them?

I have now modified the source code of GnuPG to allow me to generate 8192-bits keys just to test, and am generating such a key as I write this post. I have also increased the size of secure memory to 65K.

Can I expect problems with other PGP implementations with 8192-bit RSA keys?

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    What do you need 8192 bit keys for? Modifying the source of GnuPG will probably open you up to way more security concerns than using a 4096 bit key. – puzzlepalace Aug 8 '15 at 0:41
  • Make sure your entropy is at it's peak when generating large keys (which i do not recommend for production environments). A useful tool would be something like Haveged Read more about this tool on the arch wiki: wiki.archlinux.org/index.php/Haveged – navi Aug 8 '15 at 18:45
  • I'm sure RSA will be destroyed by Shor earlier than ordinary computers manage to break even 2048 bit keys... – grawity Aug 8 '15 at 20:22
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First of all, I feel you are quite a mysterious person because no one could pretend to break 4096-bit RSA in the foreseeable future so I wonder why you need such a very long key.

Coming back to your questions now:

But in which operation is this the case? Generating the keys? Encryption? Decryption? Signing? Verifying? All of them?

RSA keys are used in GnuPG for 2 reasons only:

  1. To sign communications
  2. To encrypt files.

Can I expect problems with other PGP implementations with 8192-bit RSA keys?

The answer is Yes in case:

  1. The destination person won't be to decrypt messages with standard secure memory limits he/she has already set by default unless if he modifies that default setting.
  2. The destination person does not have a hardware as good as yours since there is lot hardware not supporting anything bigger than 2048 bits (there are even platforms that do not handle the memory locking mechanism used to generate RSA keys)
  • I don't think am so very mysterious, this is just a test case. The key is not going to be used to other things than testing. I have still my daily 4096-bits RSA key, but I think I will change to EC keys when my daily RSA key expires. – BufferOverflow Aug 8 '15 at 22:35

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