It might not be a good idea for other reasons to have them on your screen, where other locally-installed software could view them, they would be (more strongly) broadcast in the RF spectrum, someone might see them over your shoulder, etc.
Valid points about other software, but I don't think 1000+-digit random-looking numbers would be easily memorised by someone looking over your shoulder casually.
If you had a 2048-bit public key modulus, each factor (only one factor is sufficient to reconstruct the private key) is only about 308 decimal digits, or 256 hex digits. :-)
We also know from Nadia Heninger and Hovav Shacham's research that you can reconstruct private keys relatively efficiently if you have some missing bits.
But I think you're right that human memory isn't a very significant threat to RSA private parameters. Realistically, cameras would be the threat, not a human being glancing it them.
In the era of 120fps 12MP smartphone cameras, capturing a 1000+ digit number on a screen doesn't seem so implausible, and "someone looking over your shoulder" shouldn't be taken so literally.
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Is there any way to get GPG to print out the two factors when the key is generated? 231 is absurd.
That doesn't protect against the possibility that one of the factors is itself composite.
It might not be a good idea for other reasons to have them on your screen, where other locally-installed software could view them, they would be (more strongly) broadcast in the RF spectrum, someone might see them over your shoulder, etc.
Valid points about other software, but I don't think 1000+-digit random-looking numbers would be easily memorised by someone looking over your shoulder casually.
http://www.recordholders.org/en/list/memory.html#numbers-1mi...
If you had a 2048-bit public key modulus, each factor (only one factor is sufficient to reconstruct the private key) is only about 308 decimal digits, or 256 hex digits. :-)
We also know from Nadia Heninger and Hovav Shacham's research that you can reconstruct private keys relatively efficiently if you have some missing bits.
https://eprint.iacr.org/2008/510.pdf
But I think you're right that human memory isn't a very significant threat to RSA private parameters. Realistically, cameras would be the threat, not a human being glancing it them.
In the era of 120fps 12MP smartphone cameras, capturing a 1000+ digit number on a screen doesn't seem so implausible, and "someone looking over your shoulder" shouldn't be taken so literally.