

A question on public/private key encryption - aa0

Why can&#x27;t the private key be cracked by encrypting a large enough block of static data, all bits=1 for example, with the public key?
======
deanfranks
If the cypher being used is secure, encrypting a block of 1s or 0s will
generate an apparently random stream of 0s and 1s. There will be no way to
determine the private key from the output of encrypting a block of known data
with the public key.

~~~
aa0
Couldn't a cross-comparison be used, encrypting different known blocks and
observing certain key properties? I would imagine that any kind of reversible
operation would be able to be deduced if it can be applied to specific data
that reveals its true form/operation.

~~~
deanfranks
Not with a strong cypher. Any single bit change in the source will result in
what looks like a new pseudo-random output.

Determining the private key given the public key in RSA-2048 requires
factorizing large blocks of very large numbers which is not practical given
current computing hardware. People are working on "smart" attacks that solve
the factorization problem from a theoretical math angle instead of a brute
force computational approach and there is some consensus that RSA-2048 may be
broken in the next few years. A transition to Elliptic Curve Cryptography
(ECC) is underway and RSA has never been approved for Suite-A or Suite-B
encryption which might lead one to believe that the NSA has known about the
weakness of RSA for a long time.

~~~
aa0
I see, makes sense - it is easy to multiply big nums together but insane to
factor the bignums out of them. You explained it more succinctly than I've
ever understood it, thanks a ton!

