To the most common believe of the mathematicians, experts in
public-key cryptography, nobody can decrypt any data if only the encryption key is known, and nobody can modify encrypted data if only the decryption key is known. It is equally
infeasible to find one key if another key in the pair is known. The whole idea of the public-key cryptography is based on these features.
In fact, this is not strongly proven, but this is the important conjecture which states that a
one-way function exists, that is, a function which is not feasible to invert, and the
backdoor does not exist. It's commonly believed by the specialists, that the modern public-key cryptography algorithms are the candidates for the one-way functions and that property will be proven sooner or later.
For further information, please see:
http://en.wikipedia.org/wiki/One-way_function[
^],
http://en.wikipedia.org/wiki/Backdoor_%28computing%29[
^],
http://en.wikipedia.org/wiki/Public-key_cryptography[
^],
http://en.wikipedia.org/wiki/RSA_%28algorithm%29[
^].
—SA
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