In RSA private key generation
e*d ≡ 1 mod φ
e
is public, also n is public. How to prove mathematically, generation of private key d
is not possible using the same equation and public key e
In RSA private key generation
e*d ≡ 1 mod φ
e
is public, also n is public. How to prove mathematically, generation of private key d
is not possible using the same equation and public key e
It isn't impossible. Otherwise, we wouldn't have to keep increasing key sizes of our RSA keys, see this for the history.
As stated in a comment, it is believed to be computationally hard. Though, even that has never been proven.
To solve this equation you must know:
There are no other alternatives to solve this equation. This is linked by the structure of the ring $\mathbb{Z}_n \equiv \mathbb{F}_p \times \mathbb{F}_q$, which represents the intractability of the factorization problem.