Java RSA private key generation when public key is known

Question

Is there a way to generate a RSA private key in java, when the public key is known, say 3 ?

I can't find a way to do this with Class KeyPairGenerator, from java.security package...

my question is very simple, I'm not looking for info related to cryptography. Just want to know, if I have the public exponent for RSA, is there a way in java to get the private exponent, for that public exponent, for a given modulus length , e.g. 2048? This should shed some light on the topic: https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Key_generation https://en.wikipedia.org/wiki/65,537

Answer 1

Sort answer is "no".

Long answer is to use sunrsasign Provider, which implements RSAKeyPairGenerator such that the public exponent is 65537: *"/** * RSA keypair generation. Standard algorithm, minimum key length 512 bit. * We generate two random primes until we find two where phi is relative * prime to the public exponent. Default exponent is 65537. It has only bit 0 * and bit 4 set, which makes it particularly efficient. **/*

if you want a different public exponent you need to create your own provider and integrate it with JCA.

more on the math behind this here.

Answer 2

The whole point of public-key cryptography is that the private key remains secret. If there would be a way to easily generate a private key from a public key the encryption schema would be broken.

Yes, you can probably brute-force the private key but it won't be easy:

The strength of a public key cryptography system relies on the computational effort (work factor in cryptography) required to find the private key from its paired public key. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security.