[Solved] Java RSA private key generation when public key is known

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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.

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solved Java RSA private key generation when public key is known