Is it possible to get the private key using the public key?

Question

I am using RSA asymmetric encryption, encrypting the data using the public key and decrypting the data using the private key.

The public key will be shared in clients machines.

My question is if the user get the public key is there any way to get the private key using the public one?

Yes, by going to the private key owner and applying thermorectal cryptoanalysis. — Eugene Mayevski 'Callback, Sep 18 '13 at 18:49
@EugeneMayevski'EldoSCorp No public key required for that protocol :P — Maarten Bodewes, Sep 18 '13 at 20:35
This question appears to be off-topic because it is about asymmetric cryptography. — madth3, Sep 19 '13 at 04:51
@owlstead the public key can help to find the owner of the private key (eg when you have an ssh key with the name in comments). — Eugene Mayevski 'Callback, Sep 19 '13 at 06:35
@EugeneMayevski'EldoSCorp Yeah, and for checking that the correct private key was indeed given I suppose. Otherwise any private key could have been given (well, depending on the use of course, with a PKCS#1 1.5 signature format you could recreate a signature with the private key). — Maarten Bodewes, Sep 19 '13 at 14:37

score 4 · Accepted Answer · answered Sep 18 '13 at 19:19

The keys are mathematically linked, but it is not possible to get the private key from the public key (at least no one knows or admits to knowing how to do so). However, you can obtain the public key from the private key.

If you don't have a good understanding of Public-key cryptography, you might wonder about things and ask questions. And that's OK, it's confusing when you first think about it. Here's a great book Cryptography Decrypted that I recommend to friends who wish to learn more about cryptography in general. It has a very good section on Public-key cryptography and presents it in such a way that anyone can understand.

score 2 · Answer 2 · answered Sep 18 '13 at 13:40

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No. That is the very definition of public key cryptography.

answered Sep 18 '13 at 13:40

ntoskrnl

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score -2 · Answer 3 · answered Sep 18 '13 at 19:06

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Sure. Some currently-known methods for obtaining a private key, when the public key is already known, include:

1) Brute force. Should take about a million years or so to complete, depending on hardware. Suggestion---expire the public keys once every 500,000 years or so.

2) The user is the NSA, in which case it's entirely possible that they've introduced subtle, top-secret vulnerabilities into the hardware or software you're using to generate the keypair.

3) The user has a quantum computer. They'd have to invent it first, though. Probably worth a Nobel prize right there.

answered Sep 18 '13 at 19:06

Keith Ripley

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Nonsense. It's not possible to derive the private key from the public key even with brute force. Using publicly scrutinized algorithms like RSA rules out any backdoors. While quantum computers *may* be used to attack RSA in the far future, such attacks have nothing to do with getting the private key from the public key. – ntoskrnl Sep 20 '13 at 13:05
I guess sarcasm is lost on the population of StackOverflow. RSA is not vulnerable. But if you read the news, you would know that the NSA attack vector isn't to attack cryptographic algorithms themselves, but to ensure that the *implementation* of those algorithms has an issue. Without reviewing it personally, how would you know? – Keith Ripley Nov 12 '13 at 18:31

Is it possible to get the private key using the public key?

3 Answers3