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Let's suppose I want to send you an encrypted and signed message, to demonstrating authenticity and integrity, together with the natural security of asymmetric key cryptography. The procedure is, if I'm not wrong, the following one:

  • I create a message I want to send you.
  • I generate a hash version of that message (the digest).
  • I encrypt the digest with my private key.
  • I send you a composed message consisting of the message, the encrypted digest and my public key, in a secure way (for example, encrypting again the complete package with your public key).
  • You receive and decrypt the package with your private key, and decrypt the digest with the attached public key. If decryption finishes successfully, you ensure my authenticity, because I'm the only person who can has that private key.
  • You generate again the hash version of the attached message to check integrity, because if digests agree, means the message was not corrupted on the way.

But in such case, if you decrypt the message with my public key, you can decrypt the message and, about getting my private key, isn't it easier now?

The reason of encrypting a message to you with your public key, is because a sniffer hasn't the other "factor" (ok, I know the public key is the combination of two huge prime numbers and a third prime number, and the private key is a module arithmetic based key, based on these three prime numbers; but let's me call them "the two factors" for simplicity).

But if both factors comes "together" and there's no risk at all, what would be the reason of keeping the private key in secret?

Peregring-lk
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  • How would they get the private key? – EEAA Oct 24 '14 at 19:18
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    That's not what digital signatures are. Please see http://en.wikipedia.org/wiki/Digital_signature - you may be confusing encryption with digital signatures. – Mark Allen Oct 24 '14 at 19:19
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    I'd recommend you [have a read](https://en.wikipedia.org/wiki/Public-key_cryptography). I think you have several strong misunderstandings here. – EEAA Oct 24 '14 at 19:19
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    All I can think of is: "Magnets, how do they work?!" – Evan Anderson Oct 24 '14 at 19:21
  • @EvanAnderson You referring to [this gem](https://www.youtube.com/watch?v=wMFPe-DwULM)? – EEAA Oct 24 '14 at 19:25
  • @EEAA - I was thinking of the "Insane Clown Posse", but Feynman will do. >smile – Evan Anderson Oct 24 '14 at 19:27
  • I've upload my question to show about what I'm confusing and about what I'm not (or I think I'm not). And please, no links to wikipedia... I come from there! :P – Peregring-lk Oct 24 '14 at 19:43
  • Having the public key does make it easier to guess or compute the private key, yes. However, that fact is also why keys used in asymmetric cryptology are an order of magnitude larger than those used in symmetric cryptography. (A "standard" key length for symmetric crypto is 128 or 256 bits, for asymmetric your "standard"/common key lengths are at least 1024 bits, and more and more, 2048 bits is becoming the minunmum.) So for practical purposes, having the public key won't actually be sufficient help to compute a private key of the length that is commonly used today. – HopelessN00b Oct 24 '14 at 22:17

2 Answers2

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You were on the right track, until "and, obviously, get my private key".

There's a lot of mathematics that goes into how the keys operate.

The way public/private keypairs work is that with the public key, you can verify the matching private key was used, without ever knowing what the private key is. From having the public key, there's no easy way to figure out the private key.

The signature proves that someone who knew the entire private key signed the file. The public key is used only to verify that signature is valid and that the message hasn't been altered or replaced. They can also be used the other way around - using the public key to encrypt a message to you, only the person who knows the private key can decrypt and read it.

The entire public/private key system is setup to make it easier to communicate without an existing secure channel. You can publish the public key far and wide to everyone who might want it, without compromising the private key.

Grant
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  • I've changed my question to complete it with more details. Please check it. – Peregring-lk Oct 24 '14 at 19:46
  • @Peregring-lk even with the updated question, I'm still not sure why you believe someone can get the private key. Can you please explain how you think a person you send a message to gets the private part of the key? – Grant Oct 24 '14 at 19:54
  • Statistically? I don't now, but, turning the question around, if encrypting with the private key is so sure as using only public keys, why I need to encrypt a message with your public key to send it to you? Why do you need to generate key pairs each time you want to speak with somebody using ssh, for example? It would be only neccesary to use the keys of one of the sides each time, saving lot of users of generating key-pairs. – Peregring-lk Oct 24 '14 at 20:03
  • @Peregring-lk The secure channel is only one way. For signing, someone signing something with your public key means absolutely nothing, since everyone has the public key. But signing with your private key (which you have, hopefully, kept private) means you signed it. For encryption, you encrypt with my public key. Only the my private key will decrypt it. Having my public key lets you verify I sent a signed message, or send me an encrypted message. But it does nothing to show who sent me that encrypted message, or who reads my signed message. – Grant Oct 24 '14 at 20:09
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When you encrypt plain-text with a private key, then you can decrypt cipher-text with the public key. Only one person should have the private key. The entire world has access to the public key.

When you have cipher text decrypted by the public key, you only get the plain-text back - the private key is still private as you did not obtain that.

Martin Konecny
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