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Private Security And Public Security.

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Information Security Stack Exchange is a question and answer site for information security professionals. It only takes a minute to sign up. I can understand that the public key like a padlock can encrypt lock something and only the private key can decrypt open it.

But I just can't understand the other way around. How can the public key verify digital signatures encrypted by CA's private key? A lot of material says that a public key can't be used for decryption that's fine, if imagine the public key is a padlock, then that's for sure, you're not able to unlock things. Then how can public keys be used to verify digital signatures, given that it can't be used to decrypt? A server encrypts Private Security And Public Security secrets and ask the client to decrypt it, and compares the results, then I can know whether you're the holder of the private key. But as for digital signatures, it's a different story, because I think in the digital signature, it doesn't contain the private key of the issuer, right?

Then how can the above verification can be done without private key decrypting?

The whole concept of trying to explain signatures with the terminology of encryption is flawed. It simply does not work. So let's unravel the whole thing, and this will require some formalism. Formallya cryptographic signature system consists in three algorithms:. Sign : takes as input a message m and a private key K s ; output is a signature s.

Verify : takes as input a message ma signature s and a public key K p ; output is Sdcurity boolean true on success, false if the signature is not valid.

The system is said to be sound if the algorithms operate as advertised Sign produces signatures that Verify accepts, using key pairs produced by KeyGen. The definition implies, in particular, that the private key should not be computable from the public key alone, because otherwise forgeries Secjrity be easy. None of the above says anything about how the algorithms work.

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Various systems have been invented, described and standardized. RSA is the name for an internal operation called a trapdoor permutationfrom which an asymmetric encryption system and a signature system have been derived. The RSA operation is, roughly, the following:. Knowledge of p and q is the "private key".

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Let e Private Security And Public Security some usually small integer, called the "public exponent"; e must be such that it is relatively prime to both p-1 and q Traditional values for e are 3 and Given an integer x modulo n an integer in the 0 to n-1 rangethe RSA forward operation is computing x e mod n x is raised to exponent e modulo n. This is easy enough to do. It so happens that this operation is a permutation of integers modulo n each y modulo n is equal to x e mod m for exactly one x.]