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Can a message that encrypted by public key decrypts by private key?

Can a message that encrypted by private key decrypts by public key ?

Are public key and private key generated using same algorithm ?

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closed as off-topic by owlstead, Luc M, Duncan, Woot4Moo, Neolisk Jul 12 '13 at 19:47

  • This question does not appear to be about programming within the scope defined in the help center.
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1  
Which cryptosystem / encryption are you talking about? –  Shark Jul 12 '13 at 13:32
    
In RSA encryption –  MKT Jul 12 '13 at 13:34
    
Encrypting a message with a private key typically isn't a useful operation. You should sign or decrypt with the private key, and encrypt and verify with the public key. It is absolutely essential to use proper padding for each use. i.e. signing and decryption are very different despite both using the same key. –  CodesInChaos Jul 12 '13 at 13:41
4  
voted off topic, use crypto.stackexchange.com after you have studied the subject at hand –  owlstead Jul 12 '13 at 14:11
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2 Answers

up vote 1 down vote accepted

Q: Are public key and private key generated using same algorithm ?

Generally speaking they are not generated using the same algorithm. For RSA they could have been generated identically, but most cryptography libraries use a known public exponent. This means that if the private key is known that it is easy to deduce the public key. In many key formats the public key is included with the private key or can be calculated easily from the information in the private key format.

Note that it is theoretically possible to generate a key pair where the public exponent has as much entropy as the private exponent. Some HSM's do allow such an operation.

All in all you cannot switch keys without sacrificing security for encryption purposes.

Q: Can a message that encrypted by private key decrypts by public key ?

In theory this could be the case if your cryptographic library allows it. Most libraries do not allow this however. First of all, as described above, it is not a secure operation. Furthermore, many libraries will assume that anything encrypted with a private key should use the padding mode for digital signature generation. In that case decryption is likely to fail; if it doesn't your ciphertext is not secure - so that's probably worse.

From the PKCS#1 specification:

The main mathematical operation in each primitive is exponentiation, as in the encryption and decryption primitives of Section 5.1. RSASP1 and RSAVP1 are the same as RSADP and RSAEP except for the names of their input and output arguments; they are distinguished as they are intended for different purposes.

The padding mechanism that is applied before the primitive differs significantly for encryption and signature generation.

Q: Can a message that encrypted by public key decrypts by private key?

That is the underlying idea of asymmetrical encryption. That means "yes".

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Why vote to close then answer? You were correct with the vote and I doubt this question will get migrated... –  Duncan Jul 12 '13 at 14:36
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@DuncanJones I wasn't planning to, but then I saw the other two answers. –  owlstead Jul 12 '13 at 14:39
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up vote -1 down vote

In respective order: yes, yes and yes.

Actually, only the public key can decrypt whatever was encrypted by the private one, and vice-versa.

Also notice that the names "public" and "private" are just arbitrary ones. It's just that the best use for pairs of asymetric keys is having one of them secret and the other known by everyone else, so that:

  • people with the public key can send you messages that only you can decrypt, with the private one;
  • you can send messages that can only be decrypted with your public key, so people know you are the true author.
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Normally RSA public and private keys are not created using the same method. They can be calculated the same way but often the public exponent is a pre-configured value like 3, 7 or the fourth number of Fermat (65537). This means that if you know the private key that you also know the public key. This is also the case if your private key contains the key pair generation parameters, of course. –  owlstead Jul 12 '13 at 14:09
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