Naming issue of public and private key

I heard that you can use a private key to encrypt data as a method for digital signing. In other words you can encrypt a message with your private key.

In the text they always seem to say only the public key can encrypt and the private key can decipher the text.

I'm assuming this is a bad choice of words. Is it true that a single instance of a key can do only one or the other, but which key is public or private is not a matter of it's fun开发者_JS百科ction, but of it's distribution or lack thereof.

For a beginner, the terminology is confusing. RSA can be used for 2 distinct crypto functions: data encryption and digital signatures.

For data encryption, you encrypt data using the recipient's public key; they decrypt it using their private key. Note that due to various limitations of RSA, the "data" that is encrypted and decrypted is usually just a key for a symmetric algorithm.

For digital signatures, you sign the data using your private key; they verify the signature over the data using your public key. Again, various limitations of RSA mean that what is actually operated on by the RSA algorithm is normally a secure hash of the data.

Sometimes the signing operation is called "encrypting with the private key", and the verifying operation is called "decrypting with the public key". I think this just confuses people so I always prefer the terms signing and verifying in this context. Furthermore, "encrypt" and "decrypt" make no sense for other signature algorithms like DSA and ECDSA.

You CAN generate public key from private key.

You CAN'T generate private key from public key (well, you might can, but this is extremely computationally expensive).

That is the difference between the two. They are NOT interchangeable (so, for instance, you SHOULD NOT publish your private key, and keep public key to yourself) because of the way how the algorithms works.

Take for instance RSA. The algorithm base is the problem of integer factorization. You choose two big integers p and q and multiply them to get n = p*q. Then you create public and private key:

• Public key: (n, e)
• Private key: (p, q, d)

Then:

• It is easy to calculate public key from private key:

  n = p*q

  e = d^(-1) mod φ(n), where φ(n) = (p-1)(q-1)

• It is hard to calculate private key from public key - it requires factorization of n to get p and q, which is extremely hard if p and q are big enough.

You release your encryption key to the public, and keep your decryption key private. That way anyone can send you encrypted data that only you can decrypt.

If you did it the other way around, then you would be the only one able to encrypt your data, but anyone could decrpyt it. That makes no sense. If everyone can decrypt your message you might as well send it unencrypted. There is no point encrypted a message and then making the decryption key public.

There are two types encryption one is symmetric another one is asymmetric .In symmetric the key used to encrypt and decrypt is the same . in asymmetric the key used to encrypt is public key and decrypt is private key ..

all works on the principle of a secrecy of the key .In Digital signing commonly used as a part of SSL / TLS protocols uses the asymmetric encryption for the authentication and sharing of the master key which is used further for encrypting the communication line.