Editing Talk:1553: Public Key
Please sign your posts with ~~~~ |
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 34: | Line 34: | ||
"The prime factors (or exponents derived from them) are definitely the "private" part, and the composite product is definitely the "public" part". This is completely incorrect. In PGP (or rather, RSA keys used by PGP), both the public and private keys consist of just the modulus '''n''' (composite product) and one of the exponents '''d''' or '''e'''. However, the "public" exponent is typically chosen to be small and with few bits set, so that encryption/decryption using the public key is fast. The private key has to be big in order to keep the search space wide. So by switching around the public and private keys you end up with a public exponent that is a 600 digit number and a private exponent that is probably the number 65537. [[Special:Contributions/198.41.243.252|198.41.243.252]] 09:16, 22 July 2015 (UTC) | "The prime factors (or exponents derived from them) are definitely the "private" part, and the composite product is definitely the "public" part". This is completely incorrect. In PGP (or rather, RSA keys used by PGP), both the public and private keys consist of just the modulus '''n''' (composite product) and one of the exponents '''d''' or '''e'''. However, the "public" exponent is typically chosen to be small and with few bits set, so that encryption/decryption using the public key is fast. The private key has to be big in order to keep the search space wide. So by switching around the public and private keys you end up with a public exponent that is a 600 digit number and a private exponent that is probably the number 65537. [[Special:Contributions/198.41.243.252|198.41.243.252]] 09:16, 22 July 2015 (UTC) | ||
− | :The public and private exponents are related by the p and q values. You chose one and then calculate the other. Normally you chose the public exponent and generate the private one. It's also common practice to store p and q with the private key for efficency reasons (see: https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29#Using_the_Chinese_remainder_algorithm ). So 108.162.238.181's comment wasn't too far off the mark, the public key in a typical | + | :The public and private exponents are related by the p and q values. You chose one and then calculate the other. Normally you chose the public exponent and generate the private one. It's also common practice to store p and q with the private key for efficency reasons (see: https://en.wikipedia.org/wiki/RSA_%28cryptosystem%29#Using_the_Chinese_remainder_algorithm ). So 108.162.238.181's comment wasn't too far off the mark, the public key in a typical system consists of the modulus and a well-known exponent, the private key in a typical RSA system consists of p,q and various values derived from them. You could build a RSA system with symmetry in the key pair so you can chose either key as the public one but noone does because it would be substantially more computationally intensive and would give little benefit. [[User:Plugwash|Plugwash]] ([[User talk:Plugwash|talk]]) 19:47, 23 July 2015 (UTC) |
− | |||
− | |||
− | |||
− |