Editing Talk:1553: Public Key

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"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 RSA 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)
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: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)
 
 
Is it possible everyone overthought this?  It seems to me that it's partly a play on words.  Why would people be interested in a "public" key which simply as a matter of the name seems like something that wouldn't be hidden in the first place?  It would seem that people would be more interested in a "private" key, since it seems to be something you wouldn't be able to get. [[Special:Contributions/173.245.50.149|173.245.50.149]] 18:53, 26 July 2015 (UTC)
 
 
 
:You're right in a general sense, but this wasn'the overthought. This is definitely about public/private key cryptography, and Randall has made comics about this before. His public key isn't interesting because no one wants to send secret messages to him; his private key would be very interesting because giving it out is a bad idea. [[Special:Contributions/173.245.54.37|173.245.54.37]] 01:12, 11 February 2016 (UTC)
 

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