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Aug 7 at 13:39 history edited CaffeineAddiction CC BY-SA 4.0
Updated Cert info to reflect SE's switch to lets encrypt w/ diff pubkey algo
Aug 9, 2022 at 17:04 history edited CaffeineAddiction CC BY-SA 4.0
updated stack exchange public key
Feb 10, 2017 at 8:26 comment added J.A.K. @Pascal You have no idea how often i mess that up myself ;) . The fact that people are pitching in makes this a great place, the rest will sort itself out.
Feb 9, 2017 at 20:04 comment added HSchmale Quick tip about github keys. If you use the url github.com/user.keys it will return them ready to place in authorized keys.
Feb 9, 2017 at 10:39 comment added user21820 @Pascal: No idiot will admit mistakes. Besides, I was amused that your actual answer did not state anything wrong about RSA, unlike here. =)
Feb 9, 2017 at 10:30 comment added Out of Band @user21820: Yup - you're right. Like I said, shouldn't point my finger and get it wrong, too! Next time I'll actually look it up instead of trying to wing it from memory before I make an idiot of myself ;-) And sorry, J.A.K.
Feb 9, 2017 at 10:19 comment added user21820 @J.A.K.: See my above comment. And if anyone is actually interested in security, it's up to them to understand enough mathematics to not do stupid things. A lot of security professionals who don't end up making their systems insecure for very naive reasons from a mathematical point of view.
Feb 9, 2017 at 10:17 comment added user21820 @Pascal: Your first comment about the private key is totally wrong. The modular inverse of any integer over any modulus is easily computable (in logarithmic time). The private key is the multiplicative inverse of the public key modulo (p-1) * (q-1), not p * q. p * q is published, but (p-1)*(q-1) is hard to compute without knowing p or q.
Feb 9, 2017 at 10:01 comment added dotancohen Interestingly, when I was viewing your answer over HTTP (no S) the answer said "Sure, you can publish your public and your private keys, no problem".
Feb 8, 2017 at 15:23 comment added Out of Band Well, yes, the point about reuse in fact applies to DH (see my own answer about reusing constants in DH - shouldn't gloss over the details when I point my finger... sorry!). The immediate problem with all ssh keys sharing the same RSA modulus would be that in order to compute the keypair when generating a new keypair, you need access to p and q, the factors of the modulus n. So if ssh reused the same modulus for every RSA key, its source code would contain p and q as constants. So we could simply go look for p and q in the source code - no need to calculate (or spend) anything at all :-)
Feb 8, 2017 at 13:46 comment added Peter Green @Pascal umm I think you are confusing RSA with DH. With RSA the modulus needs to be distinct for each keypair. If you have the modulus and both exponents then you can recover p and q di-mgt.com.au/rsa_factorize_n.html.
Feb 8, 2017 at 9:14 comment added Out of Band Agreed, but my comment explains what the modulus and exponent in the above stack exchange example are. Plus the fact that the modulus is not the whole key makes it possible to reuse the modulus in software like ssh and just choose different exponents, and this is why it's likely that three-letter agencies are interested in spending billions of dollars to factorize just a few numbers - if they can factorize an often used modulus, every public key which is actually available in public and based on that modulus is an instant door to the private key. So I do think it's relevant to the question.
Feb 7, 2017 at 20:49 comment added J.A.K. I don't think most people click on this page to comprehend the underlying mathematical nuances, because the question is about the basic properties of what a public key is. "The security lies in...." would have been a better phrasing, i agree. But i believe this is also why RSA-129 was generated; to show the hardness of factorization in a graspable way
Feb 7, 2017 at 17:31 history edited mattdm CC BY-SA 3.0
there -> their. Change some use of ... to standard commas and periods.
S Feb 7, 2017 at 15:50 history suggested Henders CC BY-SA 3.0
Removes typo and a few minor adjustments.
Feb 7, 2017 at 15:47 review Suggested edits
S Feb 7, 2017 at 15:50
Feb 7, 2017 at 15:43 comment added Out of Band @J.A.K: To expand on that, the private key isn't actually the product of the two primes p and q. It's the modular inverse of the public key exponent e over the modulus p * q. The modulus p * q and e are published. If you can factor p * q, you know p and q and can calculate the modular inverse of e.
Feb 7, 2017 at 15:41 history edited CaffeineAddiction CC BY-SA 3.0
added 1 character in body
Feb 7, 2017 at 15:33 history edited CaffeineAddiction CC BY-SA 3.0
added 2524 characters in body
Feb 7, 2017 at 8:13 comment added J.A.K. Simplistically, two randomly chosen prime numbers are the private key, and multiplied together form the public key. This is doable because primes are quite common. RSA is based on the (technically unproven) assumption that factoring them back to the two primes is hard.
Feb 7, 2017 at 4:06 comment added Délisson Junio I guess this could be improved by exposing the reason why private keys are private and so on
Feb 6, 2017 at 18:58 history answered CaffeineAddiction CC BY-SA 3.0