# How does public key encryption work exactly?
**URL:** https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903
**Category:** Factual Questions
**Created:** [December 21, 2004, 2:14am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903 "2004-12-21T02:14:36Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [December 21, 2004, 2:14am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/1 "2004-12-21T02:14:36Z")
Perhaps someone could demonstrate how public key encryption works using small numbers?
Say the public key is 35, meaning the “private” key would be the numbers 5 and 7? Now how can you encode something using the public key ‘35’ in a way such that you _can’t_ decrypt it using that same number, but _can_ decrypt it using the set of numbers 5 and 7?
Or on the other hand, if there’s something about this post that indicates I’ve completely misunderstood public key cryptography, please explain that as well/instead. My understanding is that it works by having a “public” key which is a very large number, which has only two very large prime factors, said prime factors being the “private” key.
I did a search here and didn’t find a straightforward explanation as to how this works.
-FrL-
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### Author:  [@caymus28](https://boards.straightdope.com/u/caymus28)
#### Post date: [December 21, 2004, 2:43am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/2 "2004-12-21T02:43:44Z")
This is not with simple numbers, but it is easily understood (to me at least…)
[Public-key encryption for dummies](http://www.nwfusion.com/news/tech/0517tech.html).
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### Author:  [@Frylock](https://boards.straightdope.com/u/Frylock)
#### Post date: [December 21, 2004, 4:14am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/3 "2004-12-21T04:14:36Z")
Thanks for the link.
I still want to know the nuts and bolts of this though–how is it that you encrypt a message using some key in such a way that you can’t decrypt the message using that same key, but _can_ decrypt it using some other key?
Also, I’m not sure the link is talking about the same thing I am asking about, though it’s clearly related. The link talks about some trusted “certification authority” being necessary, whereas I thought there were ways to send coded messages which count as “public key encryption” methods in which no “trusted” go-between would be needed–in other words, in which A’s knowing B’s public key and B having a private key related mathematically to that public key were all that was needed for A to send B a coded message.
Maybe I am wrong to think that is possible, though, and the link describes public key encryption more accurately than I have described it. If that is the case, I am still interested in knowing just how it works… like, in terms of math and stuff…
-FrL-
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### Author:  [@bitwise](https://boards.straightdope.com/u/bitwise)
#### Post date: [December 21, 2004, 4:36am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/4 "2004-12-21T04:36:06Z")
What you are looking for is RSA. There are probably other public-key systems, but I am not familiar with them.
> **[RSA](https://en.wikipedia.org/wiki/RSA)**
>
> RSA may refer to:
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### Author:  [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)
#### Post date: [December 21, 2004, 10:38am UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/5 "2004-12-21T10:38:33Z")
I _used_ to understand the math easily… man I’m getting rusty.
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### Author:  [@micco](https://boards.straightdope.com/u/micco)
#### Post date: [December 21, 2004, 2:47pm UTC](https://boards.straightdope.com/t/how-does-public-key-encryption-work-exactly/280903/6 "2004-12-21T14:47:54Z")
There is a small-number example in the wiki article **bitwise** linked to. There’s a very good RSA description and small-number example in Schneier’s “Applied Cryptography” (which is a good place to look for any crypto explanation). In the Second Edition, the RSA example is in section 19.3.
There are several other good public-key algorithms, but RSA almost certainly has the widest use. ElGamal was fairly popular when RSA was encumbered by patent.