Finite Fields in Cryptography: Why and How

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Finite Fields in Cryptography: Why and How

Рет қаралды 27,255

Күн бұрын

Learn about a practical motivation for using finite fields in cryptography, the boring definition, a slightly more fun example with monsters, and how to create fields out of some sets of integers.
Links mentioned in the video:
Learn more about floating points: floating-point...
Learn more about the etymology of words in mathematics: jeff560.tripod....
Learn more about proving that groups of prime order are fields: web.stanford.e...
Listen to a mathematically correct proof of love: • Finite Simple Group (o...

Пікірлер: 49

@elenarosinskaya6255 4 жыл бұрын

Man, that's the super coolest explannation of groups I've ever seen. The monsters group is hilarious! Thank you! I'll subscribe and will wait another 2 years for the next video.

@nuthouse145 4 жыл бұрын

Your explanation of finite fields was INCREDIBLY useful! Thank you so much for taking the time to create this content and share it with the community.

@nuthouse145 4 жыл бұрын

@CryptoClear, I shared your videos on Twitter, but could not find your Twitter handle to give you credit. If you are on Twitter, please let me know and I will update accordingly.

@CryptoClear 4 жыл бұрын

@@nuthouse145 Thank you very much, great to see you enjoy these videos! The channel has no Twitter presence at the moment, so thanks a lot for linking.

@ciaran902 4 жыл бұрын

Agreed, thank you!

@creadisc6213 4 жыл бұрын

Having no downvotes tells us a lot about the quality of your videos...

@0xjuaan 2 ай бұрын

All the explanations in this video are just perfect. Thanks for this!

@teewenhui2717 6 ай бұрын

i love the 2nd half with the island example, its so cute and intuitive

@ezohn 2 жыл бұрын

thanks for sharing. For a non-computer scientist like me, a very clear explanation why FFs are used in cryptography!

@serophots7589 Жыл бұрын

Incredibly helpful approach to the problem

@qianyingliao1675 3 жыл бұрын

Thank you for explaining the finite field in the most intuitive way!

@FitVibhav 2 жыл бұрын

Actually, I was Looking Video for my frnd But, when I saw whole Video really its awesome☺☺

@paologat 10 ай бұрын

Nitpick: additive and multiplicative identities need not be distinct, as shown by the existence of the trivial field {0}. Exercise for the reader: prove that the two identities are indeed distinct for all other (nontrivial) fields.

@azagogh 10 ай бұрын

YES! I love the example of the creatures, and how elements can be anything,.

@markandmelbamford 2 жыл бұрын

Agree with other reviewers- best explanation of fields rings groups. I’ll look for other videos too

@ByteNishi 4 жыл бұрын

Nice, Thank you! Today only I got the channel in my recommendations and I am already liking it.

@ramidaouas4933 2 жыл бұрын

I'm only 3 minutes in and I can tell this video will be very helpful. Thanks for your effort and keep going 🙌

@python360 2 жыл бұрын

Subscribed! - really nice presentation, especially liked the graphs showing perfect secrecy.

@codegeek98 8 ай бұрын

Definitely interested in the prime power fields. It's impossible to find any online explainer for them that's "accessible" to mortals (people with less than graduate-level math background)

@sachuabraham6516 2 жыл бұрын

Really nice explanation, Hoping to see more videos

@paulperegud6000 Жыл бұрын

Amazing introduction! Thank you!

@2NormalHuman Жыл бұрын

really good explanation, thank you for spending your time to make this

@SaidVSMath 2 жыл бұрын

Great video, I'm interested in learning about cryptography and this opened my eyes! Thanks!

@nyeinsoe3697 3 жыл бұрын

your vids are really helpful. I hope u will release more vids soon.

@CryptoClear 3 жыл бұрын

Thank you! I have a bad reputation, averaging to 1 video per year. But releasing a new one today, so that's something!

@oviaseshadri6120 Жыл бұрын

I found this video extremely entertaining! thank you so much for your content :)

@AhmedAli-jt1qy 2 жыл бұрын

You are a great instructor

@ahmedelmallah2390 2 жыл бұрын

Such a nice explanation man. Thanks 🙏🏻

@nomOfyourBusiness 3 жыл бұрын

4 minutes in and you caught up with 9 hours of crappy lectures. Great video!

@MrRyzale Жыл бұрын

I still don't understand

@sayalideo7823 3 жыл бұрын

Amazing lecture. Thankyou.

@harirao12345 Жыл бұрын

Awesome!!!

@Mohammad0906025 2 жыл бұрын

Cool explaination.

@dadadaPhl Жыл бұрын

thank you for the very nice video but it's very hard focus for me because of the annoying background music.

@muslimmurtazaliyev2942 2 жыл бұрын

Thank you for this!!!

@MrFrumos 4 жыл бұрын

Just amazing, thank you.

@dfkjbdfondfngg 2 жыл бұрын

Thank you!

@monkeybongos4389 3 жыл бұрын

I don't get how you get a = y_1 - b * x_1, it isn't clicking

@CryptoClear 3 жыл бұрын

We know that f(x_1) = y_1, which means that a + b * x_1 = y_1. Have a look here for more concrete examples: www.mathsisfun.com/algebra/line-equation-2points.html

@waqasaps 3 жыл бұрын

Where can i read more about it?

@CryptoClear 3 жыл бұрын

That depends a lot on what you want to learn more about. For more properties of fields and mathematical proofs, the Stanford course notes linked in the description are quite clean: web.stanford.edu/~aaronlan/assets/finite-fields.pdf. For practical use in crypto, make a Google search for "diffie hellman key exchange" or "ElGamal encryption" (using groups, not fields). Also, any good cryptography course (book) will have a lot on this topic!

@waqasaps 3 жыл бұрын

@@CryptoClear looking to implement eleptic curve cryptography for my university project. not much to find on google for me. thanks alot for the suggestions.

@waqasaps 3 жыл бұрын

I found hyperelliptic.org/ as a good source as well.

@CryptoClear 3 жыл бұрын

@@waqasaps To learn theory, I would recommend searching Google Scholar, often there are overview or introduction-level articles/books: scholar.google.com/scholar?q=introduction+elliptic+curve+cryptography. For implementation, this looks like a great start (if you're ok with python): www.johannes-bauer.com/compsci/ecc. See especially the examples using Sage library which provides most of the common operations.