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CryptoClear
Приєднався 15 тра 2010
Occasional videos explaining cryptographic concepts in an easy way.
Already averaging at one video a year!
Already averaging at one video a year!
Security with Discrete Logarithms (and How to Break It)
A high-level overview of the Number Field Sieve approach used in the Logjam attack described in the "Imperfect Forward Secrecy" paper by Adrian et al., CCS 2015.
We dive into Discrete Logarithms, why it is supposed to be a tough problem, and how the common practice of reusing the same finite fields to avoid weakening the security of Diffie-Hellman key exchange actually results in weakening the security of Diffie-Hellman key exchange.
Continue learning:
- The paper and more material: weakdh.org
- Some criticism: nohats.ca/wordpress/blog/2015/10/17/66-of-vpns-are-not-in-fact-broken/
- Math is Fun has a great introduction to properties of logarithms: www.mathsisfun.com/algebra/logarithms.html
- Find out what keys are common today: www.ssllabs.com/ssl-pulse/
- Learn all about primes: www.springer.com/gp/book/9780387252827
Bad Ideas - Silent Film Dark by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/by/4.0/
Source: incompetech.com/music/royalty-free/index.html?isrc=USUAN1100489
Artist: incompetech.com/
We dive into Discrete Logarithms, why it is supposed to be a tough problem, and how the common practice of reusing the same finite fields to avoid weakening the security of Diffie-Hellman key exchange actually results in weakening the security of Diffie-Hellman key exchange.
Continue learning:
- The paper and more material: weakdh.org
- Some criticism: nohats.ca/wordpress/blog/2015/10/17/66-of-vpns-are-not-in-fact-broken/
- Math is Fun has a great introduction to properties of logarithms: www.mathsisfun.com/algebra/logarithms.html
- Find out what keys are common today: www.ssllabs.com/ssl-pulse/
- Learn all about primes: www.springer.com/gp/book/9780387252827
Bad Ideas - Silent Film Dark by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. creativecommons.org/licenses/by/4.0/
Source: incompetech.com/music/royalty-free/index.html?isrc=USUAN1100489
Artist: incompetech.com/
Переглядів: 1 502
Відео
Finite Fields in Cryptography: Why and How
Переглядів 28 тис.4 роки тому
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-gui.de Learn more about the etymology of words in mathematics: jeff560.tripod.com/f.html Learn more about proving that gr...
Basics of Secure Multiparty Computation
Переглядів 23 тис.6 років тому
A detailed yet simple introduction to Secure multiparty computation using Shamir's secret sharing scheme. Note: At 08:27 there is an incorrect mention of "degree 3" instead of "degree 2". It's just to keep you alert.
Shamir's Secret Sharing - Solution and alternative to Lagrange
Переглядів 11 тис.6 років тому
Following up on ua-cam.com/video/kkMps3X_tEE/v-deo.html this video contains the solution to the exercise in that video and introduces variable elimination as an alternative for Lagrange interpolation to determine the polynomial through the shares of the secret.
Simple introduction to Shamir's Secret Sharing and Lagrange interpolation
Переглядів 50 тис.8 років тому
A presentation part of the cryptography course at Chalmers University, 2015. Starting with simple examples, we introduce Shamir's Secret Sharing Scheme and how Lagrange interpolation fits in. I may have misspoken at some points, but that's to keep you alert :) Solution and follow up in ua-cam.com/video/rWPZoz0aux4/v-deo.html
All the explanations in this video are just perfect. Thanks for this!
great vide man , no one on youtube has explained in this depth
I thought boo was the monster...
Excellent explanation. Thank you
12:41 isn’t prime factorization itself considered a hard problem? do we assume that factorization of h is easy?
i love the 2nd half with the island example, its so cute and intuitive
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 - I say this as a "mortal" myself... 😭
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.
YES! I love the example of the creatures, and how elements can be anything,.
Thanks for the very short but sharp explanation. My prof explained this in 2 lectures and I still didn't understand a thing hahahaha
thanks
thanks
Top quality videos
Excellent video! But how to get around when (i - j) has no inverse when working on finite fields?
This was very helpful! The use of the delta functions helped clear up some of my confusions, and it made the formula easier to remember. Thanks!
thank you for the very nice video but it's very hard focus for me because of the annoying background music.
Awesome!!!
I still don't understand
Oh my God... I get it. I understand!
5 videos posted: 1.22k subscribers. Well done.
Thank you 🙏
Amazing introduction! Thank you!
Fantastic！
12:16 You meant x - 12, and not x-13, right?
really good explanation, thank you for spending your time to make this
Did anyone try to solve the exercise (find f(0) for points f(3) = 2, f(4) = 1, f(5) = 2) in a GF(2^8) field? I got 108 and wonder if that's correct. ;)
I found this video extremely entertaining! thank you so much for your content :)
Incredibly helpful approach to the problem
Thank you for this!!!
Such a nice explanation man. Thanks 🙏🏻
Thank you!
How do you ensure that the secret shares are integer pairs? Or do you? Obviously a share constitutes an (x,y) coordinate pair on an arbitrary polynomial curve. Im just curious how many decimal values are required and how secrets are expressed for digital storage. Should I assume that the secret is expressed as an integer and so too are the shares? Introducing new members n to the scheme and giving them their own share is done easily enough, but how do you extend the number k of required shareholders to unlock the secret, for a scheme thats already in the field? Since any k-members can agree to bring new shareholders into the mix, why do we call it a (k,n) scheme and not just a k-scheme? The n seems to be meaningless to the mathematics since it is arbitrarily extendible at any time by any k of the members. Does the sharing algorithm extend well to surfaces in 3D space, or do we only ever talk about 2D curves? Im wondering if there is a practical value in this extension.
Great questions! 1) The video is mostly on the mathematical concept and theory, in practice you would indeed only use integers (for secret, secret parameters and the shares) by using a finite field rater than real numbers (see my other video on the topic of finite fields -- ua-cam.com/video/ColSUxhpn6A/v-deo.html). 2) I do not believe it is possible to increase "k" after you have already released k shares. The first k participants will be able to reconstruct the secret. You could lower "k" if the number of shares given out ("p") is strictly less than k, to any number k' between p and k. You'd do this taking the p shares already shared, generating more shares to get a total of k'-1 shares (these you can keep private), and then add the secret at f(0) to these, making a total of k' shares. You then compute the polynomial that goes through these k' points exactly and replace the old polynomial with this new one. 3) I think you are right that it is mostly k that is the true parameter here. Perhaps the name reflects some envisioned use case where both k and n are static. E.g. a country has 5 military leaders, at least 3 of them have to agree to reveal the nuclear launch codes. When using finite fields, there is the technical constraint that "n" must be smaller than the size of your field, but I doubt this would often be a real issue. 4) Interesting idea. There might be some practical value to it but I'm not sure right away what it would be.
I'm only 3 minutes in and I can tell this video will be very helpful. Thanks for your effort and keep going 🙌
Programming Bitcoin by Jimmy Song brought me here
At 6mins, why is "a" used as the exponent in the top line then in the second line "y" is used?
That's an inconsistency on my part, sorry about that!
Really nice explanation, Hoping to see more videos
thanks for sharing. For a non-computer scientist like me, a very clear explanation why FFs are used in cryptography!
Amazing job explaining the best video on this topic I've seen
Please do a video on BUSDX, Everyone is talking about xPay virtual crypto payment card
Cool explaination.
Subscribed! - really nice presentation, especially liked the graphs showing perfect secrecy.
You are a great instructor
Great video, I'm interested in learning about cryptography and this opened my eyes! Thanks!
Actually, I was Looking Video for my frnd But, when I saw whole Video really its awesome☺☺
Thank you, this helped me a lot! I'm taking the exam on Chalmers the day after tomorrow!
Magic! This is fantastic
Amazing video! Too bad the topic is too niche and doesn't attract enough traffic
The exercise answer: f(x)=10*(x^2+x+1) (mod 11). Then f(0)=10 mod 11. Edit: True it is that f(x)=x^2+3*x+6 (mod 11). Then f(0)=6 mod 11.
Agree with other reviewers- best explanation of fields rings groups. I’ll look for other videos too
You need to produce more videos, these are super accessible! great job.
Excellent video! The slide at 16:08 solved my problem. I just goofed and wasn't doing the division correctly. Thank you!