Thank you very much for providing such informative lectures. I have a question regarding your explanation around the 10:39 mark. Given that the elliptic curve is symmetric about the x-axis, wouldn't -P simply be equal to (x1, -y1)? Once again, I sincerely appreciate your efforts in clarifying these fascinating concepts.
Sir, thanks for your excellent video. Where is x-axis now? Is it shifted to P/2(17/2)? Or P is added on both sides as x+17 and x-17? Thanks in advance.
We can apply mod 17 whenever we want simplification. First I apply mod 17 to simplify 77/22 to 9/5. However, after applying inverse the number became large again, so I apply mod 17 again to simply it.
maybe the question is about the inverse? as I understand, the inverse of 5 is taken by multiplication, not by addition (5^-1 doesn't equal -5). that's why we search for a number that multiplied by 5 will give us a 1 mod 17. so 5 inverse is 7 (not 12).
@@MrRyzale The inverse of 5 (mod 17) is the number x such that 5x = 1 (mod 17). In other words, we need to find a number x such that 5x is one more than a multiple of 17. We have 5*7 = 35 = 2*17 + 1, hence the inverse of 5 (mod 17) is 7. And therefore 9 * 5^-1 (mod 17) = 9 * 7 (mod 17) = 63 (mod 17) = 12 (mod 17).
Thank you very much for providing such informative lectures. I have a question regarding your explanation around the 10:39 mark. Given that the elliptic curve is symmetric about the x-axis, wouldn't -P simply be equal to (x1, -y1)? Once again, I sincerely appreciate your efforts in clarifying these fascinating concepts.
Excellent video sir.
Can anyone help me to understand please 9*5inverse mod 17 and 63 mod 17 calculation in details explanation. Thanks in advance
th-cam.com/video/FnQNbFl72LY/w-d-xo.html
watch this: th-cam.com/video/shaQZg8bqUM/w-d-xo.html
5^-1 mod 17 (multiplicative inverse of 5 modulo 17) can be calculated using Extended Euclidean Algorithm (EEA)
Thank you! Your video has immesely helped me with my IB Extended Essay on Elliptic Curve Random Number Generation.
You are welcome. It makes me really happy that it is helpful for anyone out there.
For posterity, just adding , -131mod 17 is 5 , because -131 = 17* (-8)+5
thank u sir, u are the best. Yes u have clear all my doubts.
Good one 🔥💯
I have a question, where do you get the equation for slope?
Thank you so much sir ,I really grateful to you ❤️❤️
great!
Sir, thanks for your excellent video. Where is x-axis now? Is it shifted to P/2(17/2)? Or P is added on both sides as x+17 and x-17? Thanks in advance.
amazing explained
Thanks for the video really helped :)
Super ❤️❤️❤️❤️
Excellent video, but, did you just . . . . skip over modular inverse like it's not even there???
Yep. That was not the focus of the video so I pre-calculated it.
@@AdvancedMath can teach us how to do that? Im having difficulties on how you get 11x 10 inverse 1= 13
sir ,how i multiply 18 into (12,18) this .like let 18 is a private key and the pair form number is our base point on elliptic curve
See the previous videos please.
How are equations of x3 and y3 are obtained?
Thankyou so much for this video. It helped me out a lot :)
I am happy to know that.
i dont understand how you got 9/5 mod 17? help!
22 mod 17 = 5 as 5 is the remainder when we divide 22 by 17. Similarly 77 mod 17 = 9 as 9 is the remainder when we divide 77 by 17.
@@AdvancedMath thank you so much :)
sir 22/17 = 1.29 and 77/17 = 4.5 how to possible 9/5 please explain
How can be reverse calculation easily
Sir, is there no use of b
-6 divided 10 mod 17 how it become 11 *10^-1 mod 17 ???
Why are we doing mod17 twice? One as 77/22 and another time for 9/5^-1?
We can apply mod 17 whenever we want simplification. First I apply mod 17 to simplify 77/22 to 9/5. However, after applying inverse the number became large again, so I apply mod 17 again to simply it.
@@AdvancedMath Great! That makes a lot of sense! The videos are great, very easy to understand the maths behind it. Thank you very much sir!
I don't understand how 9*(5^-1) mod 17 which should be (9/1)*(1/5) mod 17 is equals to 63. Could you explain me that? Thank you.
th-cam.com/video/3AmkQjdiW7o/w-d-xo.html.
see this video, your doubt will clear
@@songofnature4352 Thank you, I will watch it.
th-cam.com/video/FnQNbFl72LY/w-d-xo.html
watch this: th-cam.com/video/shaQZg8bqUM/w-d-xo.html
sir can you made the video on finding the order of point P
I plan to...
Thank you sir
How 9×5inverse=63 ?
5 inverse in mod 17 is 7. Thus 9*7=63.
maybe the question is about the inverse?
as I understand, the inverse of 5 is taken by multiplication, not by addition (5^-1 doesn't equal -5). that's why we search for a number that multiplied by 5 will give us a 1 mod 17.
so 5 inverse is 7 (not 12).
@@yuliaruda8280 I still don't understand, please elaborate further
@@MrRyzale The inverse of 5 (mod 17) is the number x such that 5x = 1 (mod 17). In other words, we need to find a number x such that 5x is one more than a multiple of 17. We have 5*7 = 35 = 2*17 + 1, hence the inverse of 5 (mod 17) is 7. And therefore 9 * 5^-1 (mod 17) = 9 * 7 (mod 17) = 63 (mod 17) = 12 (mod 17).
@@AM-sg4zg Thank you so much for the explanation sir, now I understand.
Please it's not clear