Elliptic Curve #3: Example of Point Doubling and Point Addition

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  • เผยแพร่เมื่อ 31 ต.ค. 2024

ความคิดเห็น • 50

  • @eyob_g
    @eyob_g 7 หลายเดือนก่อน

    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.

  • @1UniverseGames
    @1UniverseGames 3 ปีที่แล้ว +12

    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

    • @prakashkumarojha1027
      @prakashkumarojha1027 2 ปีที่แล้ว

      th-cam.com/video/FnQNbFl72LY/w-d-xo.html

    • @niloofaralizadehsaveh7931
      @niloofaralizadehsaveh7931 2 ปีที่แล้ว

      watch this: th-cam.com/video/shaQZg8bqUM/w-d-xo.html

    • @eyob_g
      @eyob_g 7 หลายเดือนก่อน

      5^-1 mod 17 (multiplicative inverse of 5 modulo 17) can be calculated using Extended Euclidean Algorithm (EEA)

  • @PixelSergey
    @PixelSergey 4 ปีที่แล้ว +1

    Thank you! Your video has immesely helped me with my IB Extended Essay on Elliptic Curve Random Number Generation.

    • @AdvancedMath
      @AdvancedMath  4 ปีที่แล้ว +1

      You are welcome. It makes me really happy that it is helpful for anyone out there.

  • @HiteshJoshiJI
    @HiteshJoshiJI 8 หลายเดือนก่อน

    For posterity, just adding , -131mod 17 is 5 , because -131 = 17* (-8)+5

  • @barfib1871
    @barfib1871 4 ปีที่แล้ว +2

    thank u sir, u are the best. Yes u have clear all my doubts.

  • @codeaperture
    @codeaperture 3 ปีที่แล้ว +2

    Good one 🔥💯

  • @MrRyzale
    @MrRyzale ปีที่แล้ว +2

    I have a question, where do you get the equation for slope?

  • @mohonasib179
    @mohonasib179 ปีที่แล้ว

    Thank you so much sir ,I really grateful to you ❤️❤️

  • @cosminp4047
    @cosminp4047 ปีที่แล้ว +1

    great!

  • @jb0502
    @jb0502 3 ปีที่แล้ว +1

    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.

  • @manmohanpundir5619
    @manmohanpundir5619 2 ปีที่แล้ว

    amazing explained

  • @cTRINp
    @cTRINp ปีที่แล้ว

    Thanks for the video really helped :)

  • @Yoyo-ck9pm
    @Yoyo-ck9pm 3 ปีที่แล้ว +1

    Super ❤️❤️❤️❤️

  • @xl0xl0xl0
    @xl0xl0xl0 2 ปีที่แล้ว +2

    Excellent video, but, did you just . . . . skip over modular inverse like it's not even there???

    • @AdvancedMath
      @AdvancedMath  2 ปีที่แล้ว +1

      Yep. That was not the focus of the video so I pre-calculated it.

    • @jeevaneswaranmuthukumar6229
      @jeevaneswaranmuthukumar6229 8 หลายเดือนก่อน

      @@AdvancedMath can teach us how to do that? Im having difficulties on how you get 11x 10 inverse 1= 13

  • @naveedkhan-i3d
    @naveedkhan-i3d ปีที่แล้ว +1

    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

    • @AdvancedMath
      @AdvancedMath  ปีที่แล้ว

      See the previous videos please.

  • @nazmulislamananto
    @nazmulislamananto ปีที่แล้ว

    How are equations of x3 and y3 are obtained?

  • @eden9808
    @eden9808 4 ปีที่แล้ว

    Thankyou so much for this video. It helped me out a lot :)

    • @AdvancedMath
      @AdvancedMath  4 ปีที่แล้ว +1

      I am happy to know that.

  • @brycebacon2041
    @brycebacon2041 4 ปีที่แล้ว +3

    i dont understand how you got 9/5 mod 17? help!

    • @AdvancedMath
      @AdvancedMath  4 ปีที่แล้ว +4

      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.

    • @brycebacon2041
      @brycebacon2041 4 ปีที่แล้ว +1

      @@AdvancedMath thank you so much :)

    • @sai12110
      @sai12110 ปีที่แล้ว

      sir 22/17 = 1.29 and 77/17 = 4.5 how to possible 9/5 please explain

  • @MindSparks01
    @MindSparks01 11 หลายเดือนก่อน

    How can be reverse calculation easily

  • @srscoachingclasses6764
    @srscoachingclasses6764 3 ปีที่แล้ว

    Sir, is there no use of b

  • @YOGESHP-u7p
    @YOGESHP-u7p 11 วันที่ผ่านมา

    -6 divided 10 mod 17 how it become 11 *10^-1 mod 17 ???

  • @alejandroamoros5339
    @alejandroamoros5339 2 ปีที่แล้ว

    Why are we doing mod17 twice? One as 77/22 and another time for 9/5^-1?

    • @AdvancedMath
      @AdvancedMath  2 ปีที่แล้ว +2

      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.

    • @alejandroamoros5339
      @alejandroamoros5339 2 ปีที่แล้ว

      @@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!

  • @jojo2234
    @jojo2234 3 ปีที่แล้ว +4

    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.

    • @songofnature4352
      @songofnature4352 3 ปีที่แล้ว +1

      th-cam.com/video/3AmkQjdiW7o/w-d-xo.html.
      see this video, your doubt will clear

    • @jojo2234
      @jojo2234 3 ปีที่แล้ว

      @@songofnature4352 Thank you, I will watch it.

    • @prakashkumarojha1027
      @prakashkumarojha1027 2 ปีที่แล้ว

      th-cam.com/video/FnQNbFl72LY/w-d-xo.html

    • @niloofaralizadehsaveh7931
      @niloofaralizadehsaveh7931 2 ปีที่แล้ว

      watch this: th-cam.com/video/shaQZg8bqUM/w-d-xo.html

  • @sandeepkumar-vy3se
    @sandeepkumar-vy3se 3 ปีที่แล้ว

    sir can you made the video on finding the order of point P

  • @naveeningaleshwar6300
    @naveeningaleshwar6300 3 ปีที่แล้ว +2

    How 9×5inverse=63 ?

    • @AdvancedMath
      @AdvancedMath  3 ปีที่แล้ว +2

      5 inverse in mod 17 is 7. Thus 9*7=63.

    • @yuliaruda8280
      @yuliaruda8280 3 ปีที่แล้ว +4

      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
      @MrRyzale ปีที่แล้ว

      @@yuliaruda8280 I still don't understand, please elaborate further

    • @AM-sg4zg
      @AM-sg4zg 8 หลายเดือนก่อน +1

      @@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).

    • @MrRyzale
      @MrRyzale 8 หลายเดือนก่อน

      @@AM-sg4zg Thank you so much for the explanation sir, now I understand.

  • @압둘하미드이드리스
    @압둘하미드이드리스 4 หลายเดือนก่อน

    Please it's not clear