Modular Exponentiation (Part 1)

Network Security: Modular Exponentiation (Part 1)
Topics discussed:
1) Explanation of modular exponentiation with examples.
2) Solving 23 power 3 mod 30 with clear steps and shortcuts.
3) Solving 31 power 500 mod 30 with clear steps and shortcuts.
4) Solving242 power 329 mod 243 with clear steps and shortcuts.
5) Solving 1 power 7 mod 13 with clear steps and shortcuts.

Music:
Axol x Alex Skrindo - You [NCS Release]

#NetworkSecurityByNeso #Cryptography #NetworkSecurity #ModularExponentiation

[armanlalani]

For those who are still confused -
23³ mod 30
= (23 x 23 x 23) mod 30

In the prev video, we saw the property -
(a mod n x b mod n) mod n =
(a x b) mod n
Using this property of modular arithmetic from the previous video, we get
= [23 mod 30 x 23 mod 30 x 23 mod 30] mod 30

Now, since we know 23 mod 30 = 23, thus (23 x 23 x 23) mod 30 = 12167 mod 30 = 17. Alternatively, we can also substitute 23 mod 30 with -7 mod 30 which makes the calculation simpler and which is also done in the video.

= [-7 mod 30 x -7 mod 30 x -7 mod 30] mod 30
Again using the same property of modular arithmetic,
= (-7 x -7 x -7) mod 30 = (-7)³ mod 30
= (49 x -7) mod 30

Again using the property -

= [49 mod 30 x -7 mod 30] mod 30
= [19 mod 30 x -7 mod 30] mod 30
= (19 x -7) mod 30
= -113 mod 30

We see 49 x -7 mod 30 would give -343 mod 30 = 17 (since -343+30x12 = 17, to make -343 positive we had to add 30 twelve times which yielded 17). But 49 was simplified to 19. The properties of modular arithmetic have been used implicitly to make the calculation easier.

[oshikkhittt]

Hello Neso Academy, I really highly applaud you👏 for making this modular exponentiation a simply but perfectly explained one😍.❤From Bangladesh.And also my endless thanks🥰☺

[PraveenKumarK-yo]

In the calculation there are errors 23^3 mod 30, in the fifth step its -343 mod 30 and error in the calculation 11^7 mod 13 there is an error in the fourth step

[avocadorable_s]

Wow, i spend 2 hours trying to understand my lecturer's notes on modular exponentiation, even went through so many web tutorials, and still wasn't clear. This one single video just made me understand the whole concept in 10 min. Great!!! Thank you so much for the clear and concise explanation!!!

[sonikaur]

Thanks sir 🙏 the way you explain the things is splendid 👌 👏

[KenPoke-czje]

For example if the mod is 284 so how can you calculate it ? Every time you made it as 1 of course easy to calculate

[andrewporter]

Good video, but you need to put parentheses around negative bases to avoid ambiguity. Otherwise, it is parsed -(7^3).

[lindeanchuang]

Thank you very much. Your explain is much easier understand than my text book.

[davidsalasmerino]

Thank you, I didn't catch it well the modular exponentiation, but with ur video I uderstand it!!!

[rohitsharma]

Can you provide us the whole syllabus of this course or the length of this course with roadmap

[sabinomuniz]

Thank you, you explained it much simpler than my learning material!

[ogboota]

This video gave me a booster, .. thank you 😎🙏💐

[soniajadhav]

Hello sir can you do video on RSA algorithm plz 🙏🏻

[adiba-cse-]

You have explained it in the most easiest version. Thank you.

[underes]

49×7 = 343 . I don't know which math you are teaching but explain it...

[isirlasplace]

I love the way you explain!!! Way better than my current professor!!!😁💕

[anzatamveel]

But what if it is 2015^17mod 3233 ? My problem is still didn't solve

[rakesh]

How is 23 mod 30 is equal to -7 mod 30 ?

[klemo]

49 * -7 (mod 30) = -11 * -7 (mod 30) = 77 mod 30 = 17

[gusionfusion]

49 * -7 mod 30 = -113 mod 30 how it came can any1 explain?