Multiplicative Inverse

Network Security: Multiplicative Inverse
Topics discussed:
1) Explanation on the basics of Multiplicative Inverse for a given number.
2) Explanation on the basics of Multiplicative Inverse for a given number under modulus.
3) Finding the Multiplicative Inverse for smaller numbers manually.
4) Difference between the Multiplicative Inverse of normal numbers and numbers with modulus.
5) Explanation on how to determine whether there exists a Multiplicative Inverse or not.
6) Introduction to Extended Euclidean Algorithm to find the Multiplicative Inverse.

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

#NetworkSecurityByNeso #Cryptography #NetworkSecurity #MultiplicativeInverse

[mirzashemin]

Everytime i search for math related lecture in English i always have a thought my English must be poor that's why i am not understanding but when i see your lecture my all doubts gets cleared.

[iosonoi.]

Oh, I get it now. For any of you struggling, its just the notation that is "unintuitive". if you see 1 mod 5, its not literally 1 mod 5, its 1 (mod 5). So 1 "when you mod by 5".

Instead of

3*n = 1 (mod 5)

i think the simplest way of understanding it is putitng it in "normal" notation.

(3*n) mod 5 = 1

6 mod 5 = 1, so n=2

[jamm]

Thank you so much for adding the other example at the bottom for 5 and 10 not being multiplicative indexes. It really made it clear to me

[isirlasplace]

Thank you!!! I couldn't wrap my brain around this concept and you explain it so well!!!

[Thekittykat]

I was trying to answer questions in Number Theory in the Brilliant app, and I just coundn't figure them out until I watched you video. Thank you!

[Бейнесабақтар-ин]

Thank you! Finally I understood how calculate multip.inverse

[Limegreenslice]

Great video, thanks!! I was sitting here scratching my head on why my crypto book kept telling me the multiplicative inverse of 3 is 9 and not 1/3 until i found your video. Mod, gotta remember that mod

[Aaronmx]

Your videos have been very helpful, much appreciated! 1 issue though, I believe [ a mod b ] where a is less than b is equal to a. (ex. 2 mod 5 = 2, because 2 is less than 5 and therefore the remainder). You mentioned 2 mod 5 = -3, so you then perform 2 x 3 = 6 then 6 mod 5 = 1 which is different from 2 mod 5 being equal to 2.

[chamin]

Thank you so much sir . I watched many videos about modular inverse, but didnt understand. I understood very easily from your video. Thank you so much

[SequinBrain]

ty, this is EXACTLY what I didn't understand about these things. So from what you said, a relative prime will never be two even numbers, but will always be either even/odd or odd/odd. Clearly, sometimes even those won't work, but we will never have two even numbers which are relatively prime.

[DouglaStaks]

thanks bro, i have been watching videos and reading books for multiplicative inverse in modulo and all the time it was the REMAINDER that matters. LOL i thought it was the quotient that should be equal to 1 haha thanks a lot!

[chi_naemerem]

Thank you so much!
You are the best!!! ❤️

[letsimage]

thanks! But could you tell please, why do we use it?

[Mehraj_IITKGP]

For large numbers, use :
a^-1 mod p = a^(p-2) mod p, where p is prime.

[KavyaS-mr]

4 * 4 = 16 here incase if we divided 16/5 thn the reminder would be 3.2 not the 1
and since the mod is 5 we can do this by 4*1 = 4 by this we get reminder as 1

[Black-xypj]

When you say 2 into 4 it means division. When referring to multiplication you should use the word 'times' instead. I was confused through certain parts of the video. Great video though; I now understand.

[vamppyre]

Can there be more than 1 multiplicative inverse?
Like for 3(mod 5) you said multi inverse is 2.
Even 7 can be it's inverse right, because 7*3=21 and 21 mod 5 = 1.

[nz_ncht]

what about some negative numbers or fraction number??

[priyankakonduru]

for small numbers we can find it out easily what about for large numbers how to find can you give me some tips for that

[SachinKumar-fdkg]

Sir I have an assignment, can you help me?